In
general flow coefficient, K, is given as
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where
Cc º Avena
contracta/Athroat and Cv = V2 actual/V2
ideal
For
nozzles and venturi meters, the section of minimum flow area is located at the
throat. There is no vena contracta and
Cc = 1. For these cases
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where
β is given as
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The
factor 1/(1 - β4)1/2 is called the "velocity of
approach" factor.
Some
of the pressure is recovered in the diverging section. An expansion factor Y is introduced
to give a better representation of the velocity.
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For
liquids, expansion factor (Y) is 1.
Example
4.3:
How much water is flowing through a pipe if a venturi meter reads 1 in of
mercury. Water is at a temperature of
110 °F and nominal
diameters for venturi meter are 4 in and 3 in, respectively. Use the following information:
CV = 0.984 (for
Re >104); density of water = 61.86 lb/ft3
Density of mercury = 840.7 lb/ft3;
kinematic viscosity = 6.67 ´ 10-6
ft2/s
Solution
C
Pressure drop, ΔP (Equation 4.1):
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Diameter of the upstream pipe, d1
= 0.351 ft.
Diameter of the pipe at the throat, d2
= 0.256 ft.
C
Diameter ratio, β (Equation 4.6):
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C
K (Equation 4.5):
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C
Velocity of the fluid, V (Equation 4.4) as 9.93 ft/s.
C
Reynolds number (Re):
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Re is greater than 104
hence CV value is appropriate.
