Pressure Ratio across Oblique Shock Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
Pr = 1+((2*γo)/(γo+1))*(Mn1^2-1)
This formula uses 3 Variables
Variables Used
Pressure Ratio Across Oblique Shock - Pressure Ratio Across Oblique Shock indicates the ratio of pressures before and after passing through 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
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
Pr = 1+((2*γo)/(γo+1))*(Mn1^2-1) --> 1+((2*1.4)/(1.4+1))*(1.606^2-1)
Evaluating ... ...
Pr = 2.842442
STEP 3: Convert Result to Output's Unit
2.842442 --> No Conversion Required
FINAL ANSWER
2.842442 <-- Pressure Ratio Across Oblique 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 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 Ratio across Oblique Shock Formula

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)
Pr = 1+((2*γo)/(γo+1))*(Mn1^2-1)

Which inlet design of supersonic jet engine is preferable?

A normal shock inlet forms a normal shock ahead of the inlet, with an attendant large loss in total pressure. In contrast, an oblique shock inlet creates an oblique shock wave, and the flow subsequently passes through a relatively weak normal shock at the lip of the inlet. For the same flight conditions (Mach number and altitude), the total pressure loss for the oblique shock inlet is less than for a normal shock inlet. Hence, everything else being equal, the resulting engine thrust will be higher for the oblique shock inlet. Therefore, oblique shock inlets are preffered.

What does total pressure indicates?

The total pressure is an indicator of how much useful work can be done by gas. Everything else being equal, the higher the total pressure, the more useful is the flow.

How to Calculate Pressure Ratio across Oblique Shock?

Pressure Ratio across Oblique Shock calculator uses 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) to calculate the Pressure Ratio Across Oblique Shock, Pressure ratio across oblique shock formula is obtained by substituting the normal component of upstream Mach no. in the pressure ratio formula for the normal shock. Pressure Ratio Across Oblique Shock is denoted by Pr symbol.

How to calculate Pressure Ratio across Oblique Shock using this online calculator? To use this online calculator for Pressure Ratio across Oblique Shock, enter Specific Heat Ratio Oblique Shock o) & Upstream Mach Normal to Oblique Shock (Mn1) and hit the calculate button. Here is how the Pressure Ratio across Oblique Shock calculation can be explained with given input values -> 2.842442 = 1+((2*1.4)/(1.4+1))*(1.606^2-1).

FAQ

What is Pressure Ratio across Oblique Shock?
Pressure ratio across oblique shock formula is obtained by substituting the normal component of upstream Mach no. in the pressure ratio formula for the normal shock and is represented as Pr = 1+((2*γo)/(γo+1))*(Mn1^2-1) or 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). 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 Ratio across Oblique Shock?
Pressure ratio across oblique shock formula is obtained by substituting the normal component of upstream Mach no. in the pressure ratio formula for the normal shock is calculated using 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). To calculate Pressure Ratio across Oblique Shock, you need Specific Heat Ratio Oblique Shock o) & Upstream Mach Normal to Oblique Shock (Mn1). With our tool, you need to enter the respective value for 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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