Q: What is the difference between Fanno flow and Rayleigh flow?

Fanno flow is adiabatic flow with friction. Pipe wall friction increases entropy, driving both subsonic and supersonic flows toward M=1. Rayleigh flow is inviscid flow with heat addition. Heat addition changes entropy, causing subsonic flow to accelerate (M→1) and supersonic flow to decelerate (M→1) with heating. In both cases, M=1 is the maximum entropy point (critical condition).

Q: What is the critical condition in gas dynamics?

The critical condition means M=1, i.e., the flow velocity equals the local speed of sound. For isentropic flow, the critical area ratio A/A* is minimum at the nozzle throat. For air (γ=1.4): critical temperature ratio T/T₀=0.833, critical pressure ratio p/p₀=0.528, critical density ratio ρ/ρ₀=0.634. This is especially important in Laval nozzle design for rocket engines, where M=1 at the throat enables supersonic flow downstream.

Question 1

What are the basic isentropic flow relations?

Accepted Answer

For isentropic flow, using Mach number M and specific heat ratio γ: Stagnation temperature ratio T₀/T = 1 + (γ-1)/2·M²; Stagnation pressure ratio p₀/p = (1 + (γ-1)/2·M²)^(γ/(γ-1)); Density ratio ρ₀/ρ = (1 + (γ-1)/2·M²)^(1/(γ-1)); Area ratio A/A* = (1/M)[(2/(γ+1))(1+(γ-1)/2·M²)]^((γ+1)/(2(γ-1))). These form the basis of nozzle and wind tunnel design.

Question 2

What happens across a normal shock wave?

Accepted Answer

A normal shock instantaneously converts supersonic flow to subsonic flow. Key changes: ① Downstream Mach number M₂ < 1 (subsonic), ② Static pressure rises (p₂/p₁ = (2γM₁²-(γ-1))/(γ+1)), ③ Static temperature rises, ④ Total pressure decreases (p₀₂/p₀₁ < 1, entropy increases). Shock strength increases with M₁. Minimizing total pressure loss across shocks is critical in aircraft engine inlet design.

Question 3

What is the difference between Fanno flow and Rayleigh flow?

Accepted Answer

Fanno flow is adiabatic flow with friction. Pipe wall friction increases entropy, driving both subsonic and supersonic flows toward M=1. Rayleigh flow is inviscid flow with heat addition. Heat addition changes entropy, causing subsonic flow to accelerate (M→1) and supersonic flow to decelerate (M→1) with heating. In both cases, M=1 is the maximum entropy point (critical condition).

Question 4

What is the critical condition in gas dynamics?

Accepted Answer

The critical condition means M=1, i.e., the flow velocity equals the local speed of sound. For isentropic flow, the critical area ratio A/A* is minimum at the nozzle throat. For air (γ=1.4): critical temperature ratio T/T₀=0.833, critical pressure ratio p/p₀=0.528, critical density ratio ρ/ρ₀=0.634. This is especially important in Laval nozzle design for rocket engines, where M=1 at the throat enables supersonic flow downstream.

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