JNTU B.Tech III AERODYNAMICS II Previous Question Paper (October - 2020 - R13)

Compressibility refers to the change in density of a fluid due to pressure changes. As the Mach number (M) increases, the flow can no longer be treated as incompressible. For M < 0.3, density variations are negligible (less than 5%), allowing the use of incompressible flow equations. As M approaches 1.0, compressibility effects become significant, leading to shock waves and changes in pressure distribution. The relationship is governed by the Prandtl-Glauert rule, where the pressure coefficient C_p is modified by the factor 1/sqrt(1-M²), demonstrating that as M increases, the effect of compressibility significantly amplifies the pressure forces on an aerodynamic body.

Given: Stagnation pressure P₀ = 2 atm, ambient pressure P_a = 1 atm, stagnation temperature T₀ = 25°C = 298 K, and area A = 1 unit. First, check if the flow is choked by calculating the critical pressure ratio P*/P₀ = (2/(γ+1))^γ/(γ-1) = 0.528. Since P_a/P₀ = 0.5 < 0.528, the flow is choked at the exit.

For choked flow, the exit pressure P_e = P* = 0.528 × 2 atm = 1.056 atm. The exit temperature T_e = T₀ × (2/(γ+1)) = 298 × 0.833 = 248.2 K. The exit velocity is the speed of sound at T_e: V_e = sqrt(γRT_e) = sqrt(1.4 × 287 × 248.2) ≈ 315.6 m/s.

To find the mass flow rate, use the choked flow formula: ṁ = A × P₀ × sqrt(γ/RT₀) × (2/(γ+1))^{(γ+1)/(2(γ-1))}. Substituting the values: ṁ = 1 × (2 × 101325) × sqrt(1.4 / (287 × 298)) × (0.6339) ≈ 202650 × 0.0405 × 0.6339 ≈ 5204 kg/s (assuming unit area is 1 m²).