Calculator
Formula Used
Low-speed (incompressible) approximation
When compressibility is negligible, stagnation pressure is the static pressure plus dynamic pressure:
p₀ = p + ½ ρ V²
Compressible (isentropic) relation
For isentropic deceleration to zero velocity:
p₀ = p · (1 + (γ−1)/2 · M²)^(γ/(γ−1))
If Mach is not entered, the calculator estimates it using speed of sound:
a = √(γ R T), M = V/a
How to Use This Calculator
- Select a method. Use compressible for higher speeds or gases.
- Enter static pressure and choose a pressure unit.
- For compressible flows, enter Mach number or provide velocity and temperature.
- Pick a gas preset, or switch to custom and enter γ and R.
- For low-speed flows, enter density and velocity.
- Click Calculate. Use CSV or PDF to export results.
Example Data Table
These sample cases illustrate typical inputs. Use them to validate your own results.
| Case | Method | p (kPa) | V (m/s) | T (K) | M | γ |
|---|---|---|---|---|---|---|
| 1 | Low-speed | 101.325 | 30 | — | — | — |
| 2 | Compressible | 85 | 250 | 288.15 | (auto) | 1.40 |
| 3 | Compressible | 50 | — | 300 | 1.50 | 1.40 |
What Stagnation Pressure Represents
Stagnation pressure (total pressure) is the pressure a moving fluid would have if it were brought to rest without losses. It combines static pressure with the pressure rise associated with kinetic energy. Engineers use it to track energy conversion in ducts, nozzles, diffusers, and external flows.
Two Common Calculation Paths
For low-speed, nearly incompressible flow, total pressure is approximated as p₀ = p + ½ρV². When compressibility matters, an isentropic relation links total and static pressure through Mach number: p₀ = p[1 + (γ−1)M²/2]^{γ/(γ−1)}. This calculator supports both approaches side by side.
When Compressibility Becomes Important
Compressibility effects become noticeable above about M ≈ 0.3. At M = 0.6 in air (γ = 1.4) with p = 101.3 kPa, the isentropic formula gives p₀ ≈ 129.2 kPa. The incompressible equation would underpredict the total pressure and can distort comparisons.
Typical Engineering Magnitudes
In an HVAC duct at 50 m/s with ρ = 1.2 kg/m³, the dynamic component ½ρV² is 1500 Pa (1.5 kPa). A 100 kPa static pressure therefore becomes about 101.5 kPa total. In fan testing, this difference is often within sensor range, so resolution matters.
Role of γ and Gas Selection
The specific heat ratio γ controls how strongly total pressure rises with Mach number. Air is often modeled with γ ≈ 1.4, while hot combustion gases can be closer to 1.3, and monatomic gases approach 1.67. Choosing the right model improves comparisons across temperature ranges and operating points.
Practical Measurement Context
A Pitot-static probe measures stagnation pressure at the tip and static pressure via side ports. Their difference relates to dynamic pressure and can be converted to velocity for incompressible flow. For compressible flows, p₀ and p are commonly used to solve for Mach number, then infer velocity and density.
Assumptions and Data Quality Checks
The compressible option assumes isentropic deceleration, meaning no shocks and minimal viscous loss. Shocks, turbulence, or boundary layers reduce measured total pressure. If results look low, check probe alignment, blockage, and whether γ, density, and pressure units match your conditions.
Units, Outputs, and Export Workflows
Enter pressure in Pa, kPa, bar, or psi. Use kg/m³ for density and m/s for velocity in the incompressible option. The calculator converts and reports p₀ clearly, then exports results to CSV or PDF for records. Validate your setup using the example cases before applying field data.
FAQs
1. What is the difference between static and stagnation pressure?
Static pressure is the local thermodynamic pressure of the fluid. Stagnation pressure is the pressure after the flow is ideally slowed to zero velocity, so it includes the kinetic-energy contribution and is always greater than or equal to static pressure.
2. Which calculation option should I choose?
Use the incompressible option when Mach number is low (roughly below 0.3) and density changes are negligible. Use the compressible isentropic option when you know Mach number or when high-speed gas flow makes compressibility important.
3. Why does Mach number matter so much?
In compressible flow, density changes with speed. The isentropic relation raises total pressure more strongly as Mach increases, so using the incompressible formula at higher Mach can significantly underpredict stagnation pressure.
4. Can I use this to find Mach number from measurements?
Yes. If you measure total pressure and static pressure, you can compute the pressure ratio p0/p and solve the isentropic relation for Mach number. This calculator focuses on p0, but the same ratio is the key input for Mach estimation.
5. My measured total pressure seems too low. What could cause that?
Real probes experience losses: shocks, turbulence, viscous effects, misalignment, or blockage can reduce measured p0. Also confirm units, sensor calibration, and that the selected γ and gas model match your test conditions.
6. What units can I enter and what units are recommended?
You can enter pressure in Pa, kPa, bar, or psi. For the incompressible option, use density in kg/m³ and velocity in m/s for clean interpretation. Keep inputs consistent to avoid conversion mistakes.
7. What γ value should I use for air and other gases?
For many engineering problems, air is approximated with γ = 1.4. Hot combustion gases may be closer to 1.3, and monatomic gases approach 1.67. If you have a better γ for your temperature range, use it.