fundamentals of engineering supplied-reference handbook - Ventech!

FLUID MEASUREMENTS
The Pitot Tube – From the stagnation pressure equation for
an incompressible fluid,
( ρ)(
p − p ) = g(
p − p ) γ
V = 2 o s 2 o s , where
V = the velocity of the fluid,
po = the stagnation pressure, and
ps = the static pressure of the fluid at the elevation where
the measurement is taken.
•
V, P s
For a compressible fluid, use the above incompressible fluid
equation if the mach number ≤ 0.3.
MANOMETERS
♦
For a simple manometer,
If h1 = h2 = h
Ps
Po
2
V
2g
po = p2 + γ2h2 – γ1h1
po = p2 + (γ2 – γ1)h = p2 + (ρ2 –ρ1)gh
Note that the difference between the two densities is used.
♦ Bober, W. & R.A. Kenyon, Fluid Mechanics, John Wiley & Sons, Inc., 1980.
Diagrams reprinted by permission of William Bober & Richard A. Kenyon.
• Vennard, J.K., Elementary Fluid Mechanics, J.K. Vennard, 1954. Diagrams
reprinted by permission of John Wiley & Sons, Inc.
50
FLUID MECHANICS (continued)
Another device that works on the same principle as the
manometer is the simple barometer.
♦
patm = pA = pv + γh = pB + γh
pv = vapor pressure of the barometer fluid
Venturi Meters
Q
Cv
A2
⎛ p1
p2
⎞
2g⎜
+ z1
− − z ⎟ , where
2
1−
⎝ γ γ ⎠
= 2
( A A )
2
Cv = the coefficient of velocity.
1
The above equation is for incompressible fluids.
•
Orifices The cross-sectional area at the vena contracta A2 is
characterized by a coefficient of contraction Cc and given by
Cc A.
•
Q
⎛ p1
p2
2g⎜ + z1
− − z
⎝ γ γ
= CA
2
where C, the coefficient of the meter, is given by
C =
C C
v
2
c
c
( ) 2
A
1− C A
1
⎞
⎟
⎠