The MBR Book: Principles and Applications of Membrane

or
or
(A.4)
where � is the ratio of specific heat capacity at constant pressure to specific heat
capacity at constant volume (c p/c v) and is assumed to be constant. Substituting
Equation (A.4) into Equation (A.3) and integrating between points 1 and 2:
This equation can be manipulated to give:
(A.5)
This equation gives the work done per unit mass by a blower that is 100% efficient.
No mechanical process is 100% efficient so a term for the mechanical efficiency of the
system (�) is added; this accounts for any losses in the system, including friction. w is
work per unit mass and power is total work per second. Equation (A.5) can be converted
into power consumption in (W) by dividing by time. The density of air varies with
temperature according to:
(A.6)
Where T 0 is the standard temperature (273°K). The power consumed, in kW, thus
becomes:
but
p1 p
�
r r
r
l l
1
r
� 1
1
l p
1
1
1
l p p
l
1 2 dp
p1
1�1
1�1
l
ll
w � �
p � p
1 p
2
1
r ∫
( )
1 1 p l ( 1� 1 r
l)
1
⎡
p1l⎢⎛p w � ⎢
⎜
( l � 1)
r ⎢ 1 ⎝⎜
p1
⎠⎟
⎣⎢
r � r
T
T
t 0 0
⎡
P
p1l
T ⎢⎛
p
�
⎢
⎜
m 1000j( l � 1) r0t273
⎢⎝⎜
p1
⎠⎟
⎣⎢
V � qt
p
t
1
l
1�
1
⎞ l
2
⎤
⎥
� 1 ⎥
⎦⎥
1�
1
⎞ l
1 2
⎤
⎥
� 1 ⎥
⎦⎥
Appendix A: Blower power consumption 275
(A.7)
(A.8)