Compressible Flow Solver Calculator

Example data table

Formula used

How to use this calculator

1. Select a calculation mode: provide Mach, pressure ratio, or area ratio.
2. If using a ratio, choose a branch to pick subsonic or supersonic Mach.
3. Enter γ and R for your gas, plus stagnation conditions T0 and P0.
4. Enter section area A to obtain mass flow at that section.
5. Enter throat area A* to compute the choked reference mass flow.
6. Press Solve to see results under the header.
7. Use the CSV and PDF buttons to export the latest results.

Professional guide to compressible flow results

1) Why compressible flow matters

When Mach number rises above roughly 0.3, density variations affect pressure, thrust, and acoustics. This solver gives a one-dimensional, isentropic baseline for early nozzle, inlet, and duct calculations and feasibility studies.

2) Selecting gas properties

The key material inputs are the heat-capacity ratio γ and the specific gas constant R. Air is often approximated with γ ≈ 1.4 and R ≈ 287 J/(kg·K), while combustion products and noble gases differ. Small γ shifts move critical ratios and the area–Mach curve.

3) Stagnation versus static conditions

The calculator uses stagnation temperature T0 and stagnation pressure P0 as energy and total-pressure references. For isentropic flow, the static temperature follows T/T0 = 1/(1+(γ−1)M²/2), and static pressure follows P/P0 = (T/T0)^{γ/(γ−1)}. Quick check: M = 2 with γ = 1.4 gives T/T0 ≈ 0.556 and P/P0 ≈ 0.128.

4) Interpreting Mach solutions and branches

Both P/P0 and A/A* can map to two different Mach numbers: one subsonic and one supersonic. The branch selector makes the choice explicit. Converging nozzles and diffusers usually use the subsonic branch; diverging nozzles downstream of a sonic throat usually use the supersonic branch.

5) Nozzle area ratio and choking

The area relation A/A* grows rapidly for large M, so small geometry changes can strongly affect supersonic speed. Choking occurs when the throat reaches M = 1, setting a maximum mass flow for given P0, T0, A*, γ, and R. The tool reports the corresponding choked reference mass flow ṁ*.

6) Velocity, dynamic pressure, and loads

The solver computes speed of sound a = √(γRT) and velocity V = Ma. Dynamic pressure q = ½ρV² is useful for estimating aerodynamic loads, probe survivability, and sensor range.

7) Mass flow estimation and scaling

Mass flux ρV is reported so you can scale mass flow with any section area A using ṁ = (ρV)A. For quick sizing, doubling A doubles ṁ at fixed local state. For nozzles, compare section ṁ to choked ṁ* to see whether your chosen A* is limiting.

8) Practical validation and limitations

Use the example table to sanity-check trends: lower P/P0 implies higher Mach, and A/A* = 1 implies M ≈ 1 on both branches. This model excludes shocks, friction, and heat transfer; real nozzles and ducts often require losses or shock relations. Treat these results as a first-pass, then refine with loss models, measured total-pressure drop, or CFD.

FAQs

1) What is the valid range of Mach number here?

Any positive Mach is accepted, but extreme values can be nonphysical for your setup. For ratio inversion, the solver searches up to M = 50 on the supersonic branch.

2) Why can the same A/A* give two Mach numbers?

The area–Mach relation has a minimum at M = 1. Values above 1 occur on both sides of that minimum, producing one subsonic and one supersonic solution.

3) How do I know if my nozzle is choked?

If a physical throat exists and downstream conditions drive the throat to M = 1, mass flow is capped by ṁ*. Compare your operating mass flow to ṁ* for consistency.

4) Should I use static or stagnation inputs?

Use stagnation inputs for T0 and P0. The solver then computes static T and P from Mach. If you only know static values, convert to stagnation before using the tool.

5) What pressure unit should I choose?

Pick Pa, kPa, or bar to match your data. Internally the solver converts to Pa for calculations, then converts outputs back to your selected unit for display.

6) Why does my pressure-ratio solve fail sometimes?

If P/P0 is outside (0,1) or inconsistent with the chosen branch range, no sign change occurs for the bisection. Adjust the ratio, γ, or branch and try again.

7) Does this include shocks or friction?

No. The solver assumes one-dimensional, isentropic, perfect-gas flow. For shocks, use normal/oblique shock relations; for ducts, include Fanno/Rayleigh effects or loss models.