🔺 Converging-Diverging Nozzle Flow
Analyze C-D nozzle performance: operating regimes, choking, shock location, and pressure distribution along the nozzle.
📝 Configuration
Area-Mach Relation:
A/A* = (1/M)[(2/(γ+1))(1+(γ-1)/2 M²)]^((γ+1)/(2(γ-1)))
Choked Mass Flow:
ṁ = P₀A*√(γ/(RT₀)) × (2/(γ+1))^((γ+1)/(2(γ-1)))
Normal Shock:
M₂² = [(γ-1)M₁²+2] / [2γM₁²-(γ-1)]
P₂/P₁ = 1 + 2γ/(γ+1)(M₁²-1)
A/A* = (1/M)[(2/(γ+1))(1+(γ-1)/2 M²)]^((γ+1)/(2(γ-1)))
Choked Mass Flow:
ṁ = P₀A*√(γ/(RT₀)) × (2/(γ+1))^((γ+1)/(2(γ-1)))
Normal Shock:
M₂² = [(γ-1)M₁²+2] / [2γM₁²-(γ-1)]
P₂/P₁ = 1 + 2γ/(γ+1)(M₁²-1)
📊 Results & Visualization
Configure the inputs and click Calculate to see results.
ℹ️ About Converging-Diverging Nozzles
A C-D nozzle accelerates gas from subsonic to supersonic speeds. The flow behavior depends on the back pressure ratio P_b/P₀.
Operating regimes:
• Subsonic: P_b close to P₀; flow never reaches sonic speed
• Choked: M = 1 at throat; maximum mass flow rate reached
• Shock in nozzle: Normal shock forms in diverging section
• Overexpanded: Oblique shocks at exit plane
• Design: Perfectly expanded isentropic flow
• Underexpanded: Expansion fans at exit plane
A C-D nozzle accelerates gas from subsonic to supersonic speeds. The flow behavior depends on the back pressure ratio P_b/P₀.
Operating regimes:
• Subsonic: P_b close to P₀; flow never reaches sonic speed
• Choked: M = 1 at throat; maximum mass flow rate reached
• Shock in nozzle: Normal shock forms in diverging section
• Overexpanded: Oblique shocks at exit plane
• Design: Perfectly expanded isentropic flow
• Underexpanded: Expansion fans at exit plane