Compressible Flow Calculator

1. Enter γ, R, static temperature, and static pressure.
2. Provide either velocity or Mach number for the state.
3. Optionally add flow area to compute mass flow metrics.
4. Press submit to view results above this form.
5. Use the download buttons to export results.

Assumes ideal gas behavior and one-dimensional steady flow.

Run these rows to compare stagnation, choking, and shock behavior.

Why compressibility matters in high-speed flows

When velocity approaches the local speed of sound, density can no longer be treated as constant. Pressure waves steepen, temperature changes become significant, and small input differences can shift Mach number noticeably. This calculator links your static state to compressible performance metrics, so you can judge whether a low-speed assumption is acceptable for your case.

Interpreting Mach number and the speed of sound

Mach number compares flow speed to the acoustic speed, which depends on the gas model and temperature. Raising temperature increases the speed of sound, often reducing Mach at the same velocity. Changing the heat capacity ratio alters compressibility strength. Use these outputs to check subsonic, transonic, and supersonic regimes, then review the related stagnation quantities for energy consistency.

Stagnation properties for energy-based comparisons

Stagnation temperature and pressure represent the state reached after an ideal, frictionless deceleration to rest. They are useful for comparing inlet conditions, diffuser performance, and nozzle operation. In practice, losses reduce stagnation pressure, but the ideal values provide an upper bound. If you change velocity while holding static conditions, the rise in stagnation temperature quantifies added kinetic energy.

Choking and nozzle limits with area effects

For a given stagnation state, a nozzle can reach a sonic condition at the throat when the back pressure is low enough. The calculator reports critical ratios and the mass flux at choking. Entering an area enables mass flow estimates and a choked mass flow ceiling. Because the mass flux uses stagnation pressure and temperature, it remains comparable across different static states, making it convenient for sizing throats and evaluating operating margins over changing ambient conditions. during startup and off-design. Comparing your computed mass flow to the choked limit helps identify whether downstream restrictions or upstream supply dominate.

Normal shock indicators for supersonic operation

When supersonic flow is forced to slow abruptly, a normal shock can form, increasing pressure and temperature while reducing Mach. The calculator reports downstream Mach and key property ratios, plus the associated total pressure loss indicator. These values support quick feasibility checks for inlets, valves, and test sections where shocks may appear. Always validate with geometry and boundary conditions.

FAQs

1) Should I enter velocity or Mach number?

Provide either value. If Mach is entered and velocity is blank, the calculator computes velocity using the current gas model and temperature. If both are entered, velocity is used and Mach is derived from it.

2) What do stagnation values represent?

They represent ideal conditions after slowing the flow to rest without losses. Stagnation temperature reflects total energy, while stagnation pressure is sensitive to irreversibilities. Use them to compare inlet states and to evaluate nozzle and diffuser trends.

3) When will the normal shock section appear?

Normal shock outputs appear only when the computed Mach number is greater than one. In that case, the tool reports downstream Mach and property ratios for a one-dimensional normal shock, which is useful for quick supersonic checks.

4) Why is flow area optional?

Area is required only for mass flow rate. Without area, the calculator still returns Mach, stagnation properties, and choking indicators. Add area to obtain mass flow and to compare your demand against the choked mass flow limit.

5) What assumptions limit accuracy?

The relations assume a perfect gas, steady one-dimensional flow, and isentropic behavior outside shocks. Real systems may include friction, heat transfer, area changes with losses, and non-uniform profiles. Use results as a baseline for engineering decisions.

6) How should I choose γ and R?

Select values consistent with your working gas and temperature range. For air near room temperature, γ≈1.4 and R≈287 J/kg·K are common. For other gases, use reference data or mixture calculations that match your composition.