Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula Calculator

✖Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock.ⓘ Static Pressure Ahead of Normal Shock [P₁]			+10% -10%
✖The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.ⓘ Mach Number Ahead of Normal Shock [M₁]			+10% -10%

✖Stagnation Pressure Behind Normal Shock is the stagnation or total or pitot pressure after passing through shock.ⓘ Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula [p₀₂]

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Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stagnation Pressure Behind Normal Shock = Static Pressure Ahead of Normal Shock*((1-Specific Heat Ratio+2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2)/(Specific Heat Ratio+1))*(((Specific Heat Ratio+1)^2*Mach Number Ahead of Normal Shock^2)/(4*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-2*(Specific Heat Ratio-1)))^((Specific Heat Ratio)/(Specific Heat Ratio-1))
p₀₂ = P₁*((1-γ+2*γ*M₁^2)/(γ+1))*(((γ+1)^2*M₁^2)/(4*γ*M₁^2-2*(γ-1)))^((γ)/(γ-1))
This formula uses 4 Variables

Variables Used

Stagnation Pressure Behind Normal Shock - (Measured in Pascal) - Stagnation Pressure Behind Normal Shock is the stagnation or total or pitot pressure after passing through shock.
Static Pressure Ahead of Normal Shock - (Measured in Pascal) - Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Mach Number Ahead of Normal Shock - Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.

STEP 1: Convert Input(s) to Base Unit

Static Pressure Ahead of Normal Shock: 65.374 Pascal --> 65.374 Pascal No Conversion Required
Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number Ahead of Normal Shock: 1.49 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

p₀₂ = P₁*((1-γ+2*γ*M₁^2)/(γ+1))*(((γ+1)^2*M₁^2)/(4*γ*M₁^2-2*(γ-1)))^((γ)/(γ-1)) --> 65.374*((1-1.4+2*1.4*1.49^2)/(1.4+1))*(((1.4+1)^2*1.49^2)/(4*1.4*1.49^2-2*(1.4-1)))^((1.4)/(1.4-1))

Evaluating ... ...

p₀₂ = 220.677542531544

STEP 3: Convert Result to Output's Unit

220.677542531544 Pascal --> No Conversion Required

FINAL ANSWER

220.677542531544 ≈ 220.6775 Pascal <-- Stagnation Pressure Behind Normal Shock

(Calculation completed in 00.020 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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Verified by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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< Downstream Shock Waves Calculators

Mach Number behind Shock

LaTeX Go Mach Number Behind Normal Shock = ((2+Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Mach Number Ahead of Normal Shock^2)/(2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Specific Heat Ratio+1))^(1/2)

Static Pressure behind Normal Shock using Normal Shock Momentum Equation

LaTeX Go Static pressure Behind Normal shock = Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Density Behind Normal Shock*Velocity Downstream of Shock^2

Velocity behind Normal Shock

LaTeX Go Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))

Characteristic Mach Number behind Shock

LaTeX Go Characteristic Mach Number Behind Shock = 1/Characteristic Mach Number Ahead of Shock

Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula Formula

LaTeX Go

Why airspeed measurement in supersonic flow are different than subsonic flow?

Airspeed measurement in supersonic flow is qualitatively different from the subsonic flow. In supersonic flow, a bow shock wave is formed ahead of the pitot tube. As a consequence, the total pressure measured at the nose of the pitot probe in supersonic flow will not be the same value as that associated with free stream pressure. That's why a separate shock wave theory is applied to relate pitot tube measurement to a free-stream Mach number

What is the use of Rayleigh pitot tube formula?

Rayleigh pitot formula relates the Pitot pressure (stagnation pressure downstream of normal shock) and the freestream static pressure, to the freestream Mach number. Therefore it is used to calculate the upstream flow Mach number when pitot pressure and free stream static pressure are known.

How to Calculate Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula?

Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula calculator uses Stagnation Pressure Behind Normal Shock = Static Pressure Ahead of Normal Shock*((1-Specific Heat Ratio+2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2)/(Specific Heat Ratio+1))*(((Specific Heat Ratio+1)^2*Mach Number Ahead of Normal Shock^2)/(4*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-2*(Specific Heat Ratio-1)))^((Specific Heat Ratio)/(Specific Heat Ratio-1)) to calculate the Stagnation Pressure Behind Normal Shock, The Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula calculates the stagnation pressure of a fluid behind a normal shock wave using the Rayleigh Pitot Tube formula. This equation incorporates parameters such as the static pressure ahead of the shock, the Mach number ahead of the shock, and the ratio of specific heats for the fluid. It provides valuable insights into the change in stagnation pressure as the fluid passes through the shock wave, aiding in the analysis of compressible flow phenomena. Stagnation Pressure Behind Normal Shock is denoted by p₀₂ symbol.

How to calculate Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula using this online calculator? To use this online calculator for Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula, enter Static Pressure Ahead of Normal Shock (P₁), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) and hit the calculate button. Here is how the Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula calculation can be explained with given input values -> 220.6775 = 65.374*((1-1.4+2*1.4*1.49^2)/(1.4+1))*(((1.4+1)^2*1.49^2)/(4*1.4*1.49^2-2*(1.4-1)))^((1.4)/(1.4-1)).

FAQ

What is Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula?

The Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula calculates the stagnation pressure of a fluid behind a normal shock wave using the Rayleigh Pitot Tube formula. This equation incorporates parameters such as the static pressure ahead of the shock, the Mach number ahead of the shock, and the ratio of specific heats for the fluid. It provides valuable insights into the change in stagnation pressure as the fluid passes through the shock wave, aiding in the analysis of compressible flow phenomena and is represented as p₀₂ = P₁*((1-γ+2*γ*M₁^2)/(γ+1))*(((γ+1)^2*M₁^2)/(4*γ*M₁^2-2*(γ-1)))^((γ)/(γ-1)) or Stagnation Pressure Behind Normal Shock = Static Pressure Ahead of Normal Shock*((1-Specific Heat Ratio+2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2)/(Specific Heat Ratio+1))*(((Specific Heat Ratio+1)^2*Mach Number Ahead of Normal Shock^2)/(4*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-2*(Specific Heat Ratio-1)))^((Specific Heat Ratio)/(Specific Heat Ratio-1)). Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock, The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.

How to calculate Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula?

The Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula calculates the stagnation pressure of a fluid behind a normal shock wave using the Rayleigh Pitot Tube formula. This equation incorporates parameters such as the static pressure ahead of the shock, the Mach number ahead of the shock, and the ratio of specific heats for the fluid. It provides valuable insights into the change in stagnation pressure as the fluid passes through the shock wave, aiding in the analysis of compressible flow phenomena is calculated using Stagnation Pressure Behind Normal Shock = Static Pressure Ahead of Normal Shock*((1-Specific Heat Ratio+2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2)/(Specific Heat Ratio+1))*(((Specific Heat Ratio+1)^2*Mach Number Ahead of Normal Shock^2)/(4*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-2*(Specific Heat Ratio-1)))^((Specific Heat Ratio)/(Specific Heat Ratio-1)). To calculate Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula, you need Static Pressure Ahead of Normal Shock (P₁), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁). With our tool, you need to enter the respective value for Static Pressure Ahead of Normal Shock, Specific Heat Ratio & Mach Number Ahead of Normal Shock and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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