Example 4.5: Air is entering into a pipe at 1 atm and is flowing at critical conditions through a nozzle whose nominal diameters are 4 in and 3 in, respectively. Calculate the velocity and the mass flow rate of air. The following information applies:
Temperature, T = 70 °F, C = 0.984, Heat capacity ratio, k = 1.4,
Diameter ratio, β = 0.762, K = 1.209, Throat area, A2 = 0.051 ft2,
Kinematic viscosity, v = 1.85 ´ 10-4 ft2/s
Solution
Pressure ratio, r (Figure 4.2):
k = 1.4, β = 0.762 ® r = 0.58
Pressure drop, ΔP (Equation 4.9):
Expansion factor, Y (Figure 4.1):
(1 - r)/k = (1 - 0.578)/(1.4) = 0.3
β2 = 0.7622 = 0.58
Y = 0.66
Velocity of air, V (Equation 4.7):
Reynolds number, Re: