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Rocket Nozzle Design โ€” 2026-09-29 07:19:39
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๐Ÿš€ Rocket Nozzle Design (De Laval)

Size converging-diverging nozzles using isentropic compressible relations. Compute throat/exit areas, expansion ratio, thrust, and specific impulse.

โšก Fortran 90 Engine Double Precision (IEEE 754) โœ“ ISO / ASME Validated
Rocket Nozzle Design (De Laval) Fluid Mechanics
๐Ÿ“Š Solver Telemetry โ— ACTIVE
๐Ÿ‘๏ธ Views 212
โšก Solves 167
๐Ÿ’พ Downloads 561 ๐Ÿ“ฆ Fortran Code 4.5 KB
๐Ÿ“… Released Jun 2026
โฑ๏ธ Latency < 1 ms
โšก TOOLS & REPORTS:
๐Ÿ’พ Download Fortran 90

๐Ÿ”ฅ De Laval Nozzle Schematic

๐Ÿ“ Configuration

๐Ÿ”ฅ Chamber Conditions
๐Ÿ“ Nozzle Geometry
๐ŸŒซ๏ธ Pressures
Nozzle design exit pressure.
0 for vacuum.
Key Equations:

A/A* = (1/M)[(2+(ฮณโˆ’1)Mยฒ)/(ฮณ+1)](ฮณ+1)/(2(ฮณโˆ’1))
F = แนVe + (Peโˆ’Pa)Ae
CF = F/(PcAt)
Isp = F/(แนgโ‚€)
c* = โˆš(ฮณRTc)/ฮณ/โˆš[(2/(ฮณ+1))(ฮณ+1)/(ฮณโˆ’1)]

๐Ÿ“Š Results

Configure inputs and click Design to view results.

๐Ÿ“˜ Methodology

Isentropic Relations

The De Laval nozzle accelerates flow from subsonic to supersonic through a converging-diverging geometry. All thermodynamic properties along the nozzle follow from the local Mach number and isentropic relations.

Thrust & Isp

Thrust includes both momentum flux แนVe and pressure thrust (Peโˆ’Pa)Ae. Specific impulse Isp = F/(แนgโ‚€) characterizes propellant efficiency. The thrust coefficient CF normalizes thrust by chamber conditions.

Assumptions

  • Steady, quasi-1D isentropic flow.
  • Calorically perfect gas (constant ฮณ).
  • No boundary layer, friction, or heat loss.
  • Fully expanded nozzle at design Pe.
  • Choked flow at throat (M = 1).

๐Ÿ“˜ Calculation Methodology: De Laval Rocket Nozzle Isentropic Expansion

Mathematical Model & Theory

Converging-diverging de Laval nozzles accelerate chamber combustion gases isentropically to sonic speed at the throat and supersonic speed at exit:

$$\frac{A}{A^*} = \frac{1}{M}\left[\frac{2}{\gamma+1}\left(1 + \frac{\gamma-1}{2}M^2\right)\right]^{\frac{\gamma+1}{2(\gamma-1)}}, \quad F = \dot{m} V_e + (p_e - p_a)A_e$$
$$V_e = \sqrt{\frac{2\gamma}{\gamma-1} R T_c \left[1 - \left(\frac{p_e}{p_c}\right)^{\frac{\gamma-1}{\gamma}}\right]}$$

Assumptions

  • 1D steady isentropic gas expansion.
  • Choked flow at throat ($M=1$).

Academic References

  1. Sutton, G. P., & Biblarz, O.: Rocket Propulsion Elements, Wiley.
  2. Anderson, J. D.: Modern Compressible Flow.

Worked Engineering Example

Problem Statement:
A rocket chamber has $P_c = 6.0\text{ MPa}$, $T_c = 3400\text{ K}$, $\gamma = 1.22$, $M_w = 22.0\text{ g/mol}$, expanding $\dot{m} = 50\text{ kg/s}$ to $p_e = 100\text{ kPa}$. Calculate exhaust velocity and thrust.

Step-by-step Solution:
1. $V_e = \sqrt{\frac{2(1.22)}{0.22} \times 377.9 \times 3400 \times (1 - 0.01667^{0.1803})} \approx 2726.4\text{ m/s}$.
2. $F = 50 \times 2726.4 = 136,320\text{ N} = 136.32\text{ kN}$.
Final Result:
Exhaust velocity is $\mathbf{2726\text{ m/s}}$, delivering $\mathbf{136.3\text{ kN}}$ thrust.
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