## Density Ratio across Oblique Shock Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
ρshockratio = (κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2)))
This formula uses 3 Variables
Variables Used
Density Ratio across Shock - Density ratio across shock is the ratio of the downstream density to the upstream density across the 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
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
ρshockratio = (κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2))) --> (1.392758+1)*(2^2)/(2+((1.392758-1)*(2^2)))
Evaluating ... ...
ρshockratio = 2.6801865679165
STEP 3: Convert Result to Output's Unit
2.6801865679165 --> No Conversion Required
2.6801865679165 <-- Density Ratio across Shock
(Calculation completed in 00.000 seconds)
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## Credits

Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
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## < 19 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)))))
Prandtl Meyer function at upstream Mach number
Prandtl Meyer Function at upstream Mach no. = sqrt((Specific Heat Ratio Dynamic+1)/(Specific Heat Ratio Dynamic-1))*atan(sqrt(((Specific Heat Ratio Dynamic-1)*((Mach Number ahead of shock^2)-1))/(Specific Heat Ratio Dynamic+1)))-atan(sqrt(((Mach Number ahead of shock^2)-1)))
Prandtl Meyer function
Prandtl Meyer Function = sqrt((Specific Heat Ratio Dynamic+1)/(Specific Heat Ratio Dynamic-1))*atan(sqrt(((Specific Heat Ratio Dynamic-1)*((Mach Number^2)-1))/(Specific Heat Ratio Dynamic+1)))-atan(sqrt(((Mach Number^2)-1)))
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))))
Flow deflection angle
Flow Deflection angle = atan((2*cot(Oblique shock angle)*(((Mach Number ahead of shock*sin(Oblique shock angle))^2)-1))/(((Mach Number ahead of shock^2)*(Specific Heat Ratio Dynamic+cos(2*Oblique shock angle)))+2))
Pressure behind expansion fan
Pressure behind expansion fan = Pressure ahead Expansion Fan*((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2)))^((Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic-1))
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)))
Pressure Ratio across Expansion Fan
Pressure Ratio across Expansion Fan = ((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2)))^((Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic-1))
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))))
Temperature behind expansion fan
Temperature behind Expansion Fan = Temperature ahead Expansion Fan*((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2)))
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)))
Temperature Ratio across Expansion Fan
Temperature Ratio across Expansion Fan = (1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2))
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))
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)
Component of Downstream Mach normal to oblique shock
Downstream Mach Normal to Oblique Shock = Mach Number behind shock*sin(Oblique shock angle-Flow Deflection angle)
Component of Upstream Mach normal to oblique shock
Component of upstream mach normal to oblique shock = Mach Number ahead of shock*sin(Oblique shock angle)
Flow Deflection Angle using Prandtl Meyer function
Flow Deflection angle = Prandtl Meyer Function at downstream Mach no.-Prandtl Meyer Function at upstream Mach no.
Rearward Mach Angle of Expansion Fan
Rearward Mach Angle = arsin(1/Mach Number behind Expansion Fan)
Forward Mach angle of expansion fan
Forward Mach Angle = arsin(1/Mach Number ahead Expansion Fan)

## Density Ratio across Oblique Shock Formula

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)))
ρshockratio = (κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2)))

## What is oblique shock?

A shock wave that makes an oblique angle with the upstream flow, is called oblique shock. A normal shock wave is a special case of a general family of oblique shock, where the wave angle is 90°.

## What is Wave angle and Mach angle?

Wave angle is the angle that oblique shock makes with the upstream direction of flow. Mach angle is the angle formed between the Mach wave (an envelope of disturbance) and freestream direction of flow. Mach wave is the limiting case for the oblique shock (i.e., it is an infinitely weak oblique shock).

## How to Calculate Density Ratio across Oblique Shock?

Density Ratio across Oblique Shock calculator uses 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))) to calculate the Density Ratio across Shock, The Density ratio across oblique shock formula is obtained by substituting the normal component of upstream Mach no. in the density ratio formula for the normal shock. Density Ratio across Shock is denoted by ρshockratio symbol.

How to calculate Density Ratio across Oblique Shock using this online calculator? To use this online calculator for Density Ratio across Oblique Shock, enter Specific Heat Ratio Dynamic (κ) & Component of upstream mach normal to oblique shock (Mn1) and hit the calculate button. Here is how the Density Ratio across Oblique Shock calculation can be explained with given input values -> 2.680187 = (1.392758+1)*(2^2)/(2+((1.392758-1)*(2^2))).

### FAQ

What is Density Ratio across Oblique Shock?
The Density ratio across oblique shock formula is obtained by substituting the normal component of upstream Mach no. in the density ratio formula for the normal shock and is represented as ρshockratio = (κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2))) or 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))). 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 Density Ratio across Oblique Shock?
The Density ratio across oblique shock formula is obtained by substituting the normal component of upstream Mach no. in the density ratio formula for the normal shock is calculated using 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))). To calculate Density Ratio across Oblique Shock, you need 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 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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