Estimate nozzle exit speed from operating conditions. Choose gas or liquid flow, then set factors. See regime, Mach, and velocity in seconds, confidently today.
This option treats the flow as an ideal gas with an isentropic core. The back-to-stagnation pressure ratio Pb/P0 determines whether choking occurs.
This option uses Bernoulli’s equation between a high-pressure region and the nozzle exit, assuming constant density.
| Case | Model | Inputs (summary) | Typical output |
|---|---|---|---|
| 1 | Compressible | P0=10 bar, Pb=1 bar, T0=300 K, γ=1.4, R=287, η=0.98 | Choked, v ≈ 3.36e+2 m/s (order of magnitude) |
| 2 | Compressible | P0=2 bar, Pb=1.5 bar, T0=350 K, γ=1.33, R=461, η=0.95 | Unchoked, v ≈ 1.7e+2 m/s (order of magnitude) |
| 3 | Incompressible | P1=5 bar, P2=1 bar, ρ=1000 kg/m³, Cd=0.99 | v ≈ 2.8e+1 m/s (order of magnitude) |
Nozzle exit velocity is a direct indicator of how effectively pressure energy converts into kinetic energy. It influences thrust, jet penetration, spray breakup, mixing rate, and acoustic loading. In many systems, a small change in exit speed can produce a large change in performance because momentum scales with velocity.
This calculator supports two engineering cores. Use the compressible option for gases where density changes are significant, especially at higher pressure ratios. Use the incompressible option for liquids or low-speed gases where density remains nearly constant. Choosing the right model prevents unrealistic velocities.
For gas flow, stagnation pressure and stagnation temperature represent the upstream energy state. Under an isentropic core assumption, the pressure ratio implies an exit temperature drop, and that temperature drop sets the theoretical velocity rise. This provides a fast first-pass estimate for design and checks.
When the back pressure is low enough, the flow can choke. At choking, a converging nozzle reaches sonic conditions at the controlling section, limiting further increases in mass flow for a fixed upstream state. The calculator reports the critical pressure ratio for your γ value and flags the regime clearly.
Real nozzles experience friction, boundary-layer growth, nonuniform profiles, and minor losses. The compressible model uses an efficiency factor to reduce ideal velocity, while the incompressible model applies a discharge coefficient. These parameters help align the estimate with measured performance without adding heavy geometry inputs.
Engineering workflows frequently mix pressure and temperature units. The tool converts common pressure units into pascals and temperature into kelvin internally, then outputs velocity in your chosen unit. Built-in validation checks common failure modes such as reversed pressure differences or nonphysical parameter ranges.
For the gas option, the reported exit temperature helps you evaluate thermal margins and downstream material compatibility. The reference Mach estimate indicates whether compressibility is dominant and whether a more detailed nozzle area-ratio analysis is justified. Treat Mach as a diagnostic, not a substitute for full nozzle sizing.
Typical applications include preliminary sizing of air nozzles, gas blow-off jets, liquid spray nozzles, and lab test rigs. For high-accuracy thrust prediction, multi-phase flow, strong shocks, or heat transfer, use this calculator as a screening tool and then confirm with detailed models or testing.
Use it for gases when pressure ratios are large, or when the expected speed is a meaningful fraction of the speed of sound. It captures choking behavior and the energy link between pressure ratio and temperature drop.
It can be acceptable when the pressure change is small and the resulting Mach number is low. If your computed speed approaches sonic conditions, switch to the compressible model for a more realistic estimate.
Choked means the pressure ratio is low enough that a converging nozzle reaches Mach 1 at the controlling section. The exit speed is then limited to the sonic condition implied by your upstream temperature and γ.
For a smooth, well-designed nozzle, η is often between 0.95 and 0.99. If the nozzle is rough, short, or has strong losses, use a lower value. Compare with test data when available.
Cd commonly ranges from 0.6 to 0.99 depending on geometry and Reynolds number. Sharp-edged orifices trend lower, while well-contoured nozzles trend higher. Use vendor data or measurements for best accuracy.
The simplified energy relations assume flow accelerates from high to low pressure. If downstream pressure is higher, the flow may reverse or require a pump/compressor model. The calculator flags this to prevent nonphysical results.
No. It estimates exit velocity from thermodynamic or Bernoulli relations. Area ratio, mass flow, and thrust require additional geometry and momentum terms. Use this as a fast velocity estimate before deeper sizing.