VT Compressible Flow Calculator

Example Data Table

Formula Used

The calculator uses ideal gas and one dimensional compressible flow relations.

• Speed of sound: a = sqrt(gamma R T)
• Velocity: V = M a
• Density: rho = P / (R T)
• Total temperature: T0 = T [1 + ((gamma - 1) / 2) M²]
• Total pressure: P0 = P [1 + ((gamma - 1) / 2) M²]^(gamma / (gamma - 1))
• Mass flow: mdot = rho V A
• Reynolds number: Re = rho V L / mu
• Area relation: A/A* = (1/M){(2/(gamma + 1))[1 + ((gamma - 1)/2)M²]}^((gamma + 1)/(2(gamma - 1)))
• Normal shock values are added when Mach is greater than one.

How to Use This Calculator

1. Enter Mach number for the gas stream.
2. Enter static temperature in kelvin.
3. Enter static pressure in kilopascals.
4. Set gamma and gas constant for your gas.
5. Add area, length, and viscosity for flow rate and Reynolds number.
6. Press the calculate button.
7. Review the result table below the header.
8. Use CSV or PDF buttons to save results.

Overview

Compressible flow matters when speed changes density. It appears in nozzles, ducts, turbines, jets, vents, and high speed air streams. A small pressure change can create a large velocity change. That is why engineers track Mach number first. Mach number compares local speed with local sound speed. The sound speed depends on gas temperature, gas constant, and heat ratio.

Key Uses

This calculator supports quick gas state checks. It estimates velocity, density, total temperature, total pressure, dynamic pressure, mass flow, and area ratio. It also reports normal shock values when the flow is supersonic. These results help with concept design and study work. They are not a replacement for certified simulation.

Inputs That Matter

Static pressure and temperature describe the local gas state. Gamma describes energy storage in the gas. The gas constant links pressure, density, and temperature. Area converts velocity and density into mass flow. Length and viscosity allow a Reynolds number estimate. Use consistent units. Review each input before trusting any result.

Interpreting Mach Results

Subsonic flow has Mach below one. Information can travel upstream. Sonic flow is near one. Choking may limit the mass flow. Supersonic flow is above one. Shocks may appear after compression, turns, or area changes. A normal shock raises pressure and temperature. It lowers Mach number and total pressure.

Area Ratio Meaning

The area ratio compares a local section with sonic throat area. For isentropic flow, each area ratio above one can match a subsonic or supersonic branch. The calculator reports the mathematical ratio from the entered Mach number. It does not choose a nozzle branch for you. Use geometry and boundary pressure to decide.

Practical Workflow

Start with air defaults. Enter measured pressure and temperature. Set Mach from a probe, estimate, or design target. Add flow area when mass flow is needed. Add viscosity and length when scale effects matter. Submit the form. Then inspect totals and shock warnings. Export the table for reports.

Limitations

The formulas assume one dimensional, steady, ideal gas behavior. Heat transfer, friction, chemistry, humidity, and real gas effects are ignored. Shock relations apply only to a straight normal shock. Use conservative margins for hardware. For final design, compare results with experiments, standards, or validated flow software.

FAQs