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.
For gases, expansion factor (Y), can be obtained using Figure 4.1 (Crane Fig. A-20). Figure 4.1 presents Y for various values of (1 - r)/k and β2, where r is defined as
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This equation can be rearranged to the following form:
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Nozzles: If the flow of a gas is occurring under critical conditions, then pressure ratio (r) values for compressible flow through nozzles and venturi tubes is given in Figure 4.2 (Crane A-21). Pressure ratio r is plotted as a function of k and b. Now values of r and β can be utilized in Figure 4.1 (Crane A-20) to obtain expansion factor (Y).
Orifice Meters: The velocity through an orifice can be computed knowing the value of orifice coefficient CV, which is a function or Reynolds number. The expansion factor for liquids is 1.0, whereas for gases it is found from the following equation.
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