Pressure behind oblique shock for given upstream pressure and normal upstream Mach number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Static pressure behind shock = Static pressure ahead of shock*(1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))
Pb = Pa*(1+((2*κ)/(κ+1))*((Mn1^2)-1))
This formula uses 4 Variables
Variables Used
Static pressure behind shock - (Measured in Pascal) - Static pressure behind shock is the static pressure in the downstream direction of shock.
Static pressure ahead of shock - (Measured in Pascal) - Static pressure ahead of shock is the pressure in the upstream direction of shock.
Specific Heat Ratio Dynamic - The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Component of upstream mach normal to oblique shock - Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave.
STEP 1: Convert Input(s) to Base Unit
Static pressure ahead of shock: 16 Pascal --> 16 Pascal No Conversion Required
Specific Heat Ratio Dynamic: 1.392758 --> No Conversion Required
Component of upstream mach normal to oblique shock: 2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pb = Pa*(1+((2*κ)/(κ+1))*((Mn1^2)-1)) --> 16*(1+((2*1.392758)/(1.392758+1))*((2^2)-1))
Evaluating ... ...
Pb = 71.8789346854132
STEP 3: Convert Result to Output's Unit
71.8789346854132 Pascal --> No Conversion Required
FINAL ANSWER
71.8789346854132 Pascal <-- Static pressure behind shock
(Calculation completed in 00.017 seconds)

Credits

Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
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Verified by Maiarutselvan V
PSG College of Technology (PSGCT), Coimbatore
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10+ Oblique Shock and Expansion Waves Calculators

Temperature behind oblique shock for given upstream temperature and normal upstream Mach number
Temperature behind shock = Temperature ahead of shock*((1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))) Go
Temperature Ratio across Oblique Shock
Temperature ratio across shock = (1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))) Go
Pressure behind expansion fan
Pressure behind expansion fan = Pressure ahead expansion fan*((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach no. behind expansion fan^2)))^((Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic-1)) Go
Component of downstream Mach number normal to oblique shock for given normal upstream Mach number
Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*((Specific Heat Ratio Dynamic-1)*Component of upstream mach normal to oblique shock^2))/(Specific Heat Ratio Dynamic*Component of upstream mach normal to oblique shock^2-0.5*(Specific Heat Ratio Dynamic-1))) Go
Pressure Ratio across Expansion Fan
Pressure ratio across expansion fan = ((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach no. behind expansion fan^2)))^((Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic-1)) Go
Density behind oblique shock for given upstream density and normal upstream Mach number
Density behind shock = Density ahead of shock*((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))) Go
Density Ratio across Oblique Shock
Density ratio across shock = (Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))) Go
Pressure behind oblique shock for given upstream pressure and normal upstream Mach number
Static pressure behind shock = Static pressure ahead of shock*(1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1)) Go
Temperature Ratio across Expansion Fan
Temperature ratio across expansion fan = (1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach no. behind expansion fan^2)) Go
Pressure Ratio across Oblique shock
Pressure ratio across shock = 1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1) Go

Pressure behind oblique shock for given upstream pressure and normal upstream Mach number Formula

Static pressure behind shock = Static pressure ahead of shock*(1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))
Pb = Pa*(1+((2*κ)/(κ+1))*((Mn1^2)-1))

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 shock = Static pressure ahead of shock*(1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1)) to calculate the Static pressure behind shock, The Pressure behind oblique shock for given upstream pressure and normal upstream Mach number formula is obtained by multiplying the pressure ahead of an oblique shock to pressure ratio across the oblique shock. Static pressure behind shock is denoted by Pb 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 shock (Pa), Specific Heat Ratio Dynamic (κ) & Component of upstream mach normal to oblique shock (Mn1) 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 -> 71.87893 = 16*(1+((2*1.392758)/(1.392758+1))*((2^2)-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 is obtained by multiplying the pressure ahead of an oblique shock to pressure ratio across the oblique shock and is represented as Pb = Pa*(1+((2*κ)/(κ+1))*((Mn1^2)-1)) or Static pressure behind shock = Static pressure ahead of shock*(1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1)). Static pressure ahead of shock is the pressure in the upstream direction of shock, The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave.
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 is obtained by multiplying the pressure ahead of an oblique shock to pressure ratio across the oblique shock is calculated using Static pressure behind shock = Static pressure ahead of shock*(1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of 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 shock (Pa), Specific Heat Ratio Dynamic (κ) & Component of upstream mach normal to oblique shock (Mn1). With our tool, you need to enter the respective value for Static pressure ahead of shock, Specific Heat Ratio Dynamic & Component of 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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