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

This equation can be rearranged to the following form:

Example 4.4: Air is flowing through a venturi meter whose nominal diameters are 4 in and 3 in, respectively. A manometer attached to the meter reads 1 in of mercury. Air is at a temperature of 70 °F. Calculate the expansion factor for the venturi meter. What is the mass flow rate of air? Use the following information:

K = 1.209, Diameter ratio, β = 0.762, Throat area, A₂ = 0.051 ft²,

Mercury density, ρ_m = 846.7 lb/ft³, Air density, ρ = 0.075 lb/ft³,

Viscosity, μ = 1.24 ´ 10^-5 lb/(ft·s)

Solution:

C Pressure drop, ΔP (Equation 4.1):

C Pressure ratio, r (Equation 4.8):

Inlet pressure, P₁ = 14.696 psi = 2116.2 lb_f/ft²

C Expansion factor, Y (Figure 4.1):

(1 - r)/k = (1 - 0.967)/1.4 = 0.024

β² = 0.762² = 0.58, ®Y = 0.97

C Velocity of the gas, V (Equation 4.7):

C Reynolds number, Re:

C Calculate mass flow rate, w: