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, ρm = 846.7 lb/ft3, Air density, ρ = 0.075 lb/ft3,
Viscosity, μ = 1.24 ´ 10-5 lb/(ft·s)
Solution:
Pressure drop, ΔP (Equation 4.1):
Pressure ratio, r (Equation 4.8):
Inlet pressure, P1 = 14.696 psi = 2116.2 lbf/ft2
Expansion factor, Y (Figure 4.1):
(1 - r)/k = (1 - 0.967)/1.4 = 0.024
β2 = 0.7622 = 0.58, ®Y = 0.97
Velocity of the gas, V (Equation 4.7):
Reynolds number, Re:
Calculate mass flow rate, w: