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 00.004 seconds)

Credits

Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
Shikha Maurya has created this Calculator and 100+ more calculators!
Verified by Vinay Mishra
Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune
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15 Downstream Shock Waves Calculators

Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula
Go 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 Temperature behind Normal Shock for given Upstream Temperature and Mach Number
Go Temperature Behind Normal Shock = Temperature Ahead of Normal Shock*((1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)))
Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number
Go Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2))
Mach Number behind Shock
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)
Velocity behind Normal Shock by Normal Shock Momentum Equation
Go Velocity Downstream of Shock = sqrt((Static Pressure Ahead of Normal Shock-Static pressure Behind Normal shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2)/Density Behind Normal Shock)
Density behind Normal Shock using Normal Shock Momentum Equation
Go Density Behind Normal Shock = (Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Static pressure Behind Normal shock)/(Velocity Downstream of Shock^2)
Static Pressure behind Normal Shock using Normal Shock Momentum Equation
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
Density behind Normal Shock given Upstream Density and Mach Number
Go Density Behind Normal Shock = Density Ahead of Normal Shock*(((Specific Heat Ratio+1)*Mach Number^2)/(2+(Specific Heat Ratio-1)*Mach Number^2))
Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number
Go Static pressure Behind Normal shock = Static Pressure Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))
Velocity behind Normal Shock from Normal Shock Energy Equation
Go Velocity Downstream of Shock = sqrt(2*(Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2)/2-Enthalpy Behind Normal Shock))
Velocity behind Normal Shock
Go Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))
Enthalpy behind Normal Shock from Normal Shock Energy Equation
Go Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2-Velocity Downstream of Shock^2)/2
Flow Velocity Downstream of Shock Wave using Continuity Equation
Go Velocity Downstream of Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Density Behind Normal Shock
Density Downstream of Shock Wave using Continuity Equation
Go Density Behind Normal Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Velocity Downstream of Shock
Characteristic Mach Number behind Shock
Go Characteristic Mach Number Behind Shock = 1/Characteristic Mach Number Ahead of Shock

Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula Formula

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))

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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