_______أساسيات الحراريات والموائع (1)

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المؤسسة العامة للتعليم الفني والتدريب المهني
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T(
o
T(
C ) =
o
F )
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1 m = 3.2808 ft
1 mile = 5280 ft
1 mile = 1.6093 km
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א
א 1 m 2 = 10.764 ft 2
1 m 3 = 35.314 ft 3 א
1 m 3 /kg = 16.0185 ft 3 /lbm
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א 1 kg/m 3 = 0.062428 lbm/ft 3
1 N s/m 2 = 0.67197 lbm/ft s
א
1 m 3 /s =35.313 ft 3 /s
1 kg/s = 2.2046 lbm/s
1 N = 0.22481 lbf
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א
א 1 N/m 2 = 1.4504 × 10-4 lbf/in 2
5 o
(T( F ) − 32 )
9
9 o
= T( C ) + 32
5
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o
T(
K ) = T( C ) + 273
T( R )
o
= T( F ) + 460 א
1 kJ = 0.94783 BTU
1 W = 3.4123 BTU/h
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-٢-

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m / sec
miles / hr 60
(1)W
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1 ft = 0.3048 m, 1 mile = 5280 ft, 1 hr =3600 sec
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ft
5280 × =1K mile
m
0 . 3084 × = 1 ft
sec
3600 × =1 hr
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( 60) ( 5280)( 0.
3048)
m
⎛ miles ⎞ ⎛ ft ⎞⎛
m ⎞ ⎛ 1 hr ⎞
⎜60 ⎟ ⎜5280
⎟⎜0.
3048 ⎟ ⎜ ⎟ =
= 26.
8
⎝ hr ⎠ ⎝ miles ⎠⎝
ft ⎠ ⎝ 3600 sec ⎠ 3600 sec
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m
sec
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10 -3 m milli 10 3
k
kilo
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nano
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1
1 newton = × 1 kg × 1 m
g
sec
g c
c
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f
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g
ft lb
32.174
lb sec
f
c
m
2
2
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2
2
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1 Btu = 1054.35 J (or N. m)
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KW אאא،،400 kJאא
Power,P = 2×
400 kJ
hr
⎛ kJ ⎞⎛1000J
⎞⎛
hr ⎞
P = ⎜800
⎟⎜
⎟⎜
⎟
⎝ hr ⎠⎝
kJ ⎠⎝
3600sec
⎠
E 1 = 4000 J
E 2 = 10 W.hr
E 3 = 20 kN.m
= 222.
2 J = 222.
2W
sec
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∑
E
E
=
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m)
= 4 + 36 + 20 = 60 kJ
⎛
⎜
⎝
J
sec
⎞⎛
3600sec ⎞⎛
kJ ⎞
⎟⎜
⎟⎜
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hr ⎠⎝1000J
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m ⎠
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∑
E
=
⎛ 1BTU
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⎜1.055
kJ ⎟
⎝ ⎠
( 60 kJ ) ⎜ ⎟ = 56.87 BTU
-٦-

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Heat Transfer
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Modes of Heat Transfer Wאאא
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15 C 7 C 12 C 5 C
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אאאאאאW One-dimensional Steady State Heat Transfer
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Conduction Heat Transfer
אאאאאא Steady State Conduction- One Dimension
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سطح خرساني
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k A ∆T
q =
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q =
= 1690 W
0.25
- ١٣ -

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= 630 W
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- ١٤ -

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Thermal Conductivity Wאא
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سخان آهربي
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جهاز قياس القدرة
- ١٥ -

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q =
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R
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∆x
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R2
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R
3
WאאT 2 , T 3 אא
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q =
R + R + R
1
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q =
∆T
الكلية
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1
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الكلية
( 2 − 7 )
- ١٨ -

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25
o
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00651 C
kA 0.
8 × 48
W
q 15 − 4
= = 1689.
7 W ≈ W
0.
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004
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- ١٩ -

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C
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0.
32477
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אאאאאא Heat conduction through hollow
cylinders
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- ٢٠ -

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- ٢١ -

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א
∆T
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1
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40 m אאא אאאאאא
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k= 43 w/m o Cאאאא
∆T
q =
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∴ q =
= W
ln 5
528903
3
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40
W(2-9)א
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- ٢٢ -

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א
אאאאE١١٢F
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1
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Bאאאאא
- ٢٣ -

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R
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R
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אאאאאא K(k = 0.2 W/m K)א3cm ،
אאא א ،100 o Cאאא 600 o C
Kא
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r 3 r 2 r 1 אא
r 1 = 1 cm
r 2 = 2 cm
r 3 = 5 cm
- ٢٤ -

אא
אאא
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אאאא
א
E٦٢FE١٢٢F
אא،E١٢ J٢F
R
1
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r1
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2
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0013L
2π
× 19×
1
o
C
W
WEאFא
R
2
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7292L
2π
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1
o
C
W
W(2-9)אאאאא
600 −100
q =
R
∑
q 500 500
=
= = 684.
0.
0013 + 0.
7292 0.
7305
5
W
m
- ٢٥ -

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Convection Heat Transfer
W
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אאאא אאאKK
אא אKאאאאאאא
אאאאאאא
אא؟א אאאאא א א
אאאאאאא אאא
אאאאא אאKא
אאאאא Kfluid motion
- ٢٦ -

אא
אאא
١٦٢
אאאא
א
مائع
u
Τ ω
q
h
T w
אאאWE١٣٢F
אאFאWE Natural convection
אאאאאאאא
אאאאא
אא،אאא אא
אאא אאאא אאא
אאKאאאאאאFאKE
אאFאE‏:‏ Forced convection
Kאאא
אאא
א
אאאאKא
אאאא
אאK
Newton Law of Cooling
Wאאא
א
q h × A (Tw − T ) ( 2 −10
)
=
∞
א A (W/m 2 C)אאא h
אא‏(‏ WאאאאאK(m 2
- ٢٧ -

אא
אאא
١٦٢
אאאא
א
q
Tw
−T
⎛ 1 ⎞
⎜ ⎟
⎝ h×
A ⎠
=
∞
WאKאאRא
T
=
− T
R
q
w ∞
⎛
⎜
⎝
1
h× A
⎞
⎟
⎠
KאאאE١٤ J٢F
אE١٤٢F
KאאאאE٣ J٢Fא
h (W/m 2 C)
5-25
10-500
100-15000
2500-25000
5000-100000
- ٢٨ -
אאא
EאF
EאF
EF
אE٢٢Fאאאאh

אא
אאא
١٦٢
אאאא
א
WE٧٢F
120 o Cאא1000 W/m 2 אאאא
Kאאאא، 20 o C אאאא
q
q
A
אא
= h × A ( Tw
−T∞ )
= h × (T
w
− T
1000 = h × (120 − 20)
1000 W
h = = 10
100 m ° C
∴
2
∞
)
אW
אאאאאאW
kאאא
∆xE١٥ J٢Fאאא
אאאאא אאh i אאאKAh o
אאאאא
q =
R
T − T
אאא
حمل داخلي
i 1
( I
)
אא
אאאW
q =
T − T
1 2
( II )
R
توصيل
q =
R
T
2
− T
حملخارجي
o
( III)
- ٢٩ -

אא
אאא
١٦٢
אאאא
א
אאאאאE١٥٢F
אאאאאאאאאאא
q =
R
R
(T − T
i
+ R
)
+ R
convi cond conv o
1
=
h A
conv i
i
×
R ∆x
= cond k ×
1
Rconv o
=
h × A
o
o
( 2 −11)
אאאW
אאא
אאא
A
אא
אאאאאאאאאאא
K(2-11)אאאאאאאאאא
E١٦ J٢Fאאאא
Wאאאאאאא
q =
R
+
(T − T
i
∑
R
convi cond conv o
o
)
+ R
- ٣٠ -

אא
אאא
١٦٢
אאאא
א
ج)‏ شكل(‏‎١٦-٢‎
دار مكون من عدة طبقات مع حمل داخلي وآخر خارجي
WE٨٢F
א
K90 o C א 10 mmאא
אא אאאאאאא אK15 o C
א
אאא
אא אאC Cאאא 50 W/m o אאא 2800 W/m 2 o
K11 W/m 2 o Cאא
אW
אE١٧٢FאאאאאאKE٨٢F
R
convi
R cond
1
= =
h × A
i
1
2800
= 0.
000357
× 1
∆x
0.
01
= = = 0.
0002
k × A 50×
1
o
Wאאא
C
W
Wאאא
o
C
W
- ٣١ -

אא
אאא
١٦٢
אאאא
א
E٨٢FאאE١٧٢F
q =
R
R
1 1
= =
h × A 11×
1
conv o
=
o
0.
0909
אא
א
0.000357 + 0.0002 + 0.0909 = 0.0915
אאא
(T − T
i
+ R
)
+ R
convi cond conv o
o
90 −15
= ≈ 820
0.
0915
WOverall heat transfer coefficientאאאא
WאE١٨ J٢F،אאאא
q
=
o
U × A×
( T i
−T
) (2 −12)
W(2-10) אKאאאאU
W
m
2
q
(Ti −To
)
=
( 2 −13)
1
( )
UA
- ٣٢ -

אא
אאא
١٦٢
אאאא
א
אאאאE١٨٢F
1
U
1
UA
1
UA
1
= +
h
Wאא(2-11)(2-13) א
= R
1
=
h A
+ R
+ R
convi cond conv o
i
∆x
+
k
i
h o
∆x
+
kA
1
1
+
h A
o
(2 −14)
W
א אאאאאאאא(2-14)
Kh o h i אאא
E
Fאאאאא
א
WE١٩ J٢Fא
1
U
1
= +
h
i
∆x
k
∆x
k
2
1
h
o
( 2
1 2
+ +
−
1
15)
- ٣٣ -

אא
אאא
١٦٢
אאאא
א
אאאאאאE١٩٢F
Wאאאאא
1
U
1 ∆x
= + ∑ +
h k
1
i
h o
(2 −16)
∑ ∆ x
k
אאאh o h i אאא
אאאK
WE٩٢F
WאE٢٠ J٢Fאא
Uאאאא
Kאאא
T 3 אא
K50mmאאא150mmאאאאא
K١
K٢
K٣
- ٣٤ -

אא
אאא
١٦٢
אאאא
א
E٩٢FE٢٠٢F
אW
W(2-15)אUאאאא •
1
U
=
1
U
1
10
+
q
1
= +
h
∆x
k
∆x
k
1 2
+ +
i 1
2
h o
0.
15
+
1.
6
0.
05
+
0.
14
= U × A × ( T i−T
o
)
1
40
1
= 0.
57589
q = 1 . 736 × ( 1.
5×
0.
8 ) × ( 20 − ( −10
) = 62.
496
W
U
= 1.
736
2 o
m C
qאאא •
W(2-12)א
W
Wאאאאא،WT 3 אא
q
( − )
T3
− 10 T3
+ 10 T3
+ 10
= =
=
⎛ 1 ⎞ 1 0.
0208
⎜
h A
⎟
⎝
40×
1.
5×
0.
8
o
× ⎠
∴T3 = −8.
7
- ٣٥ -
o
C
•

אא
אאא
١٦٢
אאאא
א
WאאU אאאא
r o אr i אאL אE٢١٢Fא
T i אאאאאKkאאאאא
אאא אאאא h i אאאT o
WאאאאאאKh o א
אאאאאאE٢١٢F
q
R
R
R
convi
cyl
convo
1
=
h A
i
i
ro
ln
ri
=
2πkl
1
=
h A
0
o
EאFאאא
EFאא
EFאא
Wאאאא
Ti
− To
Ti
− To
= =
∑
ro
R 1 ln
ri
+ +
h A 2πkl
i
i
1
h A
o
o
( 2 −17
)
- ٣٦ -

אא
אאא
١٦٢
אאאא
א
אKאאאאאאA o A i
Wאאאא (U i ) אאאאאאא
q
אאאאא(2-17)(2-18)א
WKאאאאא
1
U
i
1
=
h
i
ro
Ai
ln
ri
+
2πkL
Ai
+
A h
אא (U o )אאאאאאא
= U
i
A
i
( Ti
− To
) ( 2 − 18 )
q
= U
o
Ao
(Ti
− To
) ( 2 −19
)
o
o
אאאW
Wאאאאאא
1
U
o
Ao
=
A h
+
i i
A
o
ln
ro
ri
2πkL
1
+
h
o
WE١٠٢F
5 cm אא (k=80w/m C)אא320 o Cא
אK5 o Cאאא5.5 cmא
אא Cאאא،3cm אאKk=0.05W/m
אאאאאC ،א18W/m 2 C60W/m 2 אא
אאאאKאאאאאK
- ٣٧ -

אא
אאא
١٦٢
אאאא
א
E١٠٢FאE٢٢٢F
אW
אאא אאאאא
אאאאאאאאJ٢F KE٢٢
Wאאאאא
R
A = 2πr l = 2π
× 0.
025×
1 0.
157 m
A
R
i i
=
= 2πr
l = 2π
× 0.
0575×
1 0.
361 m
o o
=
R
cyl
convi
insulation
R
1 1
° C
= =
= 0. 106
A h 0.157 × 60 W
i
i
2.
75
r2
ln ln
r .
° C
1
= =
2 5
= 0.
0002
2πk
1
l 2π
( 80 )( 1)
W
r3
ln
5.
75
r ln
.
° C
2
2 75
= =
= 2.
35
2πk
2l
2π
( 0.
05 )( 1)
W
1 1
° C
= = = 0.
154
h A 18×
0.
361 W
convo
o
o
0.106 + 0.0002 + 2.35 + 0.154 = 2.61 o C/W
T − T
q =
∑ R
320 − 5
=
2.
61
= 120.
i o
7
2
W
m
2
Wא
א
אאא
- ٣٨ -

אא
אאא
١٦٢
אאאא
א
q =
T
R
convi
− T
+ R
320 − T2
=
0.
106 + 0.
0002
i 2
=
cyl
Wאאאא
320
0.
1062
320 − T2
120. 7 = ⇒ T2
= 320 − 120.
7 × 0.
1062 = 307.
18 ° C
0.
1062
Thermal Insulation
אאא
Kאאא
אאאאאאא א
אאא
Kאאא אא אאא אKא
אאאאא
אא א١٩٩١אKאא
אאאאא٦٠אאא
אאאאאאK
אאאאאאא
אאאאאאא
אא
אKאאאJ٢F، אאאא، E٢٣
אאאKאאאאK
عازل
אאאאאאאE٢٣٢F
cork אאאאאאא
א
Kאfiberglassאא
- ٣٩ -

אא
אאא
١٦٢
אאאא
א
אאThickness Insulation Critical
אאאא אא א
אא Kאאא אאאא
א (A)אאאאKאאא
Kאאאאאאא
אאאא אאאאא
א אאאא
אאKאאאאאW
T 1 אאr 1 ،E٢٣٢F،א
אאא Kr o אא kא
אא qאאאאKhאאT o
q
T1
− To
=
ro
ln
r 1
1
+
2πkl
h ( 2πr
l )
o
אאאאW
א Kr o q א
o
א Wאאr o
k
ro =
( 2 − 20 )
h
o
- ٤٠ -

אא
אאא
١٦٢
אאאא
א
אE٢٣٢F
K r cr אא(2-20)אאאr o
אאא kאאאא
אאאKh o א
אאאאאK
אא r cr
אK
אאאאאW אאאא
א؟אאאא
؟אאאאאא
אאאא
אאא0.05 W/m o C
WאאK5 W/m 2 o C
W
k
0.
05
max
m ° C
rcr ,max
= ≈
= 0.
01 m = 1 cm
h W
min 5 2
m ° C
א (1mm Fאא
אאאאאאאh
Kאאא
- ٤١ -

אא
אאא
١٦٢
אאאא
א
אאא
א א אא
אאאאאאאK
WE١١٢F
7 mm 3 mmאא (k=0.15 W/m C)
אאK12 W/m 2 o Cאאא 30 o Cא5m
אאאא Voltsאאא 10A ،8
אאאאאאKאאא
אאאK
E١١٢FאE٢٤٢F
- ٤٢ -

אא
אאא
١٦٢
אאאא
א
אאאאא אאא
- ٤٣ -
אW
W(resistance heating) אא
q = V × I = 8 volts × 10 A =
KאאאE٢٤ J٢Fאא
R
R
convo
convo
R
1
=
h × ( 2πr
l )
عازل
o
80 W
1
=
= 0.76 ° C
12 × 2π
× 0.0035 × 5 W
ro
ln
3.5
r ln
1
1.5
= =
2πkl
2π
( 0.15 )( 5 )
T
q =
− T
= 0.18 ° C
W
∴T1 = To
+ q × R = 30 + 80 × ( 0.76 + 0.18 ) = 105 ° C
K١
אא
EFא
אאא
1 o
∑ R
∑
אאאאא K٢
k 0.15
∴r o
= = = 0.0125 m = 12.5 mm
h 12
1
=
h × ( 2πr
l )
R
عازل
o
1
=
= 0.2122 ° C
12 × 2π
× 0.0125 × 5
W
ro
ln
12,5
r ln
1
1.5
= =
2πkl
2π
( 0.15 )( 5 )
= 0.45 ° C
W
∴T = To + q × ∑ R = 30 + 80 × 0.6623 ≈ 83 ° C
1
אאא

אא
אאא
١٦٢
אאאא
א
אאאאאאאאא
אאאאא
אאא אאKאא
אאא אאא
אאKאא
אאאאKאא
א אאא Khאאא
אאאאאאא
אאאKאאא
Kא
K אא אא
אאאאאא
אאאאאאא
א אאא
אא
אאאאא אאא
- ٤٤ -
א
Kאאא
אא אאא
Reynolds
א אK non-dimensional
א KPrandtl numberאNusselt NumberNumber
ρ × u × l
Re l
=
µ
c
Pr = µ ×
k
p
Khאאא
אW
א
אאאאKאRe l < 5×10 5 א
Nu = 0.664 × Re × Pr
l
Wאאא
0.5
l
1
3

אא
אאא
١٦٢
אאאא
א
h
=
l
0.5 3
( k / l)
× 0.664 × Re × Pr
1
(2 − 21)
h × l
Nu =
k
Re l > 5×10 5 א
א אKאא
h
0.8
=
l
3
( k / l)
× 0.036 × Re × Pr
h = 4 ⋅ 364 × ( k / l)
(2 − 23)
Nu = 0.036 × Re × Pr
l
0.8
l
1
3
W
Wאאאא
1
Re
D
(2 − 22)
ρ × V × D
=
µ
אאאW
Re D <2300א
K،א
Nu D = 4.364
Wאאאא
Re D >2300א
אא אKאא
h = ( k / D)
× 0.023Re
D
0.8
× Pr
0.
8
D
Nu = 0.
023 Re × Pr
0.4
D
(2 − 24)
0.
4
אאW
Wאאאא
- ٤٥ -

אא
אאא
١٦٢
אאאא
א
EKKKKKKK،א،Fאאאאא
אאאאאאאW
q = h A ( Tw
− T∞
)
אאאאא אאאא
א אאא
אאאאאאK
WE١٢٢F
- ٤٦ -

אא
אאא
١٦٢
אאאא
א
60 o Cא1m، E٢٥ J٢F،15 o Cאא
c p
= 1000 J
/
kg
k = 0.
0267W / m
WאK3 m/sec
hאאא •
Kאאאאא •
o
C
µ =
0.
864×
10
אאאאW
−5
3
kg / m / s ρ = 1.
137kg / m
אאאWE٢٥٢F
ρ × u × l 1.
137×
3×
1
R l
= =
= 3.
947×
10
µ
− 5
0.
864×
10
Pr
µ ×
=
k
c p
−5
0,864 × 10 × 1000
=
= 0.325
0.0267
Wאאאא،
Nu
5
אW
א
R < 5 × 10
l
W
= 7.
657
o
m C
0.
5
5 .
l
( k / l ) . Rel
Pr ( . / ) . ( . )
0 5
1
3
3
= 0 664
1
= 0 0267 1 0 664 3 947×
10 ( 0.
325)
2
5
אאאאאW
q h × A × ( Tw − T ) = 7.657 × (1 × 1) × (60 −15)
= 344. 56W
=
∞
- ٤٧ -

אא
אאא
١٦٢
אאאא
א
אאאאאW Heat Transfer from Finned Surfaces
אאאא
q
= h × A ( T −T∞ )
w
W
אאאאאאhאא
א hאאאKAאא
AאK
א
،א Kאאאא
KאE٢٦ J٢F
r
x
x
א E٢٦J٢F
אאאאאאאאאאא
KאאאE٢٧ J٢F،אאאא
x
- ٤٨ -

אא
אאא
١٦٢
אאאא
א
q
η
=
F
F ∞
A h ( T − T ) (2 − 25)
Wאאאאא
Wאאאאאא
אא Aאאאhאη F
KאאאT ∞ אאT F
Wאאאאאא
אאאא אאאאאא،E٢٨ J٢Fא
אאאאאא אא א
Kא
q = A h ( T − T1 ) (2 − 26)
i
2π
k L
q = ( T1
− T
r2
ln
r
1
i
i
2
)
(2 − 27)
אאאאאW
אאאW
- ٤٩ -

אא
אאא
١٦٢
אאאא
א
q = Ao
h
= A h
o
o
o
( T
2
(1 +
− T
∞
) + A
AF
η
F
)( T
2−T
A
o
F
h η ( T
A 2π
× r ( L − t × n ) (2 − 29)
o
=
o F F
o
F
∞
)
2
אאאאאW
− T
∞
)
(2 − 28)
W
A π
2 2
( r − r ) 2×
n (2 − 30)
F
=
F o F
q
Ti
− T1 = = Ri
q (2 − 31)
A h
T
i
i
⎛ r2
⎞
⎜ ln ⎟
⎜ r1
T
⎟
1
− T2
= q = R q
⎜ 2 ⎟
c
π k L
⎜ ⎟
⎝ ⎠
(2 − 32)
⎛
⎞
⎜
⎟
1
=
⎜
⎟
q = R
⎜
⎟
o
q
AF
⎜ Ao
ho
(1 + ) η
F ⎟
⎝ Ao
⎠
(2 33)
2
− T ∞
−
T − T ∞
W(2-26, 2-27, 2-28)א
= q ( Ri + Rc
+ R
)
W(2-29, 2-30, 2-32)א
1 o
Wאאאא
q =
( R + R
i
T − T
i
c
∞
+ R
o
)
(2 − 34)
R c
- ٥٠ -
⎛
⎜
= ⎜
⎜
⎜
⎝
R
i
1
=
A h
i
i
r2
⎞
ln ⎟
r ⎟
π k L ⎟
⎟
⎠
2
1
W

אא
אאא
١٦٢
אאאא
א
R
o
⎛
⎜
1
=
⎜
⎜ A
⎜ Ao
ho
(1 +
⎝ A
F
o
⎞
⎟
⎟
⎟
) η
F ⎟
⎠
(2 − 35)
3 mm 10 cmאאE٢٨ J٢F
K20 cmא 3 mmאא 5050 cm
א K30 o Cאא 70 o Cאאאא
אאא אא אא ، אא
3
א15 W/m 2o CאאאאאאKאאא
A
K85%א54 W/m 2o CאאW/m 2o C
אW
Wאאא J
WאאאאW
A = 2π
r L=
2π
× 0.
05×
0.
5 0.
157m
i i
=
Wאאא
= 2π
r ( L−
n × t ) = 2π
× 0.
053×
( 0.
5−
50×
0.
003)
0.
117m
o o F F
=
A
Wא
2 2
2
2
2
F
= π ( rF
− ro
) 2×
nF
= π ( 0.
1 − 0.
053 ) × 2×
50 = 2.
259m
F
Wאאא
R
1
A h
1
=
0.
157 × 15
i
=
=
i i
0.
4246
⎛ r2
⎞
⎜ ln ⎟
5.
3
ln
r1
R
5
c
= ⎜ ⎟ =
= 0.
000344
⎜ 2π
k L ⎟ 2π
× 54×
0.
5
⎜ ⎟
⎝ ⎠
2
2
Wאאא
- ٥١ -

אא
אאא
١٦٢
אאאא
א
R
⎛
⎜
1
= ⎜
⎜ A
⎜ Ao
ho(
1+
⎝ A
o
⎞
⎟
⎟
1
=
⎟
2.
259
) ηF
⎟ 0.
117 × 3×
( 1+
) × 0.
85
⎠
0.
117
o
=
F
q
0.
165
Wאאא
Ti − T
70 − 30
=
= 67.
8 W
( R + R + R ) 0.
4246 + 0.
000344 + 0.
165
=
∞
i
c
o
q
A
Wאאא J
= 2πr
L = 2 × π × 0.
053×
0.
5 0.
1665m
o o
=
R
⎛ 1
=
⎜
⎝ Ao
h
⎞ 1
⎟ =
⎠ 0.
1665×
3
o
=
o
Wאא
2
2.
002
Ti − T
70 − 30
=
= 16.
48W
( R + R + R ) 0.
4246 + 0.
000344 + 2.
002
=
∞
i
c
o
Wאאא
K311%אאאא
T2 T + q Ro = 30 + 67.
8×
0.
165 = 41.
2
= ∞
Wאא J
o
C
- ٥٢ -

אא
אאא
١٦٢
אאאא
א
אא
אאאRadiation
W
אKאאאאאא
אאאKאאא
אאאאKאאאאאאK
אאK אאאאא אא
אאאKאאא
אאאאאא Kאאאא
א אאא
אא Kא
אאאאK
אאאאאאאK אאא
Kאא،א،אKאא
אאאאא אאאאא
אאאאאK אאאאא
א،אאאאא
אאאאא אאא
אא،אאKE٢٩٢F
30 C
5 C
نار
هواء
900 C
اشعاع
אאאאאE٢٩٢F
- ٥٣ -

אא
אאא
١٦٢
אאאא
א
אאאאאW Blackbody Radiation
Kא،א
אא
אא אאאאא א
אאאאאאKא
Kא"Black Body"א
אאאאא
KאאאKאאא
EFאא
אאWK
KE٣٠ J٢Fא،אא •
فراغ
جسم ساخن
אE٣٠٢Fאאאאא
א،אא אאאאא
KאאאאKאא
E٣١٢F •
- ٥٤ -

אא
אאא
١٦٢
אאאא
א
אFE٣١٢FאE
Kאאאאאא
א Kאאאאאא
א
.
Kאאא
Stefan-Boltzman's Law
אאאא
E b
= σ × T
σ
4
W
m
2
= 5.669×
10
−8
(2 − 36)
W
m
2
σ
Kא אא E b KאאאT
⋅ K
4
אא
- ٥٥ -

אא
אאא
١٦٢
אאאא
א
WE١٤٢F
אcmE٣٢٢F Kא20 אאK800
K5 minאאאאאאאא
800
K
20 cm
آرة
E١٤٢FE٣٢٢F
אW
אאא אא אא
4
−8
4
E W
b = σ × T = (5.669 × 10 )(800) = 23224
m
Wא
אE b אאא
2
אאאK
Wא
2 2
2
2
A = 4 π × r = πD
= π × ( 0.
2 ) = 0.
1257 m
Wאאא
W
2
Qrad = Eb
× A× ∆t
= 23224 × 0.
1257 m × 300 sec = 875.
8 kJ
2
m
- ٥٦ -

אא
אאא
١٦٢
אאאא
א
אW‏(‏ Emissivity ( ε
T s אאאאאא
q
4
emit max
= σ × A×
Ts
W
Wא
(2 − 37)
K(ε=1)אאאא
אאT s אאא
4
q
= ε × σ × A×
Ts
W (2 − 38)
،אאאאאאאKאε
אאאא ( ε = 1)אאא
( 0 ≤ ε ≤ 1)
אאEFא אאאאא
KאאE٣٢FאKאא
אאאאאאאאא
ε
=
E
E
אאאאW
E
=
σ T
b
×
4
KאאאאאאE
WAאאאא
4
E
= ε × A×
σ × T W
אא AT s א εא
אאא T surr אEF
Q
rad
4 4
= ε × σ × A×
( T − T ) W
s
surr
אאW
(2 − 39)
- ٥٧ -

אא
אאא
١٦٢
אאאא
א
א
WE١٥٢F
אא
א
אאא ?א?אאKאא
אאאאKאאC Kא22
אאאאK25 C10 Cאאאאא
1.4 א30 CאאKאאאא
K0.95אאm 2
אW
אאאאאאא
אאאא א
אε
0.90
0.85-0.93
0.93-0.96
0.82-0.92
0.96
0.95
Q
Q
Q
rad
4
s
= ε × σ× A × (T
− T
4
surr
) W
−8
4 4
rad , win
= 0.95 × 5.67 × 10 × 1.4 × (303 − 283 ) = 152
−8
4 4
rad , summer
= 0.95 × 5.67 × 10 × 1.4 × (303 − 298 ) = 40. 9
א
א
אא
אε
0.07
0.03
0.03
0.02
0.17
0.98
אאאE٣٢F
אW
Wאא
W
Wאא
W
א
אא
- ٥٨ -

אא
אאא
١٦٢
אאאא
א
א،אאW Absorptivity, Reflectivity & Transmissivity
Wאאאא،E٣٣ J٢F
אא J١
א J٢
א J٣
شعاع منعكس
الشعاع الساقط
شعاع ممتص
شعاع نافذ
אאאאאE٣٣٢F
אאα"Absorptivity" אאאא
τ"Transmissivty"אאρ" Reflectivity"
אאאאאאאא
α + ρ + τ = 1 (2 − 40)
α + ρ = 1
W
τ = 0אא
ρ = 0אאאא
α = 1
- ٥٩ -

אא
אאא
١٦٢
אאאא
א
Kאאאאאאא αא
א τאKאאאאאρא
אorientation
אאאאK
The View FactorWא
אאא
אא אא shape factorאKא
אא
F1
→
E2Fאאאא
אאאאEFא‎2KEF
F2
אאE1Fא‎1KE2F →
WE٣٤ J٢FKE1Fא
F
i→i
= 0 (2 − 41)
אFconcaveאאKconvexאאאא
אE??אאK
אאאE٣٤٢F
F
i→ j
WE٣٥ J٢F
= 1 (2 − 42)
- ٦٠ -

אא
אאא
١٦٢
אאאא
א
אאKi j
אאאאאK א
Kאאאא
دائرة ٢
دائرة ١
F 1--2
=1
אE٣٥٢F
- ٦١ -

אא
אאא
١٦٢
אאאא
א
אאא
אאא
Heat Exchangers
אאאאאאאאא
Kאאאא
אאאאאאאא
אאאK
אאאאאאאאאאאא
אK
Types of Heat Exchangersאאאא
Kאאאא
א
אאאא
Tubular or Concentric Tube HXR
אאאאא
אאאW
אאאאאאאאא JW
خروج
البارد
خروج
الساخن
دخول
الساخن
دخول
البارد
T h1
T h2
T c1
אאאE٣٦ J٢F
T c2
- ٦٢ -

אא
אאא
١٦٢
אאאא
א
دخول
البارد
خروج
الساخن
دخول
الساخن
خروج
البارد
T h1
T h2
T c2
T c1
אאE٣٧ J٢F
אא E٣٧ J٢FE٣٦ J٢Fא
אאאאאאאK
אK
Wאאאאאאא
אאא Parallel Flowאאא•
אאאאא،אJ٢ E٣٦
אאא Counter Flow אא•
E٣٧ J٢אF،א
- ٦٣ -

אא
אאא
١٦٢
אאאא
א
Compact HXR אאאא JW
אKאאאאאא
אאאאא densityאא אKarea
אא
700 m
2
m
אאאאא 3
אאאאא אאאאאK
אאאאK
אאאאאאאאא
Kאאאאcorrugated fins
EFE JFאE٣٨ J٢F
אא perpendicularאאאאא
אאflow אאKcross
KאאאE٣٨ J٢אF
Shell- and-Tube HXRאאאאא
Kאאאאאאאאאאא
אאאאאאFאE
אאKKאאאא
- ٦٤ -

אא
אאא
١٦٢
אאאא
א
KE٣٩ אאאאאאFאJ٢ אא
אא אא אbafflesא
אאאא Kאאאאאא
Kאאאאאאא
א٣٩ J٢
א
א
Kאאאאheaders
אKאאאאא
אאאאא(U-turn)אא
אאא E٤٠ J٢אFone-shell pass and two-tube passes
אאE٤١ J٢ אאFא
two-shell passes and four-tube passesא
אא Jא٤٠ J٢
- ٦٥ -

אא
אאא
١٦٢
אאאא
א
א Jא٤١ J٢
Plate HXRאאאאא
אאאאאאאKאא א
אאאאא Kאאא
אא אא
KאאאאאאאKא
- ٦٦ -

אא
אאא
١٦٢
אאאא
א
Heat Exchangers Analysisאאא
אאאא
אאא
אאא א
Kאאאאאאא
אKאאא
Kאא log mean temperature difference or (LMTD)אאא
the effectiveness and the אאאא אא
number of transfer units or (ε-NTU)
log mean temperature difference or (LMTD)אאאW
Kאאאאאאאאאא
K ∆T m
אאא אאאאא
.
Q
WאQאאאא
= U × A×∆T
m
( 2 − 43
)
אאאאU
אאא A
אאאא ∆T m
WE٤٢ J٢Fאאאאאא
.
- ٦٧ -

אא
אאא
١٦٢
אאאא
א
خروج
البارد
خروج
الساخن
دخول
الساخن
دخول
البارد
T h1
T h2
T c1
אאאE٤٢ J٢F
⋅
.
T c2
W d Q h
אאאאא
d Qh mh×
C
p
× (Th
−Th
) ( 2 44 )
h
⋅
d Q
c
= ⋅
−
2 1
⋅
W d Q c
אאאאא
= ⋅
m × C
c
pc
× (T
c2
−T
אאאאאא
c1
)
( 2 − 45
( 2 − 45 )
)
( 2 − 44 )
( 2 − 43)א
א 43)אאאא א( 2 − אאא
אאאאאאא אא
אאאאאא
אאאא אאאאא
⋅
Q
( Th
= U × A ×
2
−Tc
) −(Th
− T
2
1
⎛ Th
−T
⎞
2 c2
ln⎜
⎟
(Th
T
⎝
−
1 c2
⎠
c
2
)
( 2 − 46 )
אJW
- ٦٨ -

אא
אאא
١٦٢
אאאא
א
( T − T ) − ( T − T )
h2
c2
h1
c1
∆Tm =
( 2 − 47
Th
− T
2 c2
ln
T − T
h
1
c
1
א
אאא אא
אאאאאאאאא
אאאאאאאאFK
)
Eאאא
Wאאאאאאאאאאא
אא אאאא
א
אאאאאאאKאאא
Kאאאאא
אאאאאא א
א
Kאאאאאא
∆Tm = F × ∆Tm,
CFlow
( 2 − 48 )
אאאאא א
F
Kאא
אאאאא ∆T m,CFlow
Kא
אאאאאאE٤٥ J٢Fאא
( 2 − 48 )א ∆T m
F א
o
א80
C 20
K160
o C אאא1.2 kg sec אW
o C אאאאאא(geothermal water)
אאאאא 2
אא،
U = 640 W
m
2 o
C
kg
sec
אאא
אאאאאא1.5 cm
אאאאFKאאאאא4.18 4.31
Kאא
kJ
kg
o
C
- ٦٩ -

אא
אאא
١٦٢
אאאא
א
خروج
االماء
الساخن
دخول ماء
التكييف
ماء
جوفي
ساخن
خروج ماء
التكييف
T h1
T h2
T c2
⋅
Q
E٤٣ J٢F
T c1
אאאא
mc × C
p
× (Tout
− Tin
)
water
= 1 . 2×
4.
18×
( 80 − 20 ) = 301.
0 kW
= ⋅
⎛
⋅
⋅ ⋅
⎜ Q
Q
= ( mh
× C
p
× (Tout
− Tin
))
hot water
⇒ Tout
= Tin
−⎜
⋅
⎝ m×
C
EאאFאאא
p
⎞
⎟ 301
⎟ = 160 − = 125.
1
2×
4.
31
⎠
אאאאאא،
T
T
h
h
1
2
− T
c
− T
c
2
1
∆T
Kאאא
Wאאאא
= 160 − 80 = 80
C
= 125.
1−
20 = 105
m
=
o
o
C
( T − T ) − ( T − T )
h
1
c
2
T
ln
T
h
h
1
2
h
− T
2
c
− T
c
2
1
c
1
o
= 92.
0 C
Wאאא
o
C
- ٧٠ -

אא
אאא
١٦٢
אאאא
א
⋅
Q
= U × A× ∆T
Q
A =
U × ∆T
⋅
301000
=
640 × 92.
0
m
⇒
=
m
5.
11 m
Wאאאא
A 5.
11
A = π × D × L ⇒ L = = = 108.
4 m
π × D π × 0.
015
2
82
o
C 10
o C אאW
⋅
( m = 0.
04444
kg
o
אK104 C א 221
o C אא
)
sec
KאאאאK113 5 W אאאא
. 2 o
m
C
o
221 C
o
221 C
82
C
104
10
C
C
o
82 C
10
o
C
104
C
E٤٤ J٢F
K ∆T m
אWאאאאאא
∆T
m
T
T
=
h1
h2
− T
c2
− T
c1
= 221−
82 = 139
= 104 −10
= 94
( T − T ) − ( T − T )
h1
c2
T
ln
T
h1
h2
h2
− T
c2
− T
c1
c1
o
o
C
C
139 − 94
o
= = 115.
0 C
139
ln
94
R
P אאאאא
- ٧١ -

אא
אאא
١٦٢
אאאא
א
T
P =
T
c
h
T
R =
T
h
c
2
1
1
2
− T
− T
c
− T
c
h
− T
c
1
1
2
1
82 −10
= = 0.
34
221−10
221−104
= = 1.
625
82 −10
אאאאא
F אא
⋅
Q
= ⋅
∴∆
T m
F = 0.93
= 0 . 93×
115 = 106.
95
o
C
אאאא
Wאאאאאאא
m
c
× C
p
× (Tout
− Tin
)
water
= 0 . 04444×
4.
20×
( 82 −10
) = 13.
44 kW
Q
A =
U × ∆T
⋅
m
13.
44 × 1000
=
113.
5×
106.
95
אאאא
= 1.
107 m
2
- ٧٢ -

אא
אאא
١٦٢
אאאא
א
אאE٤٥ J٢F
- ٧٣ -

א
אא
אאא
١٦٢
אאאא
א
Wאאאאאאאא
Effectiveness and Number of Transfer Units(ε-NTU) Method:
אאאא
אאא
אא אאKאאאאא
אאאKאאאא
אאאאאK
אאאאאאא א אאא
Kאאאאא
אאא?אאאאאאאא
?אאאאאאא
אאאאא אאאא
⋅
⋅
⋅
⋅
Qc = Qh
= mc×
Cc
× (Tc
− Tc
) = mh×
Ch
× (Th
− Th
) ( 2 − 49 )
( m×
C ) p min
⋅
2
1
⋅
1
2
אW
Wאאא
( T − T ) ( 2 − )
Qmax ( m×
C
p
)
min
×
h c
50
= ⋅
1
1
אא
אאאEאאאאF
KT −
h
T
1 c 1
אאאאאאאאא
אאאאא
⋅
Q ( m×
C
p
)
c
× (Tc
− T )
actual
2 c1
ε = c
=
( 2 − 51)
⋅
Q ( m
⋅
× C ) × (T − T )
max
⋅
p
c
h1
c1
א
אאאאW
אאאאאאא
⋅
Q Th
− T
actual
1 h2
ε
h
= ⋅
=
( 2 − 52 )
Q
Th
− T
1 c1
max
Wאא
- ٧٤ -

אא
אאא
١٦٢
אאאא
א
אאאאאאאא
dimensionlessאאא Kאא
א אאא אאאא
U × A
NTU =
⋅
⎛ ⎞
⎜m×
C
p ⎟
⎝ ⎠
C
( m×
C
= ⋅
⋅
( m×
C
( 2 − 54 )
p
p
)
)
min
max
min
( 2 − 53 )
Wאא
( 2 − 54 )
( 2 − 53)
εא C אאאאאאאא א
אא‏(‏ ( 2 − 52
NTU אאא
א אאאאא א
אאאאאFKאאאJ٢ E٤٧
- ٧٥ -

אא
אאא
١٦٢
אאאא
א
אאאא،E٤٦ J٢FאאW
o
אK85 C א35
o C א 2.5 kg sec
1 09kJ
kg
. o
C
o
אא93 C א 200
W
،180
2 o
m C
אאאא
o C אאאאא
אאאא
אאאאאאאאK
خروج
الغازات
الساخنة
دخول
الماء
البارد
دخول
الغازات
الساخنة
خروج
الماء
T h1
T h2
T c2
∆T
m
(T
=
h1
− Tc
) − (T
2 h2
Th
− T
1 c2
ln
T − T
h2
c1
− T
c1
)
E٤٦ J٢F
T c1
אW
WאאאEF
( 200 − 85 ) − ( 93 − 35 ) 115 − 58 57
=
= = = 83.
3
200 − 85 115 0.
6845
ln
ln
93 − 35
58
∆T m
Wאאאאאאאאא
⋅
Q
= ⋅
mc×
C
p
× (Tc
− Tc
) = 2.
5×
4.
18×
( 85 − 35 ) 522.
5 kW
=
2 1
o
C
- ٧٦ -

אא
אאא
١٦٢
אאאא
א
∴
Q
A =
U × ∆T
⋅
⋅
Q = U × A×
∆
m
T m
522.
5×
1000
=
= 34.
85 m
180 × 83.
3
WאאאאEF
Wאאא
אאאאאאאאאא
522.
5
∴m
hot gasses
=
= 4.
48
1.
09×
107
kg
sec
אאאאאאאאאא
NTU = 1.
3
ε
U × A
=
⋅
( m×
C )
p
⋅
Q
⋅
( m×
C
⋅
( m×
C
p
p
T
)
hot gases
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cold water
− T
= 4.
48×
1.
09 = 4.
88
= 2.
5×
4.
18 = 10.
45
2
אאאאא
E2-52Fאא
200 − 93 107
= =
200 − 35 165
actual h1
h2
h
= ⋅
=
=
Q
Th
− T
1 c1
max
min
0.
648
C אאאאאאאאא
C
( m×
C
= ⋅
⋅
( m×
C
p
p
)
)
min
max
4.
88
= = 0.
467
10.
45
NTU אאאאאאא
⇒ A =
NTU × ( m×
C
⋅
U
p
)
min
1.
3×
4.
88×
1000
=
180
= 35.
24 m
אאאאא
2
- ٧٧ -

אא
אאא
١٦٢
אאאא
א
- ٧٨ -

אא
אאא
١٦٢
אאאא
א
אאאאאE٤٧ J٢F
אאאאאא
off-the-אאאאאא
אאאא،אאאאshelf
אאא אאאא
heat transfer requirements אאא
אאאאW
אcost
אsize physical
pressure drop characteristicsאא
אאא אאאאא
אאאא אKאאא
אאאאאאא
אאאאאcost אאpumping
אאא אאאאאא
אאאאאאא
Kאאאא
אאא אאאא
K١
K٢
K٣
K٤
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(prudent judgment and a consideration of all these factors will result in a proper selection or design of a
heat exchanger)
- ٧٩ -

אא
אאא
١٦٢
אאאא
א
אאאאא
אאאW
Kאאאאאאאא •
אאK20.5 Cאא20Cאא •
אא؟
Kאאאאא
Kאא
KאאאאK0.01m(1.5m * 2m)
•
•
•
אאאW
אאאאא،א אאאא
אאאאאאא
5cm א K
T 1
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T 2
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אא
א
אאcm K15
k=0.04
جدار
عازل
k=1.37
q
∆ Χ 2
- ٨٠ -

אא
אאא
١٦٢
אאאא
א
אאאW
50 Cא2.5 cmאאאאא
אאאC 0.8mmאאK3500 W/m 2 אאא 16
Kא אאאאאא אW/m C
אאאאא Cאאאא7.6W/m 2 C K20
T 2
T 1
q
r 1
r 2
h i
,T i
ho ,T o
k
T i
T 1
T 2
T o
R convi
R cyl
R convo
אאאאW
4cm 5cm אאKא 1cm א
אאא 20 C אאאא 100 C אאאא
Kאאאאא א K50 W/m 2 C א
אאא K0.04 W/m C 54W/m C
אאאW
(k= 0.156W/m C) 0.635 cm א
אK
21 C EאאFאho=8.52 W/m 2 C אאאא
EF אאא אאא65.5 Cאא
אאאFאEאK
- ٨١ -

אא
אאא
١٦٢
אאאא
א
אאאאאא
Wאאא
‏•אאאאא אאאאא
Kאאאא
• אאאאאאKא∆xא
∆x
K
kA
אאAkאאא
W،אאאאאא
•
∆T = -10 – ( -30 ) = 20 °C > 0
Kאאאאאאאא
•
אאאאאאאאאאא،∆Tאאא
K∆V = V1-V2אאא
אאאאאאאא
Kאא
אאאאאאא אא
عازل R
∆X
=
K
1
جدار R
0.05
=
0.04
1
=
∆Χ
=
K
2
2
1.25
o
C
W
0.15
= = 0.109
1.37
o
אא
אW،
•
•
A = 1.5 * 2 = 3 m 2
Wאאא
C
W
אאאאZאאHא
RTot = Rins
+ RWall
= 1.25 + 0.109 = 1.359
∆T
( 38 ) − ( −2 ) 40
q = =
= =
Σ R 1.359 1.359
Wאאא
29.43 W 2
m
- ٨٢ -

אא
אאא
١٦٢
אאאא
א
Wאאא
r i
= 1. 25
cm
ro = ri
السمك +
= 1 .25 + 0.08 = 1.33
cm
Ai = 2π
× ri
× l
2
( 0.0125 ) × l = 0.0786
= 2π
m
A
= 2π
× r
O o
×
2
( 0.0133 )*
1 0.0836 m
= 2 π
=
l
R
1
=
h A
1
=
3500*
0.
0786
COVI
=
i i
0.
00364
R
CONVO
=
h
o
1
A
O
=
1
7.6 * 0.0836
= 1.574
r
L o
n r Ln1.
33
1.
25 0.
062035
R i
cyl
= =
= =
2π
k l 2 π * 1 100 . 531
( 16)
0.
0006
∑ R = 1. 57825
∆Τ 50.20 30
q = =
= = 19
Σ R 1.57825 1.57825
W
m
- ٨٣ -

אא
אאא
١٦٢
אאאא
א
R
r
r
r
1
2
3
= 2.5 cm = 0.025 m
= 3.5 cm = 0.035 m
= r
2
= 7.5 cm = 0.075m السمك +
Wאאאא
אאאאאאא
r2
ln 3.5
ln
r1
2.5
−4
= =
= 0.00099 = 9.9 × 10
2πkl
2π
( 54 × 1)
r3
ln 7.5
ln
r2
R
3.5
2
= =
= 3.03 ° C / W
2πkl
2π
( 0.04 × 1)
1
°
C / W
1
1
R conv
= =
= 0.04244 ° C / W
h( 2πrl
) 50( 2π
( 0.075 × 1)
∆Τ 100 − 20 80
q = =
= = 26.03 W
Σ R 3.0734 3.0734
m
Wאאאאאא
T1
− T2
q =
R
T2
= T1
− q × R1
= 100 −(
26.03 × 0.00099 ) = 99.97 ° C
k 0.156
r o
= = = 0.0183 = 1.83cm
h 8.52
1
1
R conv
= =
= 1.021 ° C / W
h( 2πrl
) 8.52( 2π
( 0.0183 × 1)
ro
ln
1.83
ln
ri
R
0.65
cond
= =
= 1.056 ° C / W
2πkl
2π
× ( 0.156 × 1)
R Tot
= ΣR
= 2.0767 ° C / W
∆T
65.5 − 21 44.5
q = = = = 21.4 W / l
Σ R 2.0767 2.0767
1
Wאאא
אאאא
- ٨٤ -

٣אא
אאאא
אא
- ٨٤ -

אא
אא
١٦٢
אאאא
א
אאWאא
אאWאאאK
אאW
Wאא
Kאאאא •
אאאאאאא •
אאK
Kאאא
Kאאאא
KאאEאFאא
KאאEאF
Kאאאאאאאא
•
•
•
•
•
Wאאא
K٪٩٠אא
אאW
K١٢
אאW
Kאאאאא
Kאאאאאא
K١
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Wאא
Kאאאא K١
- ٨٥ -

אא
אא
١٦٢
אאאא
א
א אאאאאאא
אאאאאא Kאאאאאא
א Kאאאאאאאא
אאאאKאאW
•
KאאאאWאא •
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Kאאאאא
אאאאאאאאאאאא
אאKאאאאאא
אאא אאא אא אאא
אא אאאאKאא،אא
אאאא،א אא،
אא אא אK
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אאא אאא
אאאאאKאאא
Kאאא
- ٨٦ -

אא
אא
١٦٢
אאאא
א
אא
אאאא
Physical Properties of Fluids
Density:ρאL١
Kאאאאא א
W
ρ =
الكتلة
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20 Cאא K1000 kg/m 3
=
m
V
kg
3
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4ْC
אא
אאאאאאאFK1.2 kg/m 3 א
Specific weight
EE١ J٣F
γאאL٢
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γ =
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W
V
N
3
m
(3.2)
W
Wאאא
mg
γ = ρg =
V
(3.3)
Specific volume
v :אאL٣
Kאאאאאאאאאא
3
V 1 m
v = =
( 3.
4 )
m ρ kg
- ٨٧ -

אא
אא
١٦٢
אאאא
א
Specific Gravity SGאאL٤
אאא אאאא
אאאC) K(4
ρ f
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w
(3.5)
Kאאא
Wאאאאאא
P × V = m × R × T
(3.6)
ρ =
P
RT
(3.7)
p =
N
2
m
R ( R= 287 J/kg K)
T (K)
W
אא
אאא
אאא
ρ kg/m 3
א
אK3.6 m
WE١ J٣F
א K4 mא2 m אא Wא
Kא
ρ =
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=
m
V
kg
3
m
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אW
Wא
m = 9772 kg
π 2
V = d × h
4
אאא d =
- ٨٨ -

אא
אא
١٦٢
אאאא
א
אאאFאE h =
V
0.
02
3.
6
11 31 m
نحسب V:
2
3
= π × × = ⋅
4
Wאא
ρ =
m
V
9772 kg
= = 864
3
11⋅31
m
WE٢ J٣F
א אאאאא א
אkg/m3 א1000 6750‎אאFא kg
KEאא
Wא
hא
אFwא אאE F2wא
א אL w
wאא
אEאאK
WVא
V = l × w × h = 2w
× w × w = 2w
3
ρ
m
=
V
1000
=
6750
3
2w
w
3
=
6750
2000
=
3.375
3
w = 3.375 = 1. 5 m
∴l
=
∴h
2 × w
= w
=
=
2 × 1.5
1.5 m
=
3.0 m
- ٨٩ -

אא
אא
١٦٢
אאאא
א
WE٣٣F
אאאאאK 1.6 kאאא
ρ
m
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(0.001 m 3 )
1.
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אאא
א
Wאאאאאאאא
ρ
f
SG f
=
ρ
א kg/m 3
1000
70.7
682
298
13560
809
2700
921
1100
800
8900
1443
w
=
800
1000
= 0.8
א
א
א
א
א
א
א
א
א
א
א
א
R-134a
אאאאאאE١ J٣F
- ٩٠ -

אא
אא
١٦٢
אאאא
א
א Viscosity
א،אא
אאא KאK
Kאאאאאאאאא KK
KאאאאKאא
Kאאאאאא
u=U
F
مائع
y
u=0
אE١٣F
א E١٣FFאא
א אאA א y אא U
τ
- ٩١ -
KF
אאא shear stress F א
Wאτ w
τ = F
w
A
y אא u אאאא
du
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W
W

אא
אא
١٦٢
אאאא
א
du
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= µ ×
dy
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א אאµ
אאאאאKאW
µ =
⎜
⎛
⎝
τ
w
du
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⎟
⎞
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( 3 −
10
)
µ
=
N ⋅ s
m
2
=
Pa.
Sec
?א?EKKFEKKFאא
EאFאא
אאא
kinematic Viscosity
γ
=
µ
ρ
⎛
⎜
⎝
m
sec
2
⎞
⎟
⎠
( 3 .11
K m 2
sec א
אאאאאאא
אאאKאאא
אאאKאאאאא
אאאא א
)
Kא
Wאאא
Kאאא
אאאאאא
אאאאא אאא
א
אא
Kאאאא
- ٩٢ -

אא
אא
١٦٢
אאאא
א
א
א
א
אא
אאאE٢٣F
dv 1
א = 100
dy sec
WE٤٣F
א،אאאτא
τ
dv
= µ ×
dy
−
K10 3 Pa.secאא
∴τ
−
= 10 3 × 100 = 0.1 Pa
- ٩٣ -

אא
אא
١٦٢
אאאא
א
אאW
אאא
Fluid static's
W
אא אאKK אאא אאא
Kאאאאאאאאא
א Pressure
אאאאK
P
⎛
⎜
⎝
=
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m
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2
F
A
⎞
⎟
⎠
P
⎛
⎜
⎝
=
N
m
=
⎞
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( 3 12 )
2
Pascal
(Pa)
F =(N)
אא K1kN א
( Pa )
−
W
אא אאא
אאאא A= (m 2 )
( N
2 )
m
( N
2 ) = 100kPa
1bar
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m
W
E٥٣F
50mm (piston)א
KE٣ J٣Fאא،א
אW
אאאא
A =
π d
4
2
- ٩٤ -

אא
אא
١٦٢
אאאא
א
F
P =
A
∴ P =
1000
π 2 −6
4
× 50 × 10
P = 509
P = 509 kPa = 5.09
F
kN
2
m
bar
اسطوانة
٥٣E٣٣F
אאאאא
אאאא אאא
אאKאJ٣F Kא EFE٤
אJ٣F (b)אא(a)אאEFE٤
אאא(c)אאK(d)
- ٩٥ -

אא
אא
١٦٢
אאאא
א
אאE٤ J٣F
Pressure Head
אEF
אאKאאאאאאאאא
אאאאאK
אאאאאאאK
F
A
(ρ)
h
شكل ٣-٥
سمت الضغط
(ρ)E٥٣Fאאאאאא
(m)א(F)אאא
א(g)אאא(P)אW
P = ρ × g × h
( 3 − 13)
⇒ ∆P
= ρ × g ×
( ∆h) ( 3 − 14)
Khאאא
- ٩٦ -

אא
אא
١٦٢
אאאא
א
E٦٣FW
אאאאא ‎450cmא،א 250cm 300cm
KE٦ J٣Fאא،אאא1000kg/m 3 .
אW
אאאא
E٦٣FאE٦٣F
F = m × g
( V ) g
F = ρ × ×
( A×
h) g
F = ρ × ×
F
kg
m
= 1000 × 0.25 m × 0 .30 m × 0 .45 m × 9 .81
3
2
m
sec
F
=
331
N
F 331 N
P = = = 4400
A 0.30×
0.25 m
2
אאא
P = ρ × g × h
kg m
P = 1000 9.81 × 0. 45 m
3 2
m sec
N kN
P = 4400 = 4.40 = 4. 40 kPa
2 2
m m
- ٩٧ -
אאא
Kאאא

אא
אא
١٦٢
אאאא
א
E٧٣F
אאאאK 200m 300m B A
kg
K1023 m
3
א
Wא
אאאאא
אאאאE3-10FאאK
A אא
P = ρ × g ×
A
h A
P A
= 1023 × 9.81×
300
P
= 3.011
A
×
P = ρ × g ×
B
h B
10
6
Pa
Bאא
P
= 2.007
B
×
10
6
Pa
P B
= 1023 × 9.81×
200
Wאאא
P
− P
= 3.011×
10
− 2.007 × 10
= 1.004
6
6
A B
×
Wאאא
∆P
= P − P = ρ × g × ∆h
A
B
= 1023 × 9.81×
10
6
( 300 − 200) = 1.004 × 10 Pa
6
Pa
- ٩٨ -

אא
אא
١٦٢
אאאא
א
. 13.6
:
. 1000 kg/m 3
) 2 (101.325 kN/m إلى
EאאFא
E٨٣F
אא
•
•
אW
אW
אא‏(‏ )א،(101.325kN/m 2 ،(13.6)אא،(1000kg/m 3
א‏(‏ K(9.81m/sec 2
אW
אאא،אאאא
h
H 2o
= ρ
H 2o
p
× g
p = ρ × g × h
101.325×
1000 N
2
=
m
1000
kg
3 × 9.81 m
m sec
∴h
H o
= 10. 33 m
2
א
2
אK
10.33m אאא
،אאאא
Wא
Wאאאאאאא
ρ Hg
= ρ H
×13.6
2 o
- ٩٩ -

אא
אא
١٦٢
אאאא
א
ρ 1000 13.6
kg
Hg
= ×
m
Wאאאאא
101.325×
1000 N
2
h
m
Hg
=
(13.6 × 1000
kg
3)(9.81
m
m sec
h Hg
= 0. 76 m
10.33m אאא 0.76m אא
3
2
)
אאאK
- ١٠٠ -

אא
אא
١٦٢
אאאא
א
אאאאW
Kאאאאאאאאאא
Kאאאאאאא
אאאאאאאא א
KאאאאKאא
אאא אאKאאE٧ J٣Fא
אאאאKאא
אאא
1.013 bar
101.3 kN/m 2
‏(‏(standardא
אא
أو
Kאאא
אאא
אא
אאא
אא
אא 1 atm
אא
אאא
אא
EF
אE٧ J٣F
אא
- ١٠١ -

אא
אא
١٦٢
אאאא
א
E٩٣F
Kאא 0.61m3.66m אא
אאאKאאאא Kאאאאאא
917kg/m 3 א1000kg/m 3 אKאאאא
p o
K101.3 kN/m 2 אא
h 2
نفط
p 2
h 1
ماء p 1
E٨٣FאE٨٣F
- ١٠٢ -
אW
p 1 אKאאאאאp 2 אE٨٣Fא
Kאאאp 2 אאא
p
=
+
2
p0
ρ
2gh2
p N
kg m
2
= ( 101.
3×
1000 2 ) + ( 917 3 ) × ( 9.
81 2 ) × ( 3.
66 − 0.
51)m
m
m sec
= 128737 N
m
2
Wאא
p1 = p2
+ ρ1gh1
N
kg
9.81 m
1
= 128737 2 + ( 1000 3 ) ⋅ ( ) ⋅ ( 0.61m )
m
m sec
p 2
אא
p 1

אא
אא
١٦٢
אאאא
א
= 134721.1N
m
Wאאאאאאאא
2
p
=
p − p
1(
guage)
1 0( atm)
=
134721 .1 − 101.3 × 1000
= 33421.1 N
m
2
334 kN/m 2 אא
- ١٠٣ -

אא
אא
١٦٢
אאאא
א
Pressure Measurement א
אBarometer The
p
p
p
p
p
h
- ١٠٤ -
شكل-ب
شكل-أ
אE٩٣F
א E אאאאKאJ٩٣F
(p)אאא،א،
א אאאא
J٣F،אאאאא Kאאא
אאאאאאאE J٩
אאאאאאא
אאאאא
אאאKאhאאρא
אאW
p = ρ × g × h
KאאKאg
אאא א1.013 bar אאאא
1.013× 100000 = 1000 × 9. 81× h
1.013×
100000
h =
= 10. 326 m
1000 × 9.81
אW

אא
אא
١٦٢
אאאא
א
אאKאאאא10.326 mאאא
אKא13.6אאאאא
Wאאא
1.013× 100000 = 13600 × 9. 81× h
1.013×
100000
∴h =
= 0.76 m = 760 mm
13600 × 9.81
K(760 mm Hg)א760 mmאא
אאManometersW The
U אאאאאKא א
אאאא
אאאKKאאאא
אKאא Kאאא א
Kאאאאאאא
אאW
KאאE٩ J٣Fא
אא אKU
KE١٠٣Fאאאאא
אBאKC
KhאאאאאBא
KאאאאCא
- ١٠٥ -

אא
אא
١٦٢
אאאא
א
p
B
= pC
= p0 + ρ
Hg
gh (3 − 15)
A
D
C
B
h
مائع
אאE١٠٣F
אאManometer Differential
J٣FאKאאא
K(h)אאאאKאאE١١
אDאKC
אDא Kzאאhאאאp 2
אCא z)אאאp 1 K(h +
p1 + ( h + z)
ρ
Ag
= p2
+ ρBgh
+ ρ
Agz
p 1
− p 2
= ρ hg + ρ gz − ρ gz − ρ gh
B
A
A
A
- ١٠٦ -

אא
אא
١٦٢
אאאא
א
مائع
مائع
P 1
P 2
z
مائعA
C
D
h
אאE١١٣F
p1 − p2
= ( ρ
B
− ρ
A
)gh ( 3 − 16 )
אAאאאאאא
W(3-12) אKBאA
p1 − p2
= ρ
B
× g × h (3 − 17)
אאmanometerW inclined
אאKא א אאאא
xx sinθh אא אKאא
.אא θאאא
p1 − p2
= ρgx sinθ
(3 − 18)
P 1
P 2
غاز
h
x
θ
خط الصفر
سائل
אאE١٢٣F
אאW
- ١٠٧ -

אא
אא
١٦٢
אאאא
א
אאא
Fluids in Motion
Types of Fluid Flowאאאא
אאאאא אאאאא
אKאא אKאא
אאאאא
אאא(particles) א
אאאאאKא
אא،E١٣٣F(laminar flow)
אאא Kאאא
KE١٣٣F،(turbulent flow) אאאא
אאE١٣٣F
אאE١٣٣F
Fluids in Motion
אא
אאאאא
אאאKא אאאK
אאאאflow ،steady uniform אאKE١٤٣F
א
(convergent) אאא
אאFאאE١٤٣FאאK
אא אאאא
א K(steady non-uniform flow)
- ١٠٨ -

אא
אא
١٦٢
אאאא
א
A
B
A
B
A
E١٤٣F
B
A
E١٤٣F
B
Rate of FlowWא
אאאאא،E١٥ J٣F
⋅
אאא KQ
v
A
אאאאE١٥٣F
Wאאאא
Q&
= A×
v ( 3 −19
)
3
m
sec
אאא
∴
m&
אאא
W،א
الكتلة
ρ
=
الحجم
=
∴m
= V × ρ
m&
= ρ × Q&
الكثافة ×
الحجم
الكتلة
( 3 − 20 )
- ١٠٩ -

אא
אא
١٦٢
אאאא
א
E١١٣F
אא א K0.6 m/sec15mmא
Q &
m&
= π
4
( 0.015 )
2
Q & = A×
v
× 0.6
m & = ρ × Q&
= 1000 × ( 106.02 × 10
= 106.02 × 10
−6
אאK
אW
Wאאא
−6
m
3
sec
Wאאא
) = 0.106
kg
sec
- ١١٠ -

אא
אא
١٦٢
אאאא
א
Continuity EquationEאאFאא
אEאFאאאא
אאאאאאאא
⋅
m = ρ1 × A1
× v1
= ρ
2
× A2
× v2
(3−
21)
אW
אE٢١٣F Eא،אאFאא continuity equation
.
law of conservation of mass א
אאאKאאא
1
= 2
ρ ρ = ρ
A1 × v1
= A2
× v
2
(3 − 22)
∴Q
1
= Q 2
אאא converging pipe
אא ، m3 0.3
sec
Wא
W
WE١٢٣F
אאא، 0.15m א0.46m
אאאK
A 1
A 2
v 1 v 2
E١٢٣FאE١٦٣F
- ١١١ -

אא
אא
١٦٢
אאאא
א
אW
Wאא
Q = A 1
× v 1
Kאאא
v =
1
Q
A
1
WA 1 אא
2
−3
2
( 0.46 ) = 166.19∗
m
π 2 π
A1 = d1
=
4 4
10
0.3
∴v 1
=
−3
1.66019∗10
= 1.8 m
sec
v
2
=
Q
A
2
=
Kאאא
π
4
0.3
0.15
= 16.98 ≅ 17 m
2
( ) sec
KאאאKאאא
∴v
2
Kאאאאא
A ×
1
× v1
= A2
v2
A1
× v1
= =
A
2
2
× d1
× v
× d
π
4
π
4
2
2
1
π 2
× 0.46 × 1.8
4
∴v 2
=
= 16.93
π 2
× 0.15
4
m
sec
- ١١٢ -

אא
אא
١٦٢
אאאא
א
WE١٣٣F
5cmאאאא
998kg/m 3 אאא
אא 3.75cm ،א7.5cm
אW 0.015m 3 /secאא
Kאאאאאא •
•
אאאאאאK
E١٣٣FאE١٧٣F
אW
Wאאאא
m & ×
1
= ρ × A1
v1
m&
1
= ρ × Q
∴ m&
(
kg
)( . m
1
= 998 3 0 015
m
⋅
1
3
)
sec
m&
= 14.970
kg
sec
= × m
- ١١٣ -
1
2
⋅
3
אא

אא
אא
١٦٢
אאאא
א
∴m&
3
1
⋅
= × m
2
1
=
1 × 14.97 = 7.485
kg
2
sec
Wאאא
אאאא
A 1 א
A 0 = m
π 2 π
2
1
=
4
× d1
=
4
× ( . 05 ) 0.
001963
Q ×
1
= A1
v1
Q
v
1
=
A
3
0.
015m
v
sec
1
=
= 7.
6
2
0.
001963 m
1
1
m
sec
A 0 = m
π 2 π
2
3
=
4
× d3
=
4
× ( . 0375 ) 0.
001104
3
m
Q 0.
0075
3
v
sec
3
= =
= 6.
76
2
A 0.
001104 m
3
2
אאא
A 3 א
2
m
sec
- ١١٤ -

אא
אא
١٦٢
אאאא
א
Energy Of A Liquid In Motionאא
אא K?? א
."the capacity to do work"אאא
אאאאא אא
אאאאאאKאא
K??אאא
Wאא
Kא
Kא
Kא
Kאאא
(١
(٢
(٣
Potential Energy Wא
،datum line z m א אא
א
WאאאKE١٨ J٣F
⎛ m ⎞
potential energy = m × g × z ⎜kg
× × m⎟ ⎝ sec 2
⎠
אא،"J"
(3.23)
"Joule"?א?אאא
Wאאאא
m
z
datum line خط اسناد
א mאE١٨٣F
potential energy per unit mass = g × z
⎛
⎜
⎝
J
kg
⎞
⎟
⎠
(3.24)
- ١١٥ -

אא
אא
١٦٢
אאאא
א
Pressure Energy EאFא
אא א
אאpאאAאאK
אאאאKאאpAא
KQ &
KEF
work =
Q & = A×
v
&
v =
Q
A
אpAא
force × dis tan ce
work = p × A×
v
Q&
work = p × A×
A
work = p × Q
⋅
Wאאא m
אwork)‏)אאW
אא
m
& = ρ × Q&
WEFאאאאא
K
⎛ p ⎞
⎜
⎝ ρ ⎠
p × Q&
p
work done per unit mass = = ⎜
⎛ J ⎟
⎞
ρ × Q&
ρ ⎝ kg ⎠
J
kg
،אLאאאאאא
⎟אאאEאFא
pressure energy =
p
ρ
(3.25)
- ١١٦ -

אא
אא
١٦٢
אאאא
א
Kinetic EnergyWא
אא mאא
1 2
( × m × v )EאF
kinetic energy = ×
2
1 2
× m v
2
kinetic energy per unit mass =
(3.26)
W
Wאאאא
1
2
× v
2
⎛
⎜
⎝
J
kg
⎞
⎟
⎠
(3.27)
،א ،אאאאאא
WKא
אHאHא=אאאא
p
total energy per kg = g × z + + ×
ρ
1 2
v
2
(3.28)
א EאאאFאאא
W(height or head)א
(potential head)א •
(pressure head)א •
(velocity head)א •
אאאאאאאאאאאא
2
p v
total head per kg = z + +
ρ × g 2g
total head per kg = m
(3.29)
WKא
Wאאאא
N
+
m
2
3
m sec
× ×
kg m
total head per kg = m + m + m =
2
2
m
+
sec
m
2
sec
×
m
2
W
- ١١٧ -

אא
אא
١٦٢
אאאא
א
Bernoulli Equation
אFאאא ?Wא
אE א،א
W?אאא
Kא + א + א
Wאא
2
2
p1
v1
p2
v2
+ gz1
= + + gz
ρ 2 ρ 2
2
(3−
30)
Kאאא
אא
Kאאא
A
h
B
C
E١٩٣F
א E١٩ J٣Fאאא א
אא AאKhאא v
אא=AאאC
2
p
A
v
A
+
ρ 2
+ gz
א،אא
אEc
A
2
pC
vC
= +
ρ 2
+ gz
אאא
C
KאC
( 3.
31)
אאא
אFA
W
- ١١٨ -

אא
אא
١٦٢
אאאא
א
0 + 0 + gz
A
2
vC
= 0 + + 0
2
אCאאAא
WאאאK
v
C
=
=
2×
g × z
2×
g × h
Wאאאאאא
p
A
v
+
ρ 2
2
A
+ gz
A
2
p
B
v
B
= +
ρ 2
+ gz
B
+
A
energy loss between
A and B
(3.32)
WE١٤٣F
1.52m/secאאאא
אאאK9.14m/secאא
אא15.2mאאאאאK2.339kPa
אאkg/m3 kg/m3אא 998 K983
אW
Wאאא
p1
ρ
1
v
+
2
2
1
+ gz
1
p2
v
= +
ρ 2
2
2
2
+ gz
2
2
2.
339×
1000 1.
52
p2
× 1000 9.
14
+ + 9.
81×
15.
2 = + + 9.
81×
0
998 2
983 2
p2
× 1000
2.
344 + 1.
155 + 149.
112 = + 41.
77 + 0
983
p2
× 1000
110.
84×
983
152.
611 − 41.
77 =
⇒ p2
=
= 108.
955 kPa
983
1000
2
- ١١٩ -

אא
אא
١٦٢
אאאא
א
אאאאאW
Kאאאאאאא
h t
= hs
+ hv
(3.33)
אKא h v אאh s אאh t
אאא Kאאא
אאאאאK
אאא Kאאא
Wאאאאאא
v =
2
v
h v
=
2g
2ghv
(3.34)
(m/sec) א v
(m)א h v
W
WE١٥٣F
אאאאאK
KאאKאא21.6m 22m א
∴h
v
= h
אW
אאאאאאאK
t
− h
s
h
v
= 22 − 21.6
= 0.4 m
∴v
=
2gh
v
=
2 × 9.81×
0.4
= 2.8 m
sec
- ١٢٠ -

אא
אא
١٦٢
אאאא
א
WE١٦٣F
אא
13600kg/m 3 א1.2kg/m 3 אאאK20mm
p
v
= ρgh
Hg
אאא؟
אW
Wאאאא
= 13600 × 9.81×
0.02
v
p
ρ
2
v
=
air
= 2 ×
2
v
2
ρ
p v
2668.32
v = 2 × = 66.7 m
1.2
sec
air
= 2668.32 N
m
2
Wא
אאא
אאKאאאא אא
אKאאאאאK א
Kאא
- ١٢١ -

אא
אא
١٦٢
אאאא
א
Pitot TubeW
KE٢٠ J٣Fא
Kאאאא
אאאאK
WאאE٢FE١Fא
2
p1
v1
+
ρ 2
+ gz
1
2
p2
v2
= +
ρ 2
+ gz
Kאאא
2
אאE١F
א
p
ρ
2
1
p2
v2
v
2
2
2
= + ρ
2
p1
− p2
=
ρ
W
( p
1
− p
2
)
v
2
= 2 ×
( 3 . 35
ρ
)
אאא אאא p 1
אא p 2
אא
אK
א
א،אאאאאא
אאאאK
2
نقطة الرآود
اتجاه السريان
الضغط
الاستاتيكي
1
الضغط الكلي
אE٢٠٣F
- ١٢٢ -

אא
אא
١٦٢
אאאא
א
א Venturi-Meter
אא
א
KE٢١٣FאאKא
KאאאE٢FE١Fא
1 2
h
אE٢١٢F
אאא
אא אא
אאאKאאאK
אKאאא،אאאא
KאאE٢FאאE١Fא
p1
ρ
1
v
+
2
2
1
+ gz
1
2
p2
v2
= + + gz2
ρ 2
2
אאאאK
p1
∴
ρ
1
v
+
2
2
1
v
2
2
2
2
p2
v2
= +
ρ 2
− v
2
1
2
=
p
1
A
v ×
− p
ρ
2
1
= v2
A1
2
( I )
Wאאא
WאE٢Fאאא(I)
- ١٢٣ -

אא
אא
١٦٢
אאאא
א
v
2
=
2( p
1
− p
2
2
2
2
1
A
ρ × (1 −
A
)
)
(3.36)
KאאE٢FE١Fאא A 2 A 1
WE١٨٣F
EאאFאאאK25 Cא
אא2.5 cm E٢Fא7.5 cmE١Fאאא42.1 cm
אאK
אW
E٢Fאא
v
2
=
∴ v
2
2× ∆p
2
A2
ρ(1
− )
2
A
=
1
=
⎛ 0.025
1−
⎜
⎝ 0.075
2g
× ∆h
2
A2
(1 − )
2
A
2 × 9.81×
0.421
8.08
v
2
= = 8.18 = 2.86 m
0.988
sec
2
2
⎞
⎟
⎠
2
1
Wאאאא
3
⋅
0.0014 m
3
π
2
Q = A ( 0.025) 2.86 0.0014
sec
2
× v2
= × × = m =
= 1.4 lit = 84 lit
4
sec
3
sec min
0.001 m
lit
- ١٢٤ -

אא
אא
١٦٢
אאאא
א
Orifice MeterWאא
אא، א
אKא
Kא KE٢٢ J٣Fאאא
אאא אאאא
אאאK
v
2
=
2( p
1
− p
2
2
2
2
1
A
ρ × (1 −
A
)
)
(3.37)
1 2
אWE٢٢ J٣F
WE١٩٣F
אאK0.3 m/secE٢٢ J٣Fאאאא
אKאאאאא،0.06 mא0.3 m
א KC v = 0.82
Wא
v
2
= C
v
v
2
2 × ∆p
⎛ A ⎞
2
ρ × ⎜1
−
⎟
⎝ A1
⎠
v1
⋅ A1
=
A
2
2
Wאא v 2
א
- ١٢٥ -

אא
אא
١٦٢
אאאא
א
∆
v 2
= 7.5 m /
sec א
אאאא
v
2
2
× ρ ×
( 1
p =
2
2 × C
v
−
A
A
2
2
2
1
)
= 73048 .9
Pa
- ١٢٦ -

אא
אא
١٦٢
אאאא
א
אאאW
אאאאא
Fluid Flow in Pipes and Ducts
W
Kאאאאאאאאאא
אKאאאאא
א
אאאא אאאאא
Kאאאא Kאאא
אאאאאא אא
אאא אא
אאאאאא
KEא–Fאאאאא
Kאאא
Kאא
אאW
،אאאv
،אא
אא
אאאא א
אאאא
KאאאאאKא
ρ × v × d
Re =
µ
(3.38)
Wא
אρ
אµ
- ١٢٧ -

אא
אא
١٦٢
אאאא
א
אאאא
אאאא
אאאאאאאאא
Kאאאאאא
2100
Kאא
א10000
אK
100002100
Kאא
אאאאאK
WE٢٠٣F
א5cmאא ρ = 1050 kg/m 3
.10000 . µ = 995*10 -6 Pa.sec
ρ × v × D
Re = = 10000
µ
אW
−6
µ × 10000 995 × 10 × 10000
∴ v =
=
=
ρ × D 1050 × 0.05
0.1895
m
sec
Q
A
v
π
= × =
4
× (0.05)
2
× 0.1895
= 3.72 × 10
−4
m
3
sec
∴Q = 0.372
lit = 22.3 lit
sec min
אאאW
EאFאאאאא
אאKEאFאאא
אאאאKאא א
א،אא אא
אאא Kאא
אroughness Ksurface
- ١٢٨ -

אא
אא
١٦٢
אאאא
א
א Kאאא
אdrop lossאא pressure אאאא energy head
אאloss Kfriction head
1 2
اتجاه السريان
D
L
אאE٢٣٣F
אא E٢٣٣Fאא
אאא
א(1) Wאאא(2)
2
l v
p1 − p2
= f × × × ρ (3 − 39)
D 2
Kאρ،אv،אf
אאאאא KN/m 2
WHאא
2
p1
− p2
l v
H f
= = f × ×
( 3 −16
)
ρ × g D 2g
- ١٢٩ -
Kmאא
Wאאא
(Re =
ρ × V × D
µ
)
אאroughness) (Relative
∈
EאאF
D
(f)א
•
•
•

אא
אא
١٦٢
אאאא
א
א(material)
Riveted Steelא
א Concrete
Cost Iron
Galvanized Iron
Asphalted Cast Iron
Commercial Steel
Drawn Tubing
Glass
∈
mm
0.9-9
0.3-3
0.26
0.15
0.12
0.046
0.0015
Smooth
אאאאאE٢٣F
- ١٣٠ -
Moody Diagram
א (1944)E٢٤ J٣Fאא
אאאאאאאאאFאאEא
אא Reynolds Number Friction Factor
Wאא
Wא،אאא •
R e
3
≤ 2×10
אאא
0.001
אא
f
64
=
Re
Re ≥ 4×
10
( 3.41)
אאW
3
אאאא•
WאאSmooth Pipe א
f
.=
0.316
0.25
Re
(3.42)

אא
אא
١٦٢
אאאא
א
אאאאא
Rough Pipe אא אאא
Zone.
אאא אא
(Dא (∈) אאאאF
אאאאK
µ=0.014
א
•
•
Transitional Zoneאא
W
6mm15mאא
p
p
1
1
− p
− p
K848 kg/m 3 2 m/secאPa.sec
ρ × v × D 848 × 2 × 0.006
Re =
=
= 727
µ
0.014
f
=
אW
K2100
64
727
Wאא
= 0.088
Wאאאא
2
2
=
f
×
l
d
2
v
× × ρ
2
= ∆p
= 0.088 ×
f
64
=
Re
15
0.006
2
2
× × 848
2
= 373.12 kpa
1 2
اتجاه السريان
6 mm
15 m
- ١٣١ -

אא
אא
١٦٢
אאאא
א
معامل الاحتكاك
سريان
رقائقي
سريان
انتقالي
مواسير ملساء
رقم رينولدز
- اضطرابي مواسير خشنة
الخشونة النسبية
Moody DiagramE٢٤ J٣F
- ١٣٢ -

אא
אא
١٦٢
אאאא
א
Q = 20 l
10m
min אא
Q = 20
l
min
. µ =
50×
10
−
3
m
= 0.02
min
( ∆P)
WE٢F
אא
3 Pa sec
1030kg/m 3 א3.81cm
=
Q = A×
v
0.02
60
m
3
sec
= 3.333 × 10
−4
m
3
sec
אW
Wא
W
∴
=
Q
A
=
−4
3.333×
10
× ( 0.0381)
v
π
2
4
= 0.292 m sec
m
= 0.292
sec
א
ρ × v×
D 1030×
0.292×
0.0381
Re = =
= 229.2
−3 µ
50×
10
Q
Re ≤
∆p =
f
l
D
64
f = =
229.2
2100
V
2
2
64
f =
Re
ρ
0.279
2
10 (0.292)
∆p = 0.279 × × × 1030 = 3215 . 5 Pa
0.0381 2
Laminar Flow א
אא
אא
- ١٣٣ -

אא
אא
١٦٢
אאאא
א
WE٣F
אאL/sec אא3 80°C
40m 52.5mm
80 Cא
971.64 kg/m 3
0.358*10 -3 Pa.sec 80 C א
Q = 3 L = 0.003 m
sec
3
sec
Q 0.003
V = =
= 1.386 m
A π
sec
2
(0.0525)
4
א
א
ρ × v × D 971.64 × 1.386 × 0.0525
Re = =
= 197500 ≈ 200000
−3 µ
0.358 × 10
.אא40000
Kאאא
ε = 0.000046 m
אא
.א אא
ε
D
=
0.000046
0.0525
= 0.000876
0.000876
אא
Re = 197500
א
L V
∴∆p = f × ×
D 2
f
2
ρ
= 0.0208
אא
= 0.0208 ×
40
0.0525
(1.386)
2
2
× 971.64
= 14.8 kPa
- ١٣٤ -

אא
אא
١٦٢
אאאא
א
אאאאאאאא
אאאאK אא
אאאא
אאCorrection FactorאKאאאא
KE٢٦ J٣FE٢٥ J٣Fא אאא
425pa/mאאאאא50mmאאאא
K0.881.386m/sec80 CE٢٤ J٣Fאאא
∆p
∴ = 425 × 0.
88 = 374Pa / m
m
∴ ∆P
for 40m
= 374 × 40 = 15 kPa
אאm 40
- ١٣٥ -

אא
אא
١٦٢
אאאא
א
Pressure drop,
pa / m
3000
2000
1500
1000
800
500
400
300
200
150
100
80
50
40
30
0.03 0.06 0.1 0.2 0.3 0.4 0.5 1 2 3 4 5 810 20 304050 80 100 200 300
Water flow rate, L / s
50 mm
60 mm
15 mm
20 mm
25 mm
35 mm
40 mm
75 mm
100 mm
125 mm
150 mm
200 mm
250 mm
300 mm
0.5 m / s
1 m / s
Velocity
4 m / s
3 m / s
2 m / s
1.5 m / s
20°C אאE٢٥ J٣F
- ١٣٦ -

אא
אא
١٦٢
אאאא
א
EאFאאאאE٢٦ J٣F
אא
Pressure Drop in Fittings אאא
א
אאKאאאא
אא אאאK
אאK
- ١٣٧ -

אא
אא
١٦٢
אאאא
א
EKKKK،T،Fאאאא
אא،אאאא
א،אאאאאאKא
א
א
א
א
(mm)
15
20
2.5
35
40
50
60
75
100
125
150
(mm)
15.80
20.93
26.46
34.04
40.90
52.51
62.65
77.92
102.3
128.2
154.1
אאאאאFKאאE
90°
0.6
0.8
0.9
1.2
1.5
2.1
2.4
3.0
4.3
5.2
6.1
א75mm
45°
0.4
0.5
0.6
0.7
0.9
1.2
1.5
1.8
2.4
3.0
3.7
0.9
1.2
1.5
1.8
2.1
3.0
3.7
4.6
6.4
7.6
9.1
T
0.2
0.2
0.3
0.4
0.5
0.6
0.8
0.9
1.2
1.5
1.8
אאאאאאE٣٣F
EF
5
6
8
11
14
17
20
24
38
43
50
א
0.2
0.25
0.28
0.42
0.51
0.65
0.79
0.90
1.27
1.70
2.00
W
אאאא–א
o
אאאFאE א ،30mאא 90
kg
א 998.21
mg
א.
= 3.0 m
אא L/secWא 6
KאK
( 90°
)
1.008×
10
−3 Pa / sec
אW
אאאאאא
=
9 × 3=
27mא
אאאאאm = 0.90
אאm 2.7
- ١٣٨ -

אא
אא
١٦٢
אאאא
א
30
L =
m אא
30 + 27 +
2.7 EאFאא∴
= 59.7 m
Q 0.006
V = = A π
2
(0.07792)
4
Re =
= 1.258
m
א
/sec
W
p × v × D 998.21×
1.258 × 0.07792
=
−3
µ
1.008 × 10
= 97071
Kאא
∈
=
D
f
∆p
= f
=
0.00046
0.07792
= 0.0006
אא
= 0.0208 EאFא
2
L V
D 2
0.0208 ×
× ρ א
59.7
0.07792
( 1.258 )
×
2
2
×
998.21
=12587 Pa =12. 587 kPa
- ١٣٩ -

אא
אא
١٦٢
אאאא
א
אא‏:‏ Pumps And Pumping Requirements
אאאאאK
אאא אKאאא
אאאא אאאא
אאאKאאאhead) אא(pressure
K(efficiency)אא(power)אאא(flow rate)
Kאא
אE٢٧٣Fא
WE٢٧FאאE٢FאE١Fא
p1
+
ρ
v
2
1
2
+ z g + w
1
=
p2
+
ρ
v
2
2
g
+ z g +
2
∆p
ρ
frict
( 3.
43 )
- ١٤٠ -

אא
אא
١٦٢
אאאא
א
W
אאא אאאא، 2.1×10 -4 Pa sec1100 kg/m 3
אאK(w)אא50 kg/min52.51mm
אאאTא90°אא
KE٢٨ J٣FK30 kPaאא
p
ρ
v
אE٢٨F
2
p2
v2
= +
ρ g
2
1 1
+ + z1g
+ w
2
2
∆
+ z g +
ρ
אאאE١Fא،‏אE٢FE١FאאK
w
2
v2
2
∆
+ z2
g − z g +
ρ
=
1
p frict
p frict
אאאW
אHאאאHאאאאא
אאK
Wאאאא
W
ρ × v × D 1100×
v × 0.
0508
Re = =
−4
µ 2.
1×
10
- ١٤١ -
Wא

אא
אא
١٦٢
אאאא
א
Re
Q
50
v = =
= 0.
35
π
2
A 1100 × 60 × ( ( 0.
05251)
)
4
ρ × v × D 1100×
0.
35×
0.
05251
=
= 96268 〉
4
µ
2.
1×
10
=
−
- ١٤٢ -
m
sec
2100
Kא
EE٧ J٣FאFאfא
∈ 0.
15
= = 0.
00286
D 52.
51
אאE٢٣ J٣F
2
L V
∆p
= f × ρ
D 2
L = 1 + 1 + 3 + 2 + 15 + 3 + 1 + 3 + 6 × 2.1 + 1×
0.6 + 2 × 0.65
L = 29 + 12.6 + 0.6 + 1.3 = 43.5 m
( 0.
35)
43.
5
∆p = 0.
027 × × × 1100 = 1507 Pa
0.
05251 2
אא
f= 0.027
Wאאא
2
Wאאאא
∆p tot
= 1507 + 30000 = 31507 Pa
N
∆p 31507 2
tot
=
m
= 28 . 64 J
ρ kg
kg
1100 3
m
2
v
∆p 2
frict
w = + z2
g − z1g
+
2
ρ
2
0.
35
w = + 9*
9.
81 − 3*
9.
81 + 28.
64
2
w = 87.
5 J / kg
WאEF
אא

אא
אא
١٦٢
אאאא
א
Pressure Drop In Air Duct Flowאאא
אאא
Kאא אאא
אאאאאאא
∆p
=
1
∆p
= k(
ρv
2
L
k = ( f × )
D
Resistance Coeff. or Press. Loss Coefficient
2
)
L ρv
f ×
D 2
- ١٤٣ -
2
(3.44)
Kאא
אאא
W
אאאK
אאא אאאFאא
אאאא אאאא
א(Dampers)אא
אEאא
K =
Le
f
D
KD
∴ Le =
f
אאLength(m) L e = Equivalent
K =אא
f =אא
אא(m)‏=‏ אאKאאאD
אאאאא
A
D = 4×
P
KאאאPאA

אא
אא
١٦٢
אאאא
א
اختيار حجم المروحة
אאאאאאא
אאא
P = ∆p
× Q
אאאאא
אאאאאאאאאK
Wאאאא
2
L v
∆ p = f × × × ρ
D 2
Friction Loss
אאא
אאאאאאאאא
ρ v
∆p
= K
2
2
א Dynamic Press. Losses
WאEFאא
•
•
Wאאא
אאאK
• אאאW
• א
EFאא
אאאאא
אKKKK
אא אאאאאאא
א אאאאא
אאאאא אאאK
אא אאאא (Diagrams)
אאאאא אאא
KאאאאK
K١
K٢
K٣
K٤
- ١٤٤ -

אא
אא
١٦٢
אאאא
א
אאאא
- ١٤٥ -
אאאW
Kאאא،אא،א
אאאW
0.2m 3 א015m 3 אאא 012m 3 א
אאאא אאאא K1.15 kg/m 3
997
אFKאאאאאא 15002750
אאKE
אאאW
100 1/secאאאאאאאא
K0.001 Pa.secאאאא
א0.85אאא
−3
2
2.87
× 10 N sec/ m
Kאא،אא
6000NאאK7.5 cmא
אאK
E
EF
F
אאאאW
(R-134a) 7.5 mאאאאא
K1 MPaאאאא1206 kg/m 3
.95 אאFאkPaE 150 kPa א
אאK
EF
EF
EF
EF
אאאW
אאאאkPa אK101.325 . 999kg/m 3
אאאאK

אא
אא
١٦٢
אאאא
א
אאאW
750 kg/m 3 אא א
אאא א ،א2mא
3mאאK10 3 kg/m 3
K1 barאאאKאאאא
2m
نفط
3m
ماء
אאא
אאאW
Kאאא EF
אאא30 Cא1.5 barאא EF
אא،250 mmBא،400mm*300mmA
אאbar ،BA0.2 אאאאBא
אאאאאK m/secAאאR = 287J/kg K18
אאאW
אאאאאאאKאא
1
אאK
4 m
d = 100 mm
2
אא
- ١٤٦ -

אא
אא
١٦٢
אאאא
א
אאאW
Kאאאא EF
80 Cא6 L/secאא EF
801 kg/m 3
80 C אאK40m52.5 mm
K4.46*10 -3 Pa.sec80 Cאא
אאאW
K60mmאא42 mאא
א Kא 45˚א
א 90˚א
א0.02אאL/min אא،480
אFKא KE1000kg/m 3
- ١٤٧ -

אא
אא
١٦٢
אאאא
א
אאאא
Wאאאא
אאKאאאK אאאא
אאאא KאאאאKא
אK
Wאאאא
אאאאאא אא
ρ
ρ
=
V
v = m
m 1
=
V v
=
1
ρ
WאKא
Wאא
Wאאאאאאא
m = ρ ×V
m g
= 2750 × 0.12 = 330 kg
m s
= 1500 × 0.15 = 225 kg
m w
= 997 × 0.2 = 199. 4 kg
m a
= 1 .15×
0.53 = 0. 61 kg
m t
= 755
mt
=
V
755
=
1
t
=
t
kg
Wאא
Wא
Wא
Wאא
Wm t אא
Wאא
755
kg
m
3
- ١٤٨ -

אא
אא
١٦٢
אאאא
א
v
t
V =
t
m
t
=
אאאאאW
1 3
= 0.001325 m
755
kg
Wאאאא
Wאאאא
τ
du
= µ ×
dy
du
Kאאא אµאτ
dy
Wאא
τ
= 0 .001×
100 = 0.1 Pa
Wאאאאא
EF
Kאאא •
• אאאאHאאK
E F
Wאאא
p =
2 π 2 π
= × r = × D =
4
4
F
A
A π
× =
Wאא
2
2
( 0.075) 0.004418 m
6000
∴ p =
= 1358080 Pa ≈ 1358 kPa
0.004418
EF
7.5 m
R-134a
EFאאאא
- ١٤٩ -

אא
אא
١٦٢
אאאא
א
אאאאאאאאאאאאא
p = ptop
+ p134 a
= ptop
+ ( ρ × g × h)
134a
p = 1000000 + (1206×
9.81×
7.5) = 1088704 Pa = 1088. 7 kPa
Wאא
Kאאאp
EF
אאאאHאא
pabs = p
g
+ patm
= 150 + 95 = 245 kPa
p = ρ × g × h
101.325 = 999 × 9. 81× h
3
101.325 ∗10
∴h =
= 10. 34 m
999 × 9.81
Wאאאא
E13600 kg/m 3 אFאאא
p = ρ × g × h
3
101.325
× 10 = 13600 × 9. 81× h
Wאאאא
Kאאאאאאא
ρ × ρ
1
A
1
× v1
=
2
× A2
× v2
WאאEFאא
A ×
1
× v1
= A2
v2
•
- ١٥٠ -

אא
אא
١٦٢
אאאא
א
Wאאאא
A
B
אאא
אאאא
EBFאEAFאKאאא
ρ
p1
ρ1
=
RT1
5
1.5 × 10
ρ1 =
= 1. 725
kg
287 × (30 + 273)
m
p
(1.5 − 0.2) × 10
5
2
2
= =
= 1. 495
RT2
287 × (30 = 273)
Kאאאא
WE١FאAא
3
E٢FאBא
kg
m
E٢F( B)אאאאא
ρ1 × A
1
× v1
= ρ
2
× A2
× v2
אאאא אא،v 2
ρ1
× A1
× v1
1.725 × (0.4 × 0.3) × 18
v
2
=
=
= 39.87 m
2
ρ × A 1.495 × (0.25)
sec
2
2
3
Wאא
- ١٥١ -

אא
אא
١٦٢
אאאא
א
2
p1
v1
+
ρ 2
אאE١F
Wאאאא
Kאאאא
+ z
1
g
2
p2
v2
= +
ρ 2
+ z
2
g
Kאא
E٢FE١Fא
אE٢FאאאאK
⋅
v
2
2
2
= z g − z g
1
2
= g(
z
1
− z
Wאא،4m
v2
= ( 2g
× ( z1
− z2
))
v
2
=
2×
9.
81×
4
⋅
Q = A 2
× v 2
= 8.
86
2
)
m
sec
π 2
π 2
Q = ( d ) × v = (0.1) × 8.86 = 0.0695m
4
2
2
4
אאאW
( z1 − z2)
WQאא
3
sec
Wאאאא
אא א
אאאFאאאאא Kא
⋅
∆p
=
f
×
L
D
×
2
v
2
× ρ
Q 10 × 0.001
v = =
= 4.62 m
π
2
A × (0.0525) sec
4
WאEא
ρ × v × D 801×
4.62×
0.0525
Re
= =
= 43561 〉 40000
−3 µ
4.46×
10
EF
EF
W
- ١٥٢ -

אא
אא
١٦٢
אאאא
א
ε
D
=
Kאא
אאmm EאאF0.046
אא
0.000046
0.0525
= 0.000876
fאא
f = 0.025
L
= f ×
D
2
v
Wאא
∆p
× × ρ
2
2
40 (4.62)
∆p = 0.025×
× × 801 = 162827.3 Pa = 162. 8 kPa
0.0525 2
Wאאאא
Wאאא
L = 42 + 8×
2.4 + 4×
1.5 + 6×
0.79 = 71. 94 m
⋅
Q
v
= A×
v
=
Q
A
480 × 0.001
=
π
60 × ( × (0.06265)
∆p
4
E0.001m 3 אFWאא
L
= f ×
D
×
2
v
2
2
)
× ρ
= 2.6 m
sec
2
71.94 2.6
∆p = 0.02 × × × 1000 = 77333 Pa = 77. 333 kPa
0.06265 2
אא
- ١٥٣ -

אאא‎٤
אאאא
אאא

אאא
אאא
١٦٢
אאאא
א
אאאWאאא
אאWאאאאאאאא
Kאאאאא
אאW
Wאא
Kאאא K١
Kאאאא K٢
Kאאאאאאא K٣
Kאאאא K٤
אאאאאאא K٥
אאK
אאאאאאא K٦
אאK
Wאאא
K٪٩٠אא
K٪١٠٠אאאאא
אאW
KEFא١٥
אאW
Kאאאאא K١
אאאאאאאK K٢
Wאא
Kאאאא
- ١٥٤ -

אאא
אאא
١٦٢
אאאא
א
אאאThermodynamics
W
אאאאאאא
אאKאא
אK אאאאאא
אאא Kאא
Kאא
אאאK אאא
אאאאאKKאאא
אאאא، אאאא
אאאKאא אאא
אאאא
K
- ١٥٥ -

אאא
אאא
١٦٢
אאאא
א
אא
Thermodynamic Concepts & Definitions
אSystemW
אא אאאאאאא א
אאK א א
אאKאboundariesא،א
אא אאא אא
אאאאאאאא
אאא אאא
אsurroundingsאאאKflexible
א
אKא אאאclosed system
אKאsystem אopen אא
אאJ٤FK KE٢ J٤FE١
אא
א
א
אאא،אWאאE١٤F
- ١٥٦ -

אאא
אאא
١٦٢
אאאא
א
אא
א
א
אאא،אWאאE٢٤F
?א?אKא
Kאאא،א،א،א،א، אאאא
K"properties".
intensiveאאא אאא Kאאא
40 o C א
،אאאאא
extensive
אאאKאא
א،אאאאKאא homogeneous
Kא
אאאKאאאאאא
אאKא אאאא
אאKKאאא
אאא Kאאא
אאאא،
א
א אא
א
אKאאאאא
אאאאאאאא
K
- ١٥٧ -

א
א
אאא
אאא
١٦٢
אאאא
א
1-2Kא
processאאא
אאא אא(1)אK(2) אE٣ J٤F
אאאאאאK
אאאאאאאK
אא thermodynamic cycle
אJ٤F KE1-2-3-1אFE٣
אאאאE٣٤F
אReversibility
Kאא אאא
אאאאאאאא
אא אאK אאאאא
אאאאאJ٤F، אאאאKE٤
K
אאאאא
אאאאא
אKאאאאאJ٤F، KE٤
אאאאאאאאאא
K אא
Wא
אאאFKאאאא •
אאאאKE
- ١٥٨ -

אאא
אאא
١٦٢
אאאא
א
א אאא אאא א
אא
•
Kא
Kאאאאאאאאא
•
אאאאאK
אאאא
אK
p
p
v
إنعكاسي
لا إنعكاسي
אאאאאאE٤ J٤F
v
אא Pure substance
Kאאא،אאא
א אא
،אאא
אא אא א
K
Wאאא
א K،אאאא
אאאאK אאא
אאKאאאאאאא
אא ١٠٠ K١٠٠אא
אאאאאא KEFאאאאKEF
אא Kאאאאאא
אאאאK
- ١٥٩ -

אאא
אאא
١٦٢
אאאא
א
אאאא،אE٥ J٤Fא
אאאאאאאאא
אאKאאאאאא
אאאKאאאאאא
אאא JאE٥ J٤F
א אא אאE٦ J٤F
(2)אKאא
(2)א(1)א
א100 o CאKאאאאא
אkPa אאאאא K101.3 אא
،א2-3אאKEאFאאא
אאאא Fאאאאאא אא
אאKE
(3)אאא (3)אא
Kא
K(4)אאאאאאאא
- ١٦٠ -

אאא
אאא
١٦٢
אאאא
א
אאאאאא 1-2, 3-4אאאאא
Kאא
א4 o Cאאאא
אאאא
אK
אאאאE٦ J٤F
The State Of The Working Fluid א
אKאאאאאא
אא
אאא א אאא
אאאאKאאאKworking fluid
א،אא،אא،אא אאאא
אא،אאK fluid)אא (pure working
אKא
v 1
א p 1
אאאKאא
KE٧ J٤F،אאא(1)
א T 1
אאאא
אאKE٧ J٤F،אאאאאאא
אK(2)א(1)אאאא
אאאאKאא(2)
- ١٦١ -

אאא
אאא
١٦٢
אאאא
א
،אא Jאאא Kא
Kאאאא Jא،א Jאא
p
1
p
1 1
T
2
2 2
v
T
אאאאE٧٤F
אא
אאאאא אאאאK
אאאאKאאא
אאK
Kאאאאאא
- ١٦٢ -
v
אאאאW
equation of stateאאאא
אKאאאאא
אאאאאאאאW
p×
v = R×
T ( 4 −1)
p = ρ × R × T ( 4 − 2 )
p×
V = m×
R×
T ( 4 − 3)
Wאאאא
N/m 2
m 3
m 3 /kg
אא
אא
אא
p
V
v

אאא
אאא
١٦٢
אאאא
א
kg
K
J/kg K
א
אאא
אא
m
T
R
kg/m 3
אρ
W
אאאאא K101.325 kPa25 o Cאא
p × v = R × T
KR=287 J/kg Kאאא
אW
Wאאאא
( 101 . 325×
1000 ) × v = 287×
( 25 + 273)
287 × 298
∴v
=
101.325×
1000
= 0.884 m
3
kg
J/kg o Kאא
287
188.9
296.4
4124
296.8
259.8
461.5
א
אא
א
א
א
א
א
א
אאאאאE١ J٤F
- ١٦٣ -

אאא
אאא
١٦٢
אאאא
א
W
17 א100 bar30،E٨ J٤Fא
75 barאאאאאK˚C
אאC‏˚‏ KאאKאאאאK7 K260 J/kg
p × V = m × R × T
אW
Wאאא
m 2 אא،m 1 אאא
5
−3
p1
× V ( 100×
10 )( 30×
10 )
∴m1 = =
= 3.
98 kg
R×
T 260×
( 17 + 273)
1
5
−3
p2
× V ( 75×
10 )( 30×
10 )
∴m2 = =
= 3.
09 kg
R×
T 260×
( 7 + 273)
2
m − m = 3.
98 − 3.
09 0.
89 kg
1 2
=
Kאא
אאא
صمام
مقياس ضغط
مقياس ضغط
O 2
أسطوانة معدنية
אWE٨ J٤F
- ١٦٤ -

אאא
אאא
١٦٢
אאאא
א
- ١٦٥ -
אאאheatW specific
אאאאאאאאאא
،אאאא Kאאאא
אאא אאאc p אאאא Kc v
א
K
א אאאא
אאא
אאאאKאJ٤F KאאאאאE١
C p kJ/kg K
0.45
0.65
1.0
2.1
א
א
א
אא
א
C p kJ/kg K
0.9
0.386
0.8
4.187
25 o CאאאאאE٢ J٤F
אאאאאא
א
א
א
א
א
R
אאאא
א k אאא א
Kc v אc p א
אEnergy
Kאא
א
Kאא
Kא
אאא Kא
אאKאאאא
אאאא Kא
א
אE،،Fאאא
אאאאאKאאאא
Kאאאא
א Kאאאאאא
K

אאא
אאא
١٦٢
אאאא
א
אאheat
אאאא אאאא
Kאאאאאא،אא
אא אKא
Kאא אK
אאא אאאא אאאא
אאא אKאאא
אאאאאא
אאKK א
א
א
K
א work
אKא
אK א
אאKאאאאא
א،אאאאא
Kאא א א א אאא
א אאKאאא
Kאא
א
א אא אאאאא
אאאאאא،
אKאאאא
אאאא
K
אאאאE٩ J٤Fא
אFאאEאאאKL،
- ١٦٦ -

אאא
אאא
١٦٢
אאאא
א
منفاخ
F
L
بصيلة
אאE٩٤F
אאW
pE١٠ J٤Fאאאאאא
אאא pאKp 0 אאאאp 0
w out אאאא
אא
p
p 0
مكبس
اسطوانة
אאE١٠٤F
אא p 0 pא
KE J١١ J٤ J١١ J٤FאאאKw in
E١١٤F
E١١٤F
- ١٦٧ -

אאא
אאא
١٦٢
אאאא
א
Wאא
electric workאאdisplacement workאאאא
Kshaft workא
Displacement WorkWאא
WKאאאאאא
dW = F × dl ( 4 − 4 )
KאאdWFאא dl
F = p × A
KאAאp
Wא(4-4)אpF
dW = p × A × dl
WdVאאdVא dl×A
dW = pdV
WE١٢ J٤F،1-2אאא
2
W = ∫ pdV ( 4 − 5 )
1
אאE١٢ J٤F
- ١٦٨ -

אאא
אאא
١٦٢
אאאא
א
KאאKאאאאא
Kא Jאאא
Wאאאאאאא
‏•אאאKא אאא
V = C
Kא
‏•אאאK
Wאאאאאא
constant volume processWאא.١
א
KC
E١٣ J٤Fאאאאא
p
3
1
2
زيادة الضغط
V=C
نقصان الضغط
V 1
=V 2
=V 3
אאאאE١٣٤F
KאאאאאdVאא
2
W = ∫ pdV = 0 ( 4 − 6 )
1
p = C ( 4 − 7 )
- ١٦٩ -
v
constant pressure process Wאא
אאאאW،
K٢

אאא
אאא
١٦٢
אאאא
א
KC
E١٤ J٤Fאאאאא
p
انضغاط
p
تمدد
3
p 1
p 2
p 1
=p 2
=p 3
V 3
-ve
+ve
V 1
V 2
V
אאאאאE١٤ J٤F
KאV 3 V 1 V 2 V 1 אאאאא
w
12
= ∫
v2
v1
p dV
w
13
= p × (V
v
2
−V
2
)
= + ve work
3
= ∫ p dV = p × (V3
− V1
)
v1
Wאא
= −ve
work
( 4 − 8 )
Wא
Wא
Kאאאאאאאא
W
אא ،0.5 m 3 2 bar0.2 m 3
2
אאאאK
א
Wאא،אאאא
5
W = ∫ pdV = p(V2 −V1
) = 2 × 10 ( 0.
5 − 0.
2 ) = 6×
10
1
4
J
- ١٧٠ -

אאא
אאא
١٦٢
אאאא
א
isothermal processWאאא K٣
Wאאאאאאא
pV = C ( 4 − 9 )
p 3
p
3
א
pV=C
KC
p 1
p 2
1
2
V 3
אאE١٥٤F
V 1
א1-2אאKE١٥ J٤Fאאא
WאאKאא1-3אא
w
∫
V
= 2
V
1
pdV
V 2
V
אאא
mRT
p =
V
Wאאא
V
2
dV
W = mRT ∫ = mRT
V
V1
V2
W = mRT ln
( 4 −10
)
V
1
[ lnV ]
Kאאאאאאאא
V2
V1
- ١٧١ -

אאא
אאא
١٦٢
אאאא
א
0.4 אא 27 o Cא1 bar0.2 m 3 א
Kאאאאאא،m 3
א
Wא،אאאא
V
W = mRT ln
V
p 1
V 1
=
2
1
mRT
אאאאא
∴W
=
V2
5 0.4
p1 V1
ln = 1×
10 ln = 69314.7
V
0.2
1
J
p 3
p
3
א
pV k =C
p 1
p 2
1
2
V 3
V 1
- ١٧٢ -
V 2
אאאE١٦ J٤F
V
adiabatic processWאאאK٤
אאאאא אאא
Kא
אאא
K
אאאא
אKאאאא
א אאאאא
אאאKאא
אא
W

אאא
אאא
١٦٢
אאאא
א
pV k = C
אאא אKא
kאא
אJ٤F WאK،E١٦
V1
1−k
1−k
[ −V
]
−k
+ 1 2
V2
dV ⎡ V ⎤ C V2
1
w = ∫ pdV = C∫
= C⎢
⎥ =
V
k
1 V ⎣−
k + 1⎦
− k + 1
Wאאאאא
V
(p 2 v k 2)
p1V
1
− p2V2
W =
( 4 −11)
k −1
(p 1 v k 1) Cא
Kאאאאאאאא
W
אאאאKא 0.015m 3 1.02 bar22 o Cאא
אא 6.8barאאאאא
K1.4אk אKאאאאאא
p
אW
6.8 bar
pV 1.4 =C
א
1.02 bar
V
V 2
0.015 m 3
אE١٧٤F
אא،
pV k = C
k
k
V p V
p1 1
=
2 2
- ١٧٣ -

אאא
אאא
١٦٢
אאאא
א
V
V
V2
0.
015
w
12
2
1
⎛ p
=
⎜
⎝ p
1
2
⎞
⎟
⎠
⎛1.
02 ⎞
= ⎜ ⎟
⎝ 6.
8 ⎠
1/
k
1/
1.
4
V
2
= 0.
00387 m
=
3
p1V
1
− p2V2
k −1
10 5 ( 1.
02×
0.
015 − 6.
8×
0.
00387 )
w12 =
= − 2754 J = − 2.
754 kJ
1.
4 −1
W 12 א
Kאאאא
- ١٧٤ -

א
אאא
אאא
١٦٢
אאאא
א
אא
אאא
First law of thermodynamic
אא אאאא
אאK א
אאאאא אאאא
אאאאאא?אא
אאE١٨ J٤FK?א
؟אאאK1.9 kW(Q out )אאאאא1.17 kW(Q in )
Q in
Q out
سخان
אאאE١٨٤F
Wאאאאאאא
אאאאאאא،
1.17 – 1.9 = – 0.73 kW
W
אאאאאאאא
K730Wאא
אאאאאאא
WאאKאאאא
∑ ∑
Q = W ( 4 −12
)
- ١٧٥ -

אאא
אאא
١٦٢
אאאא
א
WE٧٤F
אאא‏(‏ J٤Fאא(W t E١٧
אE١٩٤F
∑
4000 − 3000 = W − 5
Q
∴W
W
= ∑ W
t
t
= 1000 + 5
= 1005 kW
t
אW
Wאאאא
- ١٧٦ -

אאא
אאא
١٦٢
אאאא
א
First Law for a Closed SystemWאאאא
E٢٠٤F
אאאאאא
אא،אאאא
אאאאK אאאאא E٢٠ ٤Fא
אאאאאאאאא
אאא E٢٠ ٤Fא
אאאאenergy Kgain in intrinsic
אאאא אא
Kloss in intrinsic energyE٢٠ ٤F
אאאאאאא
אאאאZא–אא
Eאא Fאאא
uinternal energyאאאאאא
אאאאUאאא אkJ) K(J, אאא
אאאאא Kאאא
אאאאאאאKא
- ١٧٧ -

אאא
אאא
١٦٢
אאאא
א
q − w = ∆u
( 4 −13
)
Kאאאאאא ∆u
אאאאאאא
∆ u = cv × ∆T
Kאאאאc v
אאאאאאא
אא אא אאאאאאא
K
،א אא
KאאאאאKאאאאא
W1
אאאאאאאאאאkJ/kg 45
אאאאאK90kJ / kg אא
q = −45kJ
/ kg
אאK
אW
w = −90kJ
/ kg
q − w = ∆u
אאאא
− 45 − ( −90)
= u − u
2
1
u − u 45 kJ / kg
2 1
=
Kאאאאאאא
- ١٧٨ -

אאא
אאא
١٦٢
אאאא
א
:
אאאאאאאאאאאא
،א200kJ/kgאאא420kJ/kg
אאאאאאK100kJ/kg
אW
q − w = ∆u
q −100 = (200 − 420)
q = −120kJ
/ kg
- ١٧٩ -
120kJ / kg אאאאאא

אאא
אאא
١٦٢
אאאא
א
W
K100 kPa300 Kאאא0.2 kgE١٩ J٤FFא
אאאKא5 kJpaddle wheelאאאא
אאאאאאFK Kאc v E0.7165 kJ/kg
א
א
א
W
E٢١٤F
- ١٨٠ -
אW
WאאאE٢١ J٤F
Q − W
= ∆U
אאאאא‎0K Q =
−
W
= ∆U
∴ − ( −5
kJ )
= ∆U
K5 kJאאאא
W
∆U
= + 5
KאאאU 1 U 2
∆U = mcv ( T 2
−T1)
5 = 0.2 × 0.7165 × ( T − 2
300)
∴T = 334.
89 K = 61.
89 ° C
2
אא

אאא
אאא
١٦٢
אאאא
א
E٩٤F
אK95 ˚C15 ˚C1200 Wאא 1.2kg
،4.18 kJ/kg ˚Cאאא 0.7 kJ/kg ˚Cאא0.5kgא
אאFKאאאא א
אKE אאא אאאאא
K
אW
EאHאאאFWאאאאאא
∴Q
Q
Q − W
= ∆U
Q = ∆U sys
= ( mc
= ∆ U w
+ ∆U teapot
v
∆ T )
w
+ ( mcv∆T
)
teapot
Wא
Kאאא
Q = 1.2 × 4.18 × ( 95 − 15 ) + 0.5 × 0.7 × ( 95 − 15 ) = 429.3 kJ
W429.3 kJE1.2 kJ/secF1.2 kWאאא
429.
3 kJ
t =
= 358 sec ≈ 6 min
1.
2kJ
sec
Wאאאאאאאא
Q = ∆U
sys
= 1.2 × 4.18 × ( 95 − 15 ) = 401.28 kJ
401.
28 kJ
t =
= 334.
4 sec = 5.
57 min
1.
2kJ
sec
- ١٨١ -

אאא
אאא
١٦٢
אאאא
א
אאאאאאW
אKאאאאאא
K
אאאא
אאאאא
KאE٢٢ J٤FאKא
א K(2)א (1)אאאאא
א K
א
א
א אאאא
אאאאאK
2
c 1
2
אאאW
Ku 1 אאא •
אאא
KZ 1 gאאאא
vFKpאאp 1 v 1 א א
Eא
אאאאFKQא
(1)
Q
KE
•
•
•
•
א
Z 1
Z 2
W
(2)
datum
אאE٢٢٤F
א
- ١٨٢ -

אאא
אאא
١٦٢
אאאא
א
2
c 2
2
אאאW
Ku 2 אאא •
אאא
KZ 2 gאאאא
pאאvFKp 2 v 2 אא
Eא
אWאאאK
•
•
•
•
Wאאאאאא
אאאאאא
2
2
⎛ c1
⎞
⎛ c2
⎞
m &
⎜u1 + + z1g
+ p1v1
+ − =
2
2 2 2
(4 −14)
2
⎟ Q W m&
⎜u
+ + z g + p v
2
⎟
⎝
⎠
⎝
⎠
אאאאא א
אאK
אא Kאאא אאא
h
= u + pv
אאאאWK
=
( 4 − 15)
אא،אאh
Wאא
2
2
⎛ c1
⎞
⎛ c2
⎞
m &
⎜h1 + + z1g
+ − =
2
2
(4 −16)
2
⎟ Q W m&
⎜h
+ + z g
2
⎟
⎝
⎠
⎝
⎠
א א K280kPaאא E٢٠ J٤F
אא،6m א אאאKאא
אאאFKא KE1000kg/m 3
- ١٨٣ -

אאא
אאא
١٦٢
אאאא
א
p 2
z 1
z 2
6m
W
p 1
E٢٣ J٤F
א
KאQאאאא
אאKאאאאא
אאא‎4-16) (
⎛
m &
⎜u1
⎝
2
2
c1
⎞
⎛ c2
+ + z +
⎟ + − =
⎜
1g
p1v1
Q W m&
u2
+ + z2
g + p2v2
2
⎠
⎝ 2
p v
1
1
− w
− w
− w
Wאאאאא
+ z g − w
1
= p v
2
2
∴v
=
p
− p v
= p v
1
1
1
= v2
=
− p
ρ
2
2
+ z
g
+ z g − z g
2
2
1
אא
1
ρ
אאא
+ g( z − ) 1
2 1
z 2
280 × 1000
= + 9.81×
6
1000
w = − 338.
86 J
kg
Kאאאאאא
⎞
⎟
⎠
- ١٨٤ -

אאא
אאא
١٦٢
אאאא
א
Wאאאא
Wא
אFאאWEאאאאאאאא
دخول الماء
KE٢٥ J٤FE٢٤ J٤F
Wאאאאא
K١
خروج الماء
אE٢٤ J٤F
m&
⎛
⎜h
⎝
אE٢٥٤Fאא
2
2
c ⎞
⎛
1
c2
+ + z g
⎟ + Q − W = m&
⎜
1
w
w
hw2
+ + z g
2 ⎠
⎝ 2
w w1
2
- ١٨٥ -
⎞
⎟
⎠
W
אא אא
אאא

אאא
אאא
١٦٢
אאאא
א
Q
Q
w w
( hw2 − hw
1
= m&
a a
( ha2 − ha
1
= m&
)
)
Wאא
אאאאאQ a אאאאאאQ w
m&
Q
= −
a
Q w
( hw2 − hw
1
) = m&
a
( ha
1
− ha
w 2
)
אאא
אאEvaporator Condenser &
אא E٢٦ אאאא‎٤F
אאאאאK
אאאא
⎛
&
⎜h
⎝
2
2
c1
⎞
⎛ c2
+ + z g
⎟ + Q − W = m&
1
⎜h2
+ + z g
2 ⎠
⎝ 2
m
1
2
⎞
⎟
⎠
Wאאאאא
Q = m&
( h 2
− h1)
Kאאאאאא
Q out
= m & ( h − h ) ( 4 17 )
2 3
−
Q
in
= m&
( h − h ) ( 4 18 )
1 4
−
Wא
Wא
- ١٨٦ -

אאא
אאא
١٦٢
אאאא
א
Q out
3
2
W
Q in
4 1
E٢٦ J٤F
אאאאאאאאאא
אאאא،417 kJ/kgאאR-134aא
المكثف Q
K241.63 kJ/kg
אW
h 2
h 1
E٢٧ J٤F
WאאאE٢٧ J٤F
Wאאאא
Q
m&
= ( h
− h
)
= 241.
63 − 417
2 1
= −
175.
37 kJ
kg
Kאאאא
- ١٨٧ -

אאא
אאא
١٦٢
אאאא
א
h 1
h 2
Q
E٢٨ J٤F
אאאאאאאאא،E٢٨٤Fא
אאR-134aאאkJ/kg אאאא،256
396 kJ/kg
אW
Wאאא
Wאאאא
Q
= ( h
m&
2
−
Q
= 396 − 256 = 140 kJ
m&
kg
h
1
)
אאאW Heat Exchanger
KE٢٩ J٤Fאאא
אFאאאא
QΙ
= m&
Ι
( hΙ2 − hΙ
1
)
WEאא
א
E٢٩٤F
- ١٨٨ -

אאא
אאא
١٦٢
אאאא
א
QΠ
= m&
Π
( hΠ2 − hΠ1
)
Wא
Kאאאאאאאאא
Q
Ι
= −Q
Π
W
אTurbineW
אאK אאאאא
Fאאא אאאאא
∴ − w
א
= h 2
− h 1
WE٣٠ J٤
h 1
h 2
E٣٠ J٤F
W
אאאאh 2 h 1
∴w
= h 1
− h 2
- ١٨٩ -

אאא
אאא
١٦٢
אאאא
א
אCompressorW
אאא KאE٣١ J٤Fא
אאאאאאאאאW
w = −(
h2 − h1
)
h 2
W
h 1
E٣١ J٤F
Kאאאאא
אPumpW
אאאאאE٣٢ J٤F
W
w = − ( h − 2
h1
)
Kאאאא
h 2
h 1
W
א
E٣٢ J٤F
- ١٩٠ -

אאא
אאא
١٦٢
אאאא
א
Wאא
NozzleWאאא J
KE٣٣ J٤Fאאא
Wאאאאאאא
∆c
q − w = ∆h
+
2
2
h
2
− h
1
2
c2
= − (
2
2
c1
− )
2
2
c2
2
=
2
c1
2
+ ( h − h
1
2
)
( 4 −19
)
خروج المائع
دخول المائع
1 2
E٣٣ J٤F
א J
אאא א
אאא KE٣٤ J٤F
Kאא
1 2
خروج
دخول
منحنى السرعة
منحنى الضغط
انخفاض الضغط
אE٣٤ J٤F
- ١٩١ -

אאא
אאא
١٦٢
אאאא
א
∴
q − w = h
2
1
Wאאא
c
− h +
2
2
− c
2
2
1
אאא
h = h ( 4 20 )
2 1
−
Kאא
Kאא100 kJ
א
אא
∴h
= h1
2
=
100 kJ
- ١٩٢ -

אאא
אאא
١٦٢
אאאא
א
אא
אאאא
The Second Law Of Thermodynamics
אאאאא
W
אאאאאאא אאא
אאאKאאאאאאאא
אKאאא
אאא אאאא אא
אא אא
א
אאאאאאאאK
אאאאא אאאאאא
אאאא אKאא
Kאאאאאא،
אאא
אא
א Kאא
אאאאאK אא
Kא אא אא، אא
א
20% אאאאא
Kאאאאא80%
א אאאאאא
אאא،אאא
אKאאא،אאאא
K
Wאאא
K?אאא? •
- ١٩٣ -

אאא
אאא
١٦٢
אאאא
א
אא?
K?
אא א אא
•
Kאאא
א Reversibility
Kאאאאאא
אאאאא
אאאאJ٤F KE٣٥
إتجاه الحرآة
Q out
W in
الحالة الأولى
W f
L 2
L 1
W f
Q in
W out
الحالة الثانية
إتجاه الحرآة
شكل (٤-٢٩)
الانعكاسية
אאאWאא
אאאאKW in
אאאאא אאKQ out
א אאא אאא
אאאאאאאF W(W f
W = Q + W
in
out
f
- ١٩٤ -

אאא
אאא
١٦٢
אאאא
א
Q in אאאאא אWאא
אאאאKאאW
Wאא،אא
Wאאאאאאאא
Q = W + W
in
in
- ١٩٥ -
out
out
W = W +
2W
f
f
WאQ out Q in
אאאאW f אא
אא
אאאא
Kאא
Kirreversible
אאאאא
א، אאאKאאא
אאKאאאא
א אאאאאא
Kאאאאאא
40 אאאא50 kJאא
אאאאאאאאאKkJ
אK
א
Wאאאאאאא
QQ = W out
+ W f
∴W f
= 50 − 40 = 10
Wאאאא،א50 kJ10 kJ
kJ

אאא
אאא
١٦٢
אאאא
א
η =
40
50
= 0.
8
אא אאאאא
Kאאאאאאאאא
אאאאאא אאאא
אאאאאא אא Kאא
אאאא Kאאאא
KאKא
אW
אKאאאאאאאאא
אאאאאא אא
2
∫
1
אK
Wאאאאאא
2
dQ
ds ≥ ∫
( 4 − 21)
T
1
dQא
אאאאdsאא
א> אאא=Kאאאאא
Kאאא
(dQ=0)אאאאא(4-21)א
אאאאאFאEאאא
אJ٤F KE٣٦
ds = 0(4-21)W1-2אא
ds > 0(4-22)W1-2 ' אא
- ١٩٦ -

אאא
אאא
١٦٢
אאאא
א
T
2
إجراءإنعكاسي
p=c
'
2
إجراءلاإنعكاسي
1
אאאאE٣٦ J٤F
אאאאאא
א
אאאאאאאאאאKא
η
isent
W
=
W
- ١٩٧ -
isent
actual
p=c
א Wאη isent
KאאW actual אאW isent
η
isent
h
=
h
2
'
2
− h
− h
אאאאא
1
1
א
א
אא Kאא
Kאאאאא
אאא Heat Engines
אאאאאאא
אא Kאאא
א Fאא
א SinkאאאאESource
אא אאאא K
Kאאא
E٣١ J٤Fאאאאא K
W

אאא
אאא
١٦٢
אאאא
א
، EאFא
1-2אאאאא
3אאK2-3אא
3
אK1 אא אאאאא
אאK1אאא
א אאאKE٣٧ J٤Fא
Kאאאאאא،
אE٣٧ J٤F
אאQ H אא אא E٣٨ J٤Fא
אא WאאאQ L Kאאאאא
אאאאאאאאאא
∑
Q
= ∑W
אאK
KQ L אאאQ H אאאאא
Q
H
− Q
L
= W
( 4 − 23)
- ١٩٨ -

אאא
אאא
١٦٢
אאאא
א
א
T H
Q H
W
Q L
T L
א
אE٣٨ J٤F
אאא،אאאא
Wη th אאאK
QL
η
th
= 1 −
( 4 − 25 )
Q
H
W
η
th
=
( 4 − 24 )
Q
H
η
th
QH
− Q
=
Q
H
L
Wא
Kאאאאאאא(4-25)א
J٤FאEsteam power plant)אאאאאא
KאאKאE٣٩
אQ L אQ H אKאאאEFא
אאא אא KאW
K
- ١٩٩ -

אאא
אאא
١٦٢
אאאא
א
البيئة المحيطة
الشغل W
Q H
النظام
system
الحدود
boundaries
الحرارة المزالة
אאאE٣٩ J٤F
Q L
W
אאא א K800 kJ/kg 1600 kJ/kgאא
א
T H
Kאא
Q H
= ?
W = 800 kJ/kg
Q L
= 1600
T L
א
E٤٠ J٤F
Wא
Wאאאאא،E٤٠ J٤Fא
QH − QL
= W
Q 1600 800 2400 kJ
H
= + =
kg
Wאאאאא
- ٢٠٠ -

אאא
אאא
١٦٢
אאאא
א
η
th
=
W
Q
800
ηth = = 0.
3333 = 33.
33 %
2400
H
אאאאRefrigeratorW The Heat Pump & The
אא،אאאאאא
א Q H
א T L
א Q L
KאW T H
אE٤١ J٤F
אאאא
W = Q H
− Q L
Coefficient Of אאאאאא
Q L אאא אאאאאאKPerformance(COP).
אא
QL
QL
1
COPREF = = =
> 1 ( 4 − 26 )
W QH
− QL
⎛QH
⎞
⎜ − 1
Q ⎟
⎝ L ⎠
Wאאאא،
Wא
- ٢٠١ -

אאא
אאא
١٦٢
אאאא
א
אאאא Qאא H אאא
QH
QH
1
COPHP = = =
> 1 ( 4 − 27 )
W QH
− QL
1−
⎛QL
⎞
⎜ Q ⎟
⎝ H ⎠
אאW
Wאאאאאאא
COPHP − COPREF
= 1 ( 4 − 28)
W
200 kJ/kgאאאאE٤٢ J٤Fא
אא Kאאא 600 kJ/kgאאאא
Wאאא
K •
Kא •
E٤٢ J٤F
אW
אאאאאאאא (Q A )אאא
WE٤٢ J٤Fא
W = Q L
− Q H
− 200 = Q − 600
L
Wאאא
- ٢٠٢ -

אאא
אאא
١٦٢
אאאא
א
∴Q L
= 400 kJ
kg
QL
COPREF =
W
400
COP REF
= = 2
200
COP
HP
=
QR
W
600
COP HP
= = 3
200
Wאא
Wאאאא
אאאאאאא K١ +
אאאאCycle:EF The Carnot
אאאאאאאא
אאאא אאא،אא
אאא א
K
WאאאאT-sאE٤٣ J٤F
• אא Kאאא1-2
•
•
•
אא2-3אK
אא3-4אאאאK
אא4-1אאK
T
T H
1 2
T L
4
s 1
s 2
אE٤٣ J٤F
3
s
- ٢٠٣ -

אאא
אאא
١٦٢
אאאא
א
η
th
Wאאא
QL
= 1 − (4 − 29)
Q
2
H
WאאE٢١ J٤F
2
∫ ds = ∫
dQ
T
1 1
Wאאאאאא
2
Q = ∫T
ds = T ( s2
− s1
) ( 4 − 30 )
1
QH
= TH
( s2
− s1
)
Q
L=
TL(
s1
− s2
)
W
Wאאאא
QL
TL(
s2
− s1
) TL
η
c
= 1 − = 1 −
= 1 −
( 4 − 31)
Q T ( s − s ) T
H
W = η
c
QH
( 4 − 32 )
H
2
1
H
Wאאא
אאאאFאE
WאאאאאאE٤٤ J٤Fא
• אא Kאאא1-2
•
•
•
אא2-3אאK
אא3-4אאאאK
אא4-1אK
- ٢٠٤ -

אאא
אאא
١٦٢
אאאא
א
T
T H
4
3
T L
1 2
s 1
s 2
אE٤٤ J٤F
s
WאאWQ L Q H
QL
= TL(
s2
− s1
)
Q H
= TH
( s1
− s2
)
אאאאאאאאW
∑
∑
Q = W
W = QH
+ QL
= −( TH
− TL
)( s2
− s1
)
Wאאאאא
QL
COPREF =
( 4 − 33 )
W
TL(
s2
− s1
) TL
COPREF =
=
( 4 − 34 )
(T −T
)( s − s ) T − T
H
L
2
1
H
L
אא،א
Wאאאאאא
QH
COPHP =
( 4 − 35 )
W
TH
( s2
− s1
) TH
COPHP =
=
( 4 − 36 )
(T −T
)( s − s ) T − T
H
L
2
1
H
L
- ٢٠٥ -

אאא
אאא
١٦٢
אאאא
א
Kאאא،40 o C, -10 o Cאא
COP
REF
TL
=
T − T
H
L
א
−10
+ 273
COP REF
= = 5.
26
40 + 10
- ٢٠٦ -

אאא
אאא
١٦٢
אאאא
א
אא
אאא
אא،א ،אא،אאא،
אאאW
WEF
אK
אא7°Cא 27°Cא EF
אא אאאא8m 3 K10kgא
KR = 320 J/kg Kאאאא
אאאW
2 א200 kPaאאאא، isothermalאא
אאאאא K4 m 3 אאאאאאאא،m 3
א2.3 MN/m 2
V
W = ∫ pdV = p1V1
(ln
V
2
1
)
אW
אאאW
אא
K8 cmאאאא،7.5 cmא
אאאאW
אאאאאאאא
k=1.4אK
- ٢٠٧ -

אאא
אאא
١٦٢
אאאא
א
p(kPa)
620
1
pv k = c
2
0.15 1.0
v(m3)
אאאW
אאאKאאאאאEF
K
אאאא
אאאEF
אkJ/kg Kאאאאאא،50
אאאW
אK350 m/sec2300 kJ/kgא،אא
אאאkJ/kg 70، m/sec160 א אאא
אאאK
אאא Kא
אאאW
א(nozzle)
،2790kJ/kgאא אאK60 m/sec3025kJ/kgא
אאאKאאאK
אאאאא אא0.1m 2
אkg‏/‏ K0.19 m 3
- ٢٠٨ -

אאא
אאא
١٦٢
אאאא
א
אאאW
.40%
אא אאאאא
אאאאkPa אאאאא620 אא0.1 m 3
אkJ/kg א،50 אאאאאFKאאא
KE
T
T H
1 2
T L
4
3
s 1
s 2
s
אאאW
Kאאאא،אאאא
- ٢٠٩ -

אאא
אאא
١٦٢
אאאא
א
אאא
א Kאאאא
Wאאאא
א
אאאאאKא
אK
אאאאא Kאאאא
K
אאאאאאאK
Kא× אא K٤
EF
WאאאאKאאא
V
T
pV = mRT
EF
K١
K٢
K٣
Kא
W
E١Fאא א E٢F א א
8 V2
=
(27 + 273) (7 + 273)
300 ×V2 = 8×
280
8×
280
∴V 2
= = 7. 466 m
300
ثابت =
V
⇒
T
W = ∫ pdV = p( v 2
− v1)
1
1
V
=
T
2
2
3
אאE٢F
Wא
- ٢١٠ -

אאא
אאא
١٦٢
אאאא
א
W = 120 kPa × (7.466 − 8) = − 120000×
0.534 = − 64080 J = − 64. 08 kJ
Kאאאאא
Wאאאא
WאאאKאאאא
pV = mRT
pV
ثابت = ∴ p =
1V1
p2V2
W = p V ×
V2
1 1
ln V
1
4
W = 200 × 2 × ln = 277. 26 kJ
2
אאא
Wא
Wאא
אאאא
Wאאאא
אאאאאאאW
W
= p( V ) 2
אא،אאאאK − V1
אא8 cmאא
אאW
π 2
π
2
3
V2 −V1
= d ( 0 − 0.08) = − × (0.075) × 0.08 = − 0. 00035343 m
4
4
אאאאא
אאאK
Wא
W = p( V ) 2
− V1
6
W = 2.3∗10
× ( −0.00035343)
= − 812. 9 J
- ٢١١ -

אאא
אאא
١٦٢
אאאא
א
k
Wאאאאא
אאאאאאאW
p1V1
− p2V2
W =
k − 1
1.5
Kp 2 אאא
⎛ V1
⎞ ⎛ 0.15⎞
p2 = p1
⎜ = 620 × ⎜ ⎟ = 620 × 0.0581 = 36.02 kPa
V
⎟
⎝ 2 ⎠ ⎝ 1.0 ⎠
620 × 0.15 − 36.02 × 1.0 56.98
∴W =
= ≈114 kJ
1.5 − 1
0.5
Wאאאא
אאאאאEF
Kאאאאאאאא
אאאא אאאאא
q − w = ∆u
אאW
אאאאאאא
⋅
2
2
c
⋅
1
c2
m h + + z1g)
+ Q −W
= m(
h2
+ + z
2
2
(
1 2
g
אאאאא
Wאאא
אאא
)
KאEF
אKאאאאKאא
Q
q − w = ∆u
אאK
2
1
W
- ٢١٢ -

אאא
אאא
١٦٢
אאאא
א
50 − w = 0
∴w = 50 kJ
kg
Wאאאא
אאאאK
אKא Kאאאאא
⋅
2
2
c
⋅
1
c2
m h + + z1g)
+ Q −W
= m(
h2
+ + z
2
2
(
1 2
g
Kא
)
Q out
بخار
المكثف
بخار متكثف
c 1
אאאאאאאא
Wאאc 2 א
2
2
c1
c2
h
1
+ + Q = h2
+
2
2
2
(350)
(70)
2300 + + Q = 160 +
2
2
2300 + 61.250 + Q = 160 + 2.450
∴Q = − 2198.8 kJ / kg
Wאאא
2
Kאאאא
- ٢١٣ -

אאא
אאא
١٦٢
אאאא
א
Wאאאא
אאאאא
אאאאאK
2
2
c1
c2
h 1
+ = h2
+
2 2
2
2
J 60 J
J c2
3025 × 1000( ) + ( ) = 2790 × 1000( ) +
kg 2 kg
kg 2
3025000 + 1800 − 2790000 =
2
c2
2
= 236800
2
c2
2
∴c
=
236800 × 2 =
688 m
sec
W m& א
WאאEאאFא m& א
A×
c
m&
= ρ × A×
c =
v
0.1×
688
m & = = 31.6
kg
0.19
sec
- ٢١٤ -

אאא
אאא
١٦٢
אאאא
א
Wאאאא
WאאאT 1
אאא
p ×
1
× v1
= R T1
3
p1
× v1
620×
10 × 0.1
∴T1 = =
= 216 K
R 287
WאאאT L
אאא
η
therm
T
= 1−
T
L
H
TL
0.4
= 1−
216
∴T L
= 129. 6
K
COP
TL
=
T − T
129.6
=
216 − 129.6
ref
=
H L
1.5
Wאאאא
- ٢١٥ -

٥
אאאא

אא
١٦٢
אאאא
א
אאW
אאWאאאאאאאאא
Kאאאאאאאא
אאW
Wאאא
Kאאאאאאאא
אאאאאK
אאאאאאאאא
Kא
Khאאא
Kאאאאא
Kאאאאאא
Kאאאאא
אאאאאאא
אאאאאK
Kאאאאא
KאאאאK١٠
אאאאאאK١١
Kא
KאאאאאK١٢
KאאאאאאאאK١٣
K١
K٢
K٣
K٤
K٥
K٦
K٧
K٨
K٩
Wאאא
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- ٢١٦ -

אא
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- ٢١٧ -

אא
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- ٢١٨ -

אא
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k A ( T
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thermal conductivityאאא،kאאKa
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∑ R
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- ٢١٩ -

אא
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אאאא
א
W
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K∆V = V1-V2אאא
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A = 1.5 * 2 = 3 m 2
אW،
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אאאאאK
•
•
•
- ٢٢٠ -

אא
١٦٢
אאאא
א
k A ∆T
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q = =
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m
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k 0.04 W
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∴( R + R ) = 1. 359 ° C
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W
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- ٢٢١ -

אא
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אאאא
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א9cmא 5cm
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אא
١٦٢
אאאא
א
א 1cm5cmא(k = 54 W/m C)א
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K٥
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r
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4
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R
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0.5108256
339.292
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- ٢٢٣ -

אא
١٦٢
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א
R
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R
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0.247562
0.238761
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1.3563 + 1.03686 = 2.39467
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315 − 38
q = = = 115. 65 W
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אא
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אאאK
KKאאא
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- ٢٢٥ -

אא
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- ٢٢٧ -

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- ٢٣٠ -

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- ٢٣١ -

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- ٢٣٢ -

אא
١٦٢
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א
حديد زهر
q
T 3
T 2 T 1
h i
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k 1
r 3
r 2
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h o
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T 1
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אא
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r cr - r o = 5.67 - 2.5 =3.17 cm
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( T − T )
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r
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1
+
2πkL
2πr
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o
- ٢٣٣ -

אא
١٦٢
אאאא
א
(200 − 20)
q =
= 105. 7 W
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1
m
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3.0
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q = 3 .0 × 2π
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א،אאאאא3.17 cm
אאאK
- ٢٣٤ -

אא
١٦٢
אאאא
א
אאא אא
- ٢٣٥ -
W
אאאאKq
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15 W/m 2 10000 W/m 2 ˚Cאאאא אאא
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- ٢٣٦ -

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110
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א 0.2
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Kאאאאאאאאאא
١١E٩ J٥F
- ٢٣٧ -

אא
١٦٢
אאאא
א
אא–אא
אאWאא
- ٢٣٨ -
Wאא
אאKאאאKאאאא
אאאאKאאאאKא
אKאאאאK
W
א015m 3 אאא012m 3 א
אאK1.15 kg/m 3 אאאא0.2m 3
2750 אאאאאאFKאאא
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ρ
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Wאא
Wאאאאאאא
m = ρ ×V
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m w
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m a
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0.53 = 0. 61 kg
Wאא
Wא
Wא
Wאא

אא
١٦٢
אאאא
א
v
t
ρ
m t
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755
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V =
t
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5
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100 1/secאאאאאאאא
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τ
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- ٢٣٩ -

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א
2.87*10 - א0.85EאאFאאא
K
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- ٢٤٠ -
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u(
r)
= u
⎡
⎢
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−
⎜
⎝
r
r
1
⎞
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1.031 bar
1.031 bar
1.031 bar
אאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
אא
אא
אאאאאא
אא
•
K١
K٢
K٣
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•
K١
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•
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אא
١٦٢
אאאא
א
אאWאא
Wאא
•
אאאאאא •
אאאK
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p = ρ × g × h
אאאאHאאK
Kאאא
•
•
•
- ٢٤١ -

אא
١٦٢
אאאא
א
W
6000NאאאK7.5 cmא
p =
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= × r = × D =
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4
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K١
אW
Wאאא
F
A
A π
× =
Wאא
2
2
( 0.075) 0.004418 m
6000
∴ p =
= 1358080 Pa ≈ 1358 kPa
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1206 (R-134a)7.5 mאאאאא
K1 MPaאאאאkg/m3
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R-134a
٣אE١٠٥F
אW
אאאאאאאאאאאאא
= + = + ( ρ × ×
p ptop
p134 a
ptop
g h)
134a
p = 1000000 + (1206 × 9.81×
7.5) = 1088704 Pa = 1088. 7 kPa
Wאא
Kאאאp
- ٢٤٢ -

אא
١٦٢
אאאא
א
.95 kPaEאFאא150 kPa א K٣
אאK
אW
אאאאHאא
pabs = p
g
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אאאאkPa אK101.325 . 999kg/m 3
p = ρ × g × h
101.325 = 999 × 9. 81× h
3
101.325 ∗10
∴h =
= 10. 34 m
999 × 9.81
Kאאאא
K٤
אW
E13600 kg/m 3 אFאאא
p = ρ × g × h
3
101.325 × 10 = 13600 × 9. 81× h
- ٢٤٣ -

אא
١٦٢
אאאא
א
אK2kNא10cmא
אאאא K500m
אאK
200m
1000kg/m 3 א
750 kg/m 3 אאא K٣
אאאאKא2mא3mאאK10 3 kg/m 3
K1 barאאאKאאאא
K١
K٢
2m
نفط
3m
ماء
٣אE١١٥F
Kא 5m/sec15mmא
K20 Cאא 2barEFאאא
אאK30Cאא
אאbarEF 1.4
א1.03barאאאK אא
אK187.8R
אאא2000m Kא א
א‏(‏ K(1002kg/m 2
אאאאאאFאא12mE
א K101KN /m 2 אאאא10 3 kg/m 3 אKא
אאאbar K600kg/m 3 1
K٤
K٥
K٦
- ٢٤٤ -

אא
١٦٢
אאאא
א
800kg/mא 3 8mאאא
13.6אאא400mmא
7.9kg/m 2 (specific weight)אאא 400mm א
אאbar 0.97.
אאאאW
•
•
K٧
K٨
- ٢٤٥ -

אא
١٦٢
אאאא
א
אאWאאא
Wאא
אWאאאאא •
Kא
אאאאאאאא
אאאK
Kאאאאאאא
ρ1 × A
1
× v1
= ρ
2
× A2
× v2
WאאEFאא
A ×
1
× v1
= A2
v2
אאאאאאא
אK
אא
Kא
•
•
•
•
•
W
אא30 Cא1.5 barאא
א،400mm*300mmAאmmB 250،
Bאאאא،BA0.2 barאאאא
AאאR = 287J/kg Kאאאאא
K18 m/sec
K١
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A
B
١אE١٢٥F
- ٢٤٦ -

אא
١٦٢
אאאא
א
אאאא
EBFאEAFאKאאא
ρ
p1
ρ1
=
RT1
5
1.5 × 10
ρ1 =
= 1. 725
kg
287 × (30 + 273)
m
p
( 1.
5 − 0.
2 ) × 10
5
2
2
= =
= 1.
495
RT2
287 × ( 30 + 273 )
Kאאאא
WE١FאAא
3
(٢)אBא
kg
m
E٢F( B)אאאאא
ρ1 × A
1
× v1
= ρ
2
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× v2
אאאא אא،v 2
ρ1
× A1
× v1
1.725 × (0.4 × 0.3) × 18
v
2
=
=
= 39.87 m
2
ρ × A 1.495 × (0.25)
sec
2
2
3
Wאא
אאאאאאאKא
אאאK
K٢
1
4 m
d = 100 mm
2
אאE١٣٥F
- ٢٤٧ -

אא
١٦٢
אאאא
א
2
p1
v1
+
ρ 2
אW
Kאאאא
+ z
1
g
2
p2
v2
= +
ρ 2
E١FאאKאאE٢FE١Fא
אE٢FאאאאK
⋅
v
2
2
2
= z g − z g
1
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z
1
− z
2
+ z
)
2
g
אאאW
Wאא،4m
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= 2×
g × ( z1
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v
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2 × 9.
81×
4
⋅
Q = A 2
× v 2
= 8.
86
m
sec
π 2
π 2
Q = ( d ) × v = (0.1) × 8.86 = 0.0695m
4
2
2
4
( z )
1
− z2
WQאא
3
sec
- ٢٤٨ -

אא
١٦٢
אאאא
א
א0.150.3mאא1800lit/min
KאאאאK
0.5m/sec12mmאאאא
K١
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אאאאK3mm
37 Cא3.09 bar 0.15mאא K٣
אא4m/secאאאאK
K4m/secאאא100mm(1)א
א(2)אmm K50 א (2)אא א
KאאKאאא
אא K 0.1m AB0.015m 3 אK٥
א0.05mBE0.025mBD0.025mBCBא
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אאאאאK4 m/sBDא
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K0.056m 3 930 kg/m 3 015 mAאC
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אKC
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- ٢٤٩ -

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אאאא
א
Kא hאא Aא
Q = A 2gh
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400 kPa3m/sec0.5 m800 kg/m 3
K30 mא0.15 mא
K٧
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אאmK EאאאFK3.5
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z 2
- ٢٥٠ -

אא
١٦٢
אאאא
א
אאאWאאאא
Wאאא
אאא
אאאFאאאאאKא
∆p
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L
D
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2
v
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WאEא
אאKאא
f
64
=
Re
Wאא
Kאאא
K١
K٢
K٣
W
80 Cא6 L/secאא J١
801 80 C אאK40m52.5 mm
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⋅
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v = =
= 4.62 m
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2
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4
ρ × v × D 801×
4.62×
0.0525
Re = =
= 43561 〉 40000
−3 µ
4.46×
10
ε
D
=
אW
W
Kאא
אאmm EאאF0.046
0.000046
0.0525
= 0.000876
אא
fאא
f = 0.025
- ٢٥١ -

אא
١٦٢
אאאא
א
L
= f ×
D
2
v
Wאא
∆p
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40 (4.62)
∆p = 0.025×
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0.0525 2
K60mmאא42 mאא
אא‎90˚ 45˚א אKא
א0.02אאL/min אא،480
אFKא KE1000kg/m 3
K٢
אW
Wאאאא
L = 42 + 8×
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0.79 = 71. 94 m
⋅
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= A×
v
E0.001m 3 אFWאא
v
=
Q
A
480×
0.001
=
π
60×
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4
L
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×
2
v
2
2
)
× ρ
= 2.6 m
sec
אא
2
71.94 2.6
∆p = 0.02×
× × 1000 = 77333 Pa = 77. 333 kPa
0.06265 2
אK0.5m 3 /min150mm
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Kאא •
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- ٢٥٢ -
K١
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א K870 kg/m 3
EאאFWאאא
K٣

אא
١٦٢
אאאא
א
150
K0.0001אא50000
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K60mmאאא42mאאא
45˚א490˚א8א
א 0.02 fאא Kא6
Kאאאאא480 l/minא
•
•
•
K٤
- ٢٥٣ -

אא
١٦٢
אאאא
א
אאWאאאE١٢F
אאW
Wאא
אאאא
אאKאKאאא
אאאK
אK
אKאאאאKאאאא
אאאאאאאא
K
אאאאאאאK
אאאאאאאא
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אאאK
K١
K٢
K٣
K٤
K٥
K٦
W
אא 7°Cא 27°Cא
אאאאא
אא 8m 3
KR = 320 J/kg KאאאאK10kg
K١
אW
WאאאאKאאא
V
T
pV = mRT
= Cons tan t ⇒
W،א
E١FאאאE٢Fאא
V
T
1
1
V
=
T
2
2
אאE٢F
- ٢٥٤ -

אא
١٦٢
אאאא
א
8
2
V
=
(27 + 273) (7 + 273)
300×V2 = 8×
280
8×
280
∴V 2
= = 7. 466 m
300
W = ∫ pdV = p( v 2
− v1)
W = 120 kPa × (7.466 − 8) = − 120000×
0.534 = − 64080 J = − 64. 08 kJ
3
Wא
Kאאאאא
1.549 m 3
0.178 m 3 אא200kPa
אאאKאאאאא،א
W = ∫ pdV = p( v 2
− v1)
3
W = 200 kPa × (1.549 − 0.178) m = 274. 2 kJ
K٢
אW
אW
Wאא
200 kPaאאאא،isothermalאא
אאK4 m 3 אאאאאאאא،2 m 3 א
V
W = ∫ pdV = p1V1
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2
1
)
אאאאW
K٣
- ٢٥٥ -

אא
١٦٢
אאאא
א
Kאאא،אא،אא،א،אא
אא2.3 MN/m 2 אא K٢
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אא50kJאאאא K٣
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אא5m 3 אא 520 Cאאא1kgאא K٤
אאא W10m 3
Kאא •
Kאאא •
•
R = 287 J/kg Kאאא
אאK
אא 10 m 3 إلى 5 m 3 אאאאאא K٥
אאbar Wא،5 kg3
Kאאא •
•
אאK
אא 0.15m 3 אאא K٦
K0.286 kJ/kg Kאא57Cאאאא0.42kg
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K0.286 kJ/kg Kאא15 barאא0.12 kgאא
אאאא אאאא
אkg barאא0.1 Cאא1.12 Kאא 97 KR=0.286 kJ/kg
אאאאא
אא
א א1.1bar , 0.1 m 3 אאא 0.005 m 3
א Kא k =1.4
K١
K٨
K٩
- ٢٥٦ -

אא
١٦٢
אאאא
א
אאאא0.73 kJ/kg K אאאא
K١٠
KאאK1.09 kJ/kg K
،א،א،אאא،א،אאW
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KאאאK15 Cא،12 bar80 kgאא K١٢
א 60Cאאאאאא
אאא
אFאאK ER=0.286 kJ/kg
4 m 3 אא 10 m 3 אא
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V i =0.01m 3 אאאא K١٧
אאאא אא
KאאKV 2 =0.02 m 3 אאp=140 kPa
Kאאאאא
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K4 m 3 2 m 3 אא300 K
אא א אאאא
אKK
K١١
K١٣
K١٤
K١٥
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K١٨
K١٩
K٢٠
- ٢٥٧ -

אא
١٦٢
אאאא
א
p(kPa)
620
1
pv k = c
2
0.15 1.0
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٢٠אE١٦٥F
Kאא
אאאKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
אאאאאא
אאאאא
אאאאא
אאאאא
אאאKKKKKKKKKKKKKKKKK
אאאאאא
אאאאא
אאאאא
K٢١
•
K١
K٢
K٣
K٤
•
K١
K٢
K٣
- ٢٥٨ -

אא
١٦٢
אאאא
א
אאWאאאא
Wאא
אאאאא
Kאאאאאאאא
אאאא אאאא
q − w = ∆u
Wאאא
אאאאאאא
⋅
2
2
c
⋅
1
c2
m h + + z1g)
+ Q −W
= m(
h2
+ + z
2
2
(
1 2
g
Wאאא
)
K١
K٢
K٣
W
אאאאאאא
Kאאאאאא،50 kJ/kgא
K١
אW
אKאאאאאאאא
אKאאאאKאא
Q
q − w = ∆u
אאK
2
1
W
אE١F
- ٢٥٩ -

אא
١٦٢
אאאא
א
50 − w = 0
∴w = 50 kJ kg
Kא22 kJ א 20 kJ אאאאא
אאאאאאK
K٢
אW
אאאאאK
KאאKKאאא
Q − W = ∆U
Q − ( −22)
=
20
∴Q = 42 kJ
אא
350 2300 kJ/kgא،אא
،70 m/sec160 kJ/kgאאאאKm/sec
אאאאאאאK
K٣
אW
אאKE٢٠٥F
אKאKאאאאא
⋅
2
2
c
⋅
1
c2
m h + + z1g)
+ Q −W
= m(
h2
+ + z
2
2
(
1 2
g
Kא
)
Q out
بخار
المكثف
بخار متكثف
אJ٥F ٣E١٧
- ٢٦٠ -

אא
١٦٢
אאאא
א
c 1 אאאאאאאא
Wאאc 2 א
2
2
c1
c2
h
1
+ + Q = h2
+
2
2
2
(350)
(70)
2300 + + Q = 160 +
2
2
2300 + 61.250 + Q = 160 + 2.450
∴Q = − 2198.8 kJ / kg
Wאאא
Kאאאא
650 kJ/kgאאא20 kg/minEF K٤
Kא200 m/sec300 m/secאאKאא360 kJ/kg
2
אאאאאK
אW
KאאאKאאאאאאאא
אאאKאאאאא
KאאאאKא
- ٢٦١ -

אא
١٦٢
אאאא
א
⋅
2
2
c
⋅
1
c2
m h + + z1g)
+ Q −W
= m(
h2
+ + z
2
2
(
1 2
g
20 (300)
(650 +
60 2
2
2
c1
c2
m & ( h1 + ) + Q = m & ( h2
+
2
2
2
2
20 (200) kg
) + Q = (360 + ) , ( ×
60 2 sec
231 .667 + Q = 126.667
)
Wאאא
)
Wאאא
Q 104 kW = − ∴
Kאאאא
kJ
kg
)
- ٢٦٢ -

אא
١٦٢
אאאא
א
אW אאKאאאא3750
Kאאאאא،
420 אאאאאאאאא
אאאאKא200 kJ/kg אkJ/kg
אאאאאאאאאkJ/kg K100
אאאאאאאאא
אC kJ/kgאאא1850 אאאK1090
Kאאאא0.73 kJ/kg K
אאK27 Cא5 barsאK300 Litersא
אאאC אאאK127
K0718 kJ/kg Kא
K١
K٢
K٣
K٤
- ٢٦٣ -

אא
١٦٢
אאאא
א
אאWאאאא
Wאא
אאאאאא
Kאא
א
η
W
Q
− Q
H L
th
= = = 1
QH
QH
COP
COP
REF
HP
QL
=
W
Q
=
W
H
Kא
Wאאאא
H
Q
−
Q
L
H
Wאאא
QL
=
Q − Q
L
Wאאאא
QH
=
Q − Q
Wאאא
η
W
Q
− Q
H L
L
th
= = = 1−
= 1
QH
QH
QH
H
Q
L
T
−
T
L
H
K١
K٢
K٣
K٤
K٥
E٤٥F
א،אאאאא אא 175 kJ/kg
אkJ/kg KאאאאאK144
Q out
3
2
W
Q in
4 1
- ٢٦٤ -

אא
١٦٢
אאאא
א
אW
אאאא،EFאא
COP
REF
QL
=
W
QL
=
Q − Q
H
L
אKאא
144 144
= = = 4.65
175 − 144 31
،EFאא
COP
HP
Q
=
W
H
QH
=
Q − Q
H
L
175 175
= = = 5.65
175 − 144 31
E٥ J٥F
אאK30%(shaft power)
136 hp
אאK35000kJ/kgאאא
kW
W =η
th
× QH
= 136 hp × 0.7355 = 100 kW
hp
W
η
th
=
Q
H
אK
אאא
∴Q
H
W
=
η
th
100
= = 333.4 kW
0.3
∴Q
⋅
L
m q
⋅
m
= Q
H
H
− W = 333.4 −100
= 244.3 kW
= Q
H
333.4
kW
=
= 0.0095
kg
35000 kJ
sec
kg
א
- ٢٦٥ -

אא
١٦٢
אאאא
א
E٦٥F
البيئة المحيطة
w out
Q in
النظام
system
الحدود
boundary
w in
Q out
Q in = 4000kW W out =1000 kW א،אאאאאא
KQ out = 3000kW
אW
W 1000
η = = = 0.
25 = %
thermal
Q 4000
25
H
- ٢٦٦ -

אא
١٦٢
אאאא
א
אאK300 Kא100 kPaאא
אא، 3.5א א
K١
(k=1.4)Kאאאא،80%
אא20 C200 CאE٣٧ J٤Fא
KQ L Q H א15 kWא
א .30% אא אאאאא K٣
אאא 500 kPaא אא אא
אא kJ/kgאאא 0.15 m 3 אאאא،45
EאאאFKאא
Kאאאא،אאאאא
172 kJ/kgאאאא، 20 C200 CאK٥
אאאאKאאאאאK
אאא
אאא
600 kJ/minQ L אQ H א120 C-30 Cאא
K٢
K٤
K٦
- ٢٦٧ -

אא
١٦٢
אאאא
א
אא
אא אא אא א
A
Area
2
m
א
c
C p
Velocity
Specific heat at constant pressure
m
sec
kJ
kg. k
א
אאא
C v
Specific heat at constant volume
kJ
kg ⋅ k
אאא
COP
Coefficient of performance
-
אא
d , D
Diameter
m
א
E
Total energy
kJ
אא
E b
Blackbody emissive Flux
2
W / m
אאא
אא
f
Friction Factor
-
א
F
Force
N
א
F ij
View factor
-
א
g
G
Gr
Gravitational acceleration
Incident radiation
Grashof number
m
sec
W
2
m
2
אא
אא
א
h
h
Enthalpy
Convection heat transfer coefficient
kJ
kg
W
m
2
⋅° C
א
אאא
k
Thermal conductivity
W
m ° C
אאא
L
m
Length; half thickness of a plane wall
Mass
m
kg
א‏،א
א

אא
١٦٢
אאאא
א
m&
Nu
Mass flow rate
Nusselt number
kg
sec
-
אא
p
perimeter
m
א
Ρ
pressure
kPa
א
Ρr
Prandtl number
-
א
Q
Total amount heat transfer
kJ
אא
q&
Heat flux
W
2
m
אאא
אאא
Q &
r
Volume flow rate
Radius
3
m
sec
m
אא
א
r
cr
Critical radius of insulation
m
אא
R
Gas constant
kJ
kg ⋅ K
אא
R
R u
Re
Thermal resistance
Universal gas constant
Reynolds number
° C
W
kJ
kmol ⋅ K
m
אאא
אאא
x
Thickness
m
א
t
Time
sec
א
T
Temperature
° C or K
אא
T i
Initial Temperature ,inside
Temperature
° C or K
،אאאא
אא
u
Internal energy, velocity
kJ
kg
m
s
אא
אא‏،א
U
Overall heat transfer coefficient
W
m
2
⋅° C
אאא
א
v
Specific volume ,velocity
m 3
kg
m
אא‏،א s
V
Total volume
3
m
א

אא
١٦٢
אאאא
א
W &
power
kW
א
α
ε
η fin
Absorptivity ; Thermal diffusivity,
Emissivity ;heat exchanger or fin
effectiveness
Fin efficiency
2
m
sec
-
-
א
א
א
µ
v
ρ
σ
Dynamic viscosity
Kinematic viscosity
Density
Stefan-Boltzmann constant
kg
m ⋅sec
m
kg
, Pa ⋅ sec
2
sec
3
m
-
אא
אא
א
τ
Transmissivity, Shear stress
א،א -
atm
Atmospheric
-
cyl
Cylinder
-
א
e
Electrical
-
i
Inlet
-
o
Outlet
-
rad
Radiation
-
א
s
Surface
-
א
surr
Surrounding Surface
-
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sys
System
-
w
wall
-
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∆
∞
Difference
Ambient conditions
-
-
א
אא

אא
١٦٢
אאאא
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1. Heat Transfer: A practical Approach- Yunus A. Cengel, McGraw-Hill
1998
2. Heat Transfer, J P Holman, 8 th edition – 1997.
3. Heat Transfer, Lindon C. Thomas,1992.
4. Principles of Refrigeration, Dossat,4 th ed. 1997.
5. Engineering Fluid Mechanics, Roberson-Crowe.1995.
6. Applied Thermodynamics, Eastop & McConkey, 5 th ed. 1996.
7. Classical Thermodynamics, Gordon Van Wylen, Richard Sonntag, 4 th ed
1994.
אאא
K،א،K،אאא
KאאK،אא
K١٩٨٢Kא،Kאאא
١٩٨٢KאK،אא
אאאא،אLKאKL،
אאאא،אJ K
אאJL، K١٩٩٢
K١
K٢
K٣
K٤
K٥
K٦
K٧

א
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אאאא
א
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..................................................................................................................................................................
..................................................................................................................................................................
אאWאאאא‎١.......................................................................................................................
אאWאאא ...................................................................................................................................٨
٨..........................................................................................................................................................
٩.................................................................................................. Modes Of Heat Transferאאא
- ١٠ - .................................
אאאאאאTransferW One-dimensional Steady State Heat
אאא .....................................................................................................................................١١
אאאאאאDimension ١١.................................... Steady State Conduction- One
١٥.................................................................................................. Thermal ConductivityWאא
١٦...........................................................................................................................Wאא
אאאאאא‎١٦...................................................................................................W
אאאאאwall ١٧.......................................................................A composite plane
אאאאאאcylinders ٢٠................................ Heat conduction through hollow
אאאאאאאCylinders: ٢٢........................................................Composite
אאא ........................................................................................................................................٢٦
- ٢٦ - ....................................................................................................................................................W
אאFאconvectionWE ٢٧...................................................................................................... Natural
אאFאE‏:‏ ................................................................................................ Forced convection - ٢٧ -
- ٢٧ - ............................................................................................Newton Law of Cooling
אאאאאאW‏..................................................................‏ - ٢٩ -
- ٣٢ - ..................................................................... WOverall heat transfer coefficientאאאא
- ٣٦ - .................................................................... WאאU אאאא
אאאInsulation .......................................................................................................... Thermal - ٣٩ -
אאThickness ٣٩........................................................................................ Insulation Critical
- ٤٣ - .................................................................................................................... אאא
אW ............................................................................................................................... - ٤٤ -
אאאW ................................................................................................................................ - ٤٥ -
אאאאאSurfacesW ٤٧.......................................................... Heat Transfer from Finned
אאאRadiation‏................................................................................................................‏ - ٥٣ -
- ٥٣ - ....................................................................................................................................................W
אאאאאRadiationW ..................................................................................Blackbody - ٥٤ -

א
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אאאא
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٥٤.............................................................................................Stefan Boltzman's Law
אW‏(‏ ٥٦..........................................................................................................................Emissivity ( ε
- ٦٠ - ................................................................................................................The View FactorWא
אאא٦١KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
٦١KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKTypes of Heat Exchangersאאאא
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אאאאא‏...........................................................................................................................‏ - ٨٠ -
- ٨٢ - ............................................................................................................... אאאאאא
אאWאא‏............................................................................................................................‏ - ٨٥ -
٨٥..........................................................................................................................................................
אאאא ...................................................................................................................................٨٦
א ٩٠....................................................................................................................................... Viscosity
٩١............................................................................................................................Wאאא
אאא ........................................................................................................................................٩٣
٩٣.........................................................................................................................................................W
אPressure ...........................................................................................................................................٩٣
٩٤................................................................................................................ Wאאאא
٩٥..............................................................................................................Pressure Head
אEF
אאאאW‏.........................................................................................................................-‏ - ١٠١
١٠٣........................................................................................................ Pressure Measurementא
אאManometersW ١٠٤................................................................................................................... The
אאmanometer ١٠٥....................................................................................................differential
אאmanometerW ١٠٦............................................................................................................inclined
אאא ......................................................................................................................................١٠٧
١٠٧......................................................................................................Types of Fluid Flowאאאא
١٠٧....................................................................................................................Fluids in Motion אא
١٠٨........................................................................................................................Rate of FlowWא
١١٠....................................................................................... Continuity EquationEאאFאא
١١٤.................................................................................... Energy of a liquid in motionאא
١١٤....................................................................................................................potential energyWא
١١٥................................................................................................................... Pressure Energyא
١١٦.......................................................................................................................kinetic energyWא
١١٧............................................................................................................Bernoulli Equation

א
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א
١١٩..............................................................................................................................
١٢٠..............................................................................................................................................Wא
١٢١..............................................................................................................................Pitot TubeW
א‎١٢٢........................................................................................................................Venturi-Meter
١٢٤......................................................................................................Orifice MeterWאא
١٢٦........................................................................................................................ אאאאא
١٢٦.......................................................................................................................................................W
אאW ..........................................................................................................................١٢٦
אאא‎١٢٧.......................................................................................................................W
١٢٩................................................................................................................... Moody Diagram
١٣٦.............................................................................. Pressure Drop in Fittingsאאא
אאrequirements: ١٣٩....................................................................... pumps and pumping
١٤٢....................................................................... Pressure Drop in Air Duct Flowאאא
١٤٢..............................................................................................................אאא
אא .........................................................................................................................................١٤٣
١٤٣...................................................................................................... WאEFאא
אאאא‎١٤٧.........................................................................................................................
אאאWאאא‎١٥٣..........................................................................................................................
١٥٤.......................................................................................................................................................W
١٥٥.........................................................................................................................
אreversibility .............................................................................................................................١٥٧
אא‎١٥٨..................................................................................................................................................
אאאאW .............................................................................................................................١٦١
אאאheatW ١٦٤...................................................................................................................... specific
אEnergy .........................................................................................................................................١٦٤
אא‎١٦٥.............................................................................................................................................heat
١٦٨....................................................................................................................... Wאאאאאא
אאאא .........................................................................................................................١٧٤
١٧٤........................................................................................................................................................
١٧٦....................................... First Law for a non-flow SystemWאאאא
אאאאאא‎١٨١...............................................................................................W
١٨٤..........................................................................................................Wאאאא
אאEvaporator ١٨٥.................................................................................................. Condenser &
א‎١٨٩...............................................................................................................................CompressorW

א
١٦٢
אאאא
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אPumpW ...........................................................................................................................................١٨٩
١٩٠...................................................................................................................... Wאא
אאאא‎١٩٢........................................................................................................................
١٩٢.......................................................................................................................................................W
א‎١٩٣...................................................................................................................................................
אאאאRefrigeratorW ٢٠٠...................................................................The Heat Pump & The
אאאאCycle:EF ٢٠٢..................................................................................... The Carnot
אאאאFא‎٢٠٣.......................................................................................................E
٢٠٩.................................................................................................................................... אאא
אא‎٢١٥..........................................................................................................................W
٢١٧.......................................................................................................................................................W
אאWאא-אאא‎٢١٨.............................................................................................
٢١٨................................................................................................................... אאאWאא
٢٢٤..............................................................................................................................................
אאWאאא .....................................................................................................................٢٢٨
٢٣٤..............................................................................................................................................
אאWאאJ ٢٣٧........................................................................................אא
אאWאאא‎٢٣٧..................................................................................................................................
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אאWאא‎٢٤٠......................................................................................................................
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אאWאאא .....................................................................................................................٢٤٥
٢٤٨..............................................................................................................................................
אאאWאאאא‎٢٥٠.........................................................................................................
אאWאאאJ אאא ٢٥٣..................................................................................
אא‎٢٥٣.............................................................................................................................W
٢٥٥..............................................................................................................................................
אאWאאאא ........................................................................................................٢٥٨
٢٦٢..............................................................................................................................................
אאWאאאא‎٢٦٣.......................................................................................................
٢٦٦..............................................................................................................................................
אא ..........................................................................................................................................٢٦٧
אאא .............................................................................................................................................٢٧٠
אאא ..............................................................................................................................................٢٧٠