Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number Calculator

↳

⤿

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

⤿

Normal Shock Wave

Governing Equations and Sound Wave

Oblique Shock and Expansion Waves

⤿

Downstream Shock Waves

Normal Shock Relations

Property Change Across Shock Waves

Upstream Shock Waves

✖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%

✖Static Pressure Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave.ⓘ Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number [P₂]

⎘ Copy

👎

Formula

✖

Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number

Formula

`"P"_{"2"} = "P"_{"1"}*(1+((2*"γ")/("γ"+1))*("M"_{"1"}^2-1))`

Example

`"158.4306Pa"="65.374Pa"*(1+((2*"1.4")/("1.4"+1))*(("1.49")^2-1))`

Calculator

LaTeX

Reset

👍

Download Normal Shock Wave Formulas PDF

Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
P₂ = P₁*(1+((2*γ)/(γ+1))*(M₁^2-1))
This formula uses 4 Variables

Variables Used

Static pressure Behind Normal shock - (Measured in Pascal) - Static Pressure Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave.
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

P₂ = P₁*(1+((2*γ)/(γ+1))*(M₁^2-1)) --> 65.374*(1+((2*1.4)/(1.4+1))*(1.49^2-1))

Evaluating ... ...

P₂ = 158.4306203

STEP 3: Convert Result to Output's Unit

158.4306203 Pascal --> No Conversion Required

FINAL ANSWER

158.4306203 ≈ 158.4306 Pascal <-- Static pressure Behind Normal shock

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Aerodynamics » Compressible Flow » Normal Shock Wave » Downstream Shock Waves » Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number

Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

Maiarutselvan V has verified this Calculator and 300+ more calculators!

< 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

Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number Formula

How to obtain pressure ratio across normal shock?

Pressure ratio across normal shock is obtained by rearranging the momentum equation and applying the continuity equation and density ratio formula. It is also a function of specific heat ratio and upstream Mach number.

How to Calculate Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number?

Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number calculator uses 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)) to calculate the Static pressure Behind Normal shock, The Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number calculates the static pressure of a fluid behind a normal shock wave using the provided upstream pressure and Mach number. This formula incorporates the ratio of specific heats for the fluid and accounts for the change in pressure resulting from the shock wave passage. Static pressure Behind Normal shock is denoted by P₂ symbol.

How to calculate Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number using this online calculator? To use this online calculator for Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number, 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 Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number calculation can be explained with given input values -> 65.52662 = 65.374*(1+((2*1.4)/(1.4+1))*(1.49^2-1)).

FAQ

What is Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number?

The Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number calculates the static pressure of a fluid behind a normal shock wave using the provided upstream pressure and Mach number. This formula incorporates the ratio of specific heats for the fluid and accounts for the change in pressure resulting from the shock wave passage and is represented as P₂ = P₁*(1+((2*γ)/(γ+1))*(M₁^2-1)) or 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)). 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 Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number?

The Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number calculates the static pressure of a fluid behind a normal shock wave using the provided upstream pressure and Mach number. This formula incorporates the ratio of specific heats for the fluid and accounts for the change in pressure resulting from the shock wave passage is calculated using 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)). To calculate Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number, 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.

How many ways are there to calculate Static pressure Behind Normal shock?

In this formula, Static pressure Behind Normal shock uses Static Pressure Ahead of Normal Shock, Specific Heat Ratio & Mach Number Ahead of Normal Shock. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search