Nozzle Exit Velocity Calculator
Plotly Graph
The graph shows how ideal and actual exit velocity change as exit or back pressure varies for the current input set.
Example Data Table
| Case | Nozzle Type | P0 (kPa abs) | Pe (kPa abs) | T0 (K) | γ | R (J/kg·K) | η | D (mm) | Actual Velocity (m/s) | Mach | Mass Flow (kg/s) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Converging-Diverging | 600 | 100 | 600 | 1.33 | 287 | 0.95 | 25 | 687.939 | 1.842 | 0.300 |
| 2 | Converging | 500 | 220 | 520 | 1.40 | 287 | 0.92 | 20 | 400.230 | 1.000 | 0.259 |
| 3 | Converging | 800 | 90 | 700 | 1.30 | 300 | 0.94 | 30 | 472.385 | 1.000 | 0.790 |
These rows are illustrative sample cases to help verify input handling and expected output trends.
Formula Used
1) Ideal exit velocity
Videal = √[(2γ / (γ - 1)) · R · T0 · (1 - (Pe/P0)(γ - 1)/γ)]
2) Actual exit velocity
Vactual = √η · Videal
3) Critical pressure ratio
(P* / P0) = (2 / (γ + 1))γ / (γ - 1)
4) Exit Mach number
M = √[(2 / (γ - 1)) · ((P0/Pe)(γ - 1)/γ - 1)]
5) Exit temperature and density
Te = T0 · (Pe/P0)(γ - 1)/γ
ρe = Pe / (R · Te)
6) Flow area and mass flow
A = πD² / 4
ṁ = Cd · ρe · A · Vactual
This calculator assumes one-dimensional isentropic behavior with efficiency adjustment. Use absolute pressures for consistent engineering results.
How to Use This Calculator
- Choose the nozzle type. Select converging for throat-limited flow or converging-diverging for expanded nozzle estimates.
- Enter chamber pressure and exit or back pressure in absolute units, not gauge values.
- Provide stagnation temperature, specific heat ratio, and gas constant for the working fluid.
- Enter nozzle efficiency and discharge coefficient as decimals between 0 and 1.
- Add exit diameter to estimate area, volumetric flow, and mass flow.
- Press the calculate button. The result appears above the form, followed by graph, table, formulas, downloads, and FAQs.
Frequently Asked Questions
1) Should I use absolute pressure or gauge pressure?
Use absolute pressure. The thermodynamic relations in compressible nozzle flow depend on absolute pressure ratios, so gauge values can produce misleading velocity and Mach estimates.
2) What happens when the nozzle is choked?
Choking occurs when the pressure ratio reaches the critical limit. In a converging nozzle, the exit or throat reaches Mach 1 and further back-pressure reduction no longer increases local mass flow.
3) Why does the calculator ask for γ and R?
These fluid properties define how pressure energy converts into kinetic energy. Different gases expand differently, so accurate γ and R values improve exit velocity, temperature, and density predictions.
4) Why is actual velocity lower than ideal velocity?
Real nozzles have friction, turbulence, boundary-layer losses, and nonideal expansion. Efficiency accounts for these effects, reducing the ideal isentropic velocity to a more practical engineering estimate.
5) Does discharge coefficient change velocity?
In this calculator, discharge coefficient mainly affects mass flow. Velocity is adjusted by nozzle efficiency, while discharge coefficient modifies the effective delivered flow through the exit area.
6) Can this tool be used for liquids?
This version is designed for compressible gas nozzle calculations. Liquid nozzles often use Bernoulli-based relations with density and pressure drop, which follow a different modeling approach.
7) Why does nozzle type matter here?
A converging nozzle cannot continue isentropic expansion below the critical exit pressure. A converging-diverging nozzle can support further expansion and potentially supersonic exit conditions when geometry allows.
8) Can I save the results for reporting?
Yes. After calculation, use the CSV button for spreadsheet work or the PDF button for a compact report that includes the key performance outputs and engineering inputs.