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

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

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Oblique Shock and Expansion Waves

Governing Equations and Sound Wave

Normal Shock Wave

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Oblique Shock

Expansion Waves

✖Static Pressure Ahead of Oblique Shock represents the pressure of a fluid or airflow before encountering an oblique shock wave.ⓘ Static Pressure Ahead of Oblique Shock [P_a]			+10% -10%
✖The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio Oblique Shock [γ_o]			+10% -10%
✖Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.ⓘ Upstream Mach Normal to Oblique Shock [M_n1]			+10% -10%

✖Static Pressure Behind Oblique Shock signifies the pressure of a fluid or airflow after passing through an oblique shock wave.ⓘ Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number [P_b]

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Formula

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

Formula

`"P"_{"b"} = "P"_{"a"}*(1+((2*"γ"_{"o"})/("γ"_{"o"}+1))*("M"_{"n1"}^2-1))`

Example

`"166.2829Pa"="58.5Pa"*(1+((2*"1.4")/("1.4"+1))*(("1.606")^2-1))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Static Pressure Behind Oblique Shock = Static Pressure Ahead of Oblique Shock*(1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))
P_b = P_a*(1+((2*γ_o)/(γ_o+1))*(M_n1^2-1))
This formula uses 4 Variables

Variables Used

Static Pressure Behind Oblique Shock - (Measured in Pascal) - Static Pressure Behind Oblique Shock signifies the pressure of a fluid or airflow after passing through an oblique shock wave.
Static Pressure Ahead of Oblique Shock - (Measured in Pascal) - Static Pressure Ahead of Oblique Shock represents the pressure of a fluid or airflow before encountering an oblique shock wave.
Specific Heat Ratio Oblique Shock - The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Upstream Mach Normal to Oblique Shock - Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.

STEP 1: Convert Input(s) to Base Unit

Static Pressure Ahead of Oblique Shock: 58.5 Pascal --> 58.5 Pascal No Conversion Required
Specific Heat Ratio Oblique Shock: 1.4 --> No Conversion Required
Upstream Mach Normal to Oblique Shock: 1.606 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_b = P_a*(1+((2*γ_o)/(γ_o+1))*(M_n1^2-1)) --> 58.5*(1+((2*1.4)/(1.4+1))*(1.606^2-1))

Evaluating ... ...

P_b = 166.282857

STEP 3: Convert Result to Output's Unit

166.282857 Pascal --> No Conversion Required

FINAL ANSWER

166.282857 ≈ 166.2829 Pascal <-- Static Pressure Behind Oblique Shock

(Calculation completed in 00.004 seconds)

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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

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< 10+ Oblique Shock Calculators

Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number

Go Temperature Behind Oblique Shock = Temperature Ahead of Oblique Shock*((1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)))

Flow Deflection Angle due to Oblique Shock

Go Flow Deflection Angle Oblique Shock = atan((2*cot(Oblique Shock Angle)*((Mach Number Ahead of Oblique Shock*sin(Oblique Shock Angle))^2-1))/(Mach Number Ahead of Oblique Shock^2*(Specific Heat Ratio Oblique Shock+cos(2*Oblique Shock Angle))+2))

Temperature Ratio across Oblique Shock

Go Temperature Ratio Across Oblique Shock = (1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2))

Component of Downstream Mach Number Normal to Oblique Shock for given Normal Upstream Mach Number

Go Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)/(Specific Heat Ratio Oblique Shock*Upstream Mach Normal to Oblique Shock^2-0.5*(Specific Heat Ratio Oblique Shock-1)))

Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number

Go Density Behind Oblique Shock = Density Ahead of Oblique Shock*((Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2))

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

Go Static Pressure Behind Oblique Shock = Static Pressure Ahead of Oblique Shock*(1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))

Density Ratio across Oblique Shock

Go Density Ratio Across Oblique Shock = (Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)

Component of Downstream Mach Normal to Oblique Shock

Go Downstream Mach Normal to Oblique Shock = Mach Number Behind Oblique Shock*sin(Oblique Shock Angle-Flow Deflection Angle Oblique Shock)

Pressure Ratio across Oblique Shock

Go Pressure Ratio Across Oblique Shock = 1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1)

Component of Upstream Mach Normal to Oblique Shock

Go Upstream Mach Normal to Oblique Shock = Mach Number Ahead of Oblique Shock*sin(Oblique Shock Angle)

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

What does total pressure loss indicates?

The loss of total pressure is an index of the efficiency of a fluid flow, the lower the total pressure loss, the more efficient is the flow process. The total pressure loss is higher for a single, strong normal shock than the oblique shock for the same flight conditions.

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

Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number calculator uses Static Pressure Behind Oblique Shock = Static Pressure Ahead of Oblique Shock*(1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1)) to calculate the Static Pressure Behind Oblique Shock, The Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number formula calculates the pressure of the fluid immediately behind an oblique shock wave, considering the upstream pressure and normal upstream Mach number. Static Pressure Behind Oblique Shock is denoted by P_b symbol.

How to calculate Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number using this online calculator? To use this online calculator for Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number, enter Static Pressure Ahead of Oblique Shock (P_a), Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1) and hit the calculate button. Here is how the Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number calculation can be explained with given input values -> 166.2829 = 58.5*(1+((2*1.4)/(1.4+1))*(1.606^2-1)).

FAQ

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

The Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number formula calculates the pressure of the fluid immediately behind an oblique shock wave, considering the upstream pressure and normal upstream Mach number and is represented as P_b = P_a*(1+((2*γ_o)/(γ_o+1))*(M_n1^2-1)) or Static Pressure Behind Oblique Shock = Static Pressure Ahead of Oblique Shock*(1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1)). Static Pressure Ahead of Oblique Shock represents the pressure of a fluid or airflow before encountering an oblique shock wave, The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.

How to calculate Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number?

The Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number formula calculates the pressure of the fluid immediately behind an oblique shock wave, considering the upstream pressure and normal upstream Mach number is calculated using Static Pressure Behind Oblique Shock = Static Pressure Ahead of Oblique Shock*(1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1)). To calculate Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number, you need Static Pressure Ahead of Oblique Shock (P_a), Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1). With our tool, you need to enter the respective value for Static Pressure Ahead of Oblique Shock, Specific Heat Ratio Oblique Shock & Upstream Mach Normal to Oblique 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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