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).

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

C Pressure ratio, r (Figure 4.2):

k = 1.4, β = 0.762 ® r = 0.58

$ Pressure drop, ΔP (Equation 4.9):

C Expansion factor, Y (Figure 4.1):

(1 - r)/k = (1 - 0.578)/(1.4) = 0.3

β² = 0.762² = 0.58

Y = 0.66

C Velocity of air, V (Equation 4.7):

C

C Reynolds number, Re: