Nozzle Flow Calculator
A 100 cm² throat fed at 7 MPa and 3000 K chokes at a mass flow of 44.3031 kg/s, and an expansion ratio of 10 accelerates it to supersonic exit speed.
Air 1.4; hot combustion gases about 1.3; helium 1.667.
Air 287; rocket exhaust roughly 300–400 (R = 8314/molar mass).
44.3031131761166 kg/s
Full answer, then cut to fewer decimals (not rounded):
- 44.3031131761166 kg/s
- 44.303113176116 kg/s
- 44.30311317611 kg/s
- 44.3031131761 kg/s
- 44.303113176 kg/s
- 44.30311317 kg/s
- 44.3031131 kg/s
- 44.303113 kg/s
- 44.30311 kg/s
- 44.3031 kg/s
- 44.303 kg/s
- 44.30 kg/s
- 44.3 kg/s
- Exit Mach number Mₑ
- 3.278340793
- Exit pressure pₑ
- 87.76090542 kPa
- Exit temperature Tₑ
- 1445.956065 K
- Exit velocity vₑ
- 2554.796377 m/s
- Thrust
- 121.9615236 kN
- Specific impulse
- 280.716487 s
- Characteristic velocity c* = p₀A*/ṁ
- 1580.024404 m/s
Step-by-step solution
- ṁ = A* p₀ √(γ/(RT₀)) (2/(γ+1))^((γ+1)/(2(γ−1))) = 44.30311318 kg/s (choked)
- Aₑ/A* = 10 → Mₑ = 3.278340793 (supersonic branch)
- vₑ = Mₑ√(γRTₑ) = 2554.796377 m/s; F = ṁvₑ + (pₑ − pₐ)Aₑ = 121.9615236 kN
Nozzle Flow Formula
ṁ = A* p₀ √(γ/(RT₀)) (2/(γ+1))^((γ+1)/(2(γ−1)))
exit Mach from Aₑ/A* (supersonic branch); vₑ = Mₑ√(γRTₑ); F = ṁvₑ + (pₑ − pₐ)Aₑ
Worked Example
A rocket nozzle with 7 MPa, 3000 K chamber, 100 cm² throat and expansion ratio 10, in vacuum:
- ṁ = A* p₀ √(γ/(RT₀)) (2/(γ+1))^((γ+1)/(2(γ−1))) = 44.30311318 kg/s (choked)
- Aₑ/A* = 10 → Mₑ = 3.278340793 (supersonic branch)
- vₑ = Mₑ√(γRTₑ) = 2554.796377 m/s; F = ṁvₑ + (pₑ − pₐ)Aₑ = 121.9615236 kN
Exit pressure pₑ: 87.76090542 kPa · Exit temperature Tₑ: 1445.956065 K · Exit velocity vₑ: 2554.796377 m/s · Thrust: 121.9615236 kN · Specific impulse: 280.716487 s · Characteristic velocity c* = p₀A*/ṁ: 1580.024404 m/s
GATE tip
Characteristic velocity c* = p₀A*/ṁ depends only on the propellant combustion; the thrust coefficient C_F = F/(p₀A*) depends on the nozzle. F = ṁ c* C_F links them.
More Compressible Flow Calculators
-
Isentropic Flow Calculator
T₀/T = 1 + (γ − 1)M²/2, p₀/p = (T₀/T)^(γ/(γ−1))
A/A* = (1/M)[(2/(γ+1))(1 + (γ−1)M²/2)]^((γ+1)/(2(γ−1)))
Example: Air (γ = 1.4) at Mach 2: Pressure ratio p/p₀ = 0.127805.
-
Normal Shock Calculator
M₂² = (1 + (γ−1)M₁²/2) / (γM₁² − (γ−1)/2)
p₂/p₁ = 1 + 2γ(M₁² − 1)/(γ + 1); ρ₂/ρ₁ = (γ+1)M₁²/((γ−1)M₁² + 2)
Example: A normal shock in air at M₁ = 2: Downstream Mach number M₂ = 0.57735.
-
Oblique Shock Calculator
tan θ = 2 cot β (M₁² sin²β − 1) / (M₁²(γ + cos 2β) + 2)
normal component M₁ sin β obeys the normal-shock relations; M₂ = Mₙ₂ / sin(β − θ)
Example: Mach 2 flow turned by a 10° wedge: Shock wave angle β (weak) = 39.3139 °.
-
Prandtl-Meyer Expansion Calculator
ν(M) = √((γ+1)/(γ−1)) arctan √((γ−1)(M²−1)/(γ+1)) − arctan √(M² − 1)
expansion by θ: ν(M₂) = ν(M₁) + θ, isentropic
Example: Mach 2 air expanding round a 10° corner: Downstream Mach number M₂ = 2.38489.
Frequently asked questions
What does choked mean?
The throat is at Mach 1, so lowering the back pressure further cannot increase the mass flow; only the chamber pressure, temperature and throat area set it.
When is a nozzle perfectly expanded?
When the exit pressure equals ambient pressure; it then gives the most thrust for that altitude. Rocket nozzles are a compromise across the ascent.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Nozzle Flow Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/nozzle-flow-calculator/
IEEE
Scientific Converters, "Nozzle Flow Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/nozzle-flow-calculator/