## Component of downstream Mach number normal to oblique shock for given normal upstream Mach number Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
Mn2 = sqrt((1+0.5*((κ-1)*Mn1^2))/(κ*Mn1^2-0.5*(κ-1)))
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Downstream Mach Normal to Oblique Shock - Downstream Mach Normal to Oblique Shock is that component of downstream Mach number which is normal to oblique shockwave.
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
Mn2 = sqrt((1+0.5*((κ-1)*Mn1^2))/(κ*Mn1^2-0.5*(κ-1))) --> sqrt((1+0.5*((1.392758-1)*2^2))/(1.392758*2^2-0.5*(1.392758-1)))
Evaluating ... ...
Mn2 = 0.576377020834194
STEP 3: Convert Result to Output's Unit
0.576377020834194 --> No Conversion Required
0.576377020834194 <-- Downstream Mach Normal to Oblique 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)

## Component of downstream Mach number normal to oblique shock for given normal upstream Mach number Formula

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)))
Mn2 = sqrt((1+0.5*((κ-1)*Mn1^2))/(κ*Mn1^2-0.5*(κ-1)))

## What happens when flow deflection angle is 0° in supersonic flow?

When flow deflection is 0° then the wave angle will be either 90° or μ. The case of β= 90° corresponds to a normal shock wave and β=μ corresponds to Mach wave. In both cases, the flow streamlines experience no deflection across the wave.

## How to Calculate Component of downstream Mach number normal to oblique shock for given normal upstream Mach number?

Component of downstream Mach number normal to oblique shock for given normal upstream Mach number calculator uses 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))) to calculate the Downstream Mach Normal to Oblique Shock, The Component of downstream Mach number normal to oblique shock for given normal upstream Mach number formula is a function of the ratio of specific heat & normal component of upstream Mach no. Downstream Mach Normal to Oblique Shock is denoted by Mn2 symbol.

How to calculate Component of downstream Mach number normal to oblique shock for given normal upstream Mach number using this online calculator? To use this online calculator for Component of downstream Mach number normal to oblique shock for given normal upstream Mach number, enter Specific Heat Ratio Dynamic (κ) & Component of upstream mach normal to oblique shock (Mn1) and hit the calculate button. Here is how the Component of downstream Mach number normal to oblique shock for given normal upstream Mach number calculation can be explained with given input values -> 0.576377 = sqrt((1+0.5*((1.392758-1)*2^2))/(1.392758*2^2-0.5*(1.392758-1))).

### FAQ

What is Component of downstream Mach number normal to oblique shock for given normal upstream Mach number?
The Component of downstream Mach number normal to oblique shock for given normal upstream Mach number formula is a function of the ratio of specific heat & normal component of upstream Mach no and is represented as Mn2 = sqrt((1+0.5*((κ-1)*Mn1^2))/(κ*Mn1^2-0.5*(κ-1))) or 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))). 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 Component of downstream Mach number normal to oblique shock for given normal upstream Mach number?
The Component of downstream Mach number normal to oblique shock for given normal upstream Mach number formula is a function of the ratio of specific heat & normal component of upstream Mach no is calculated using 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))). To calculate Component of downstream Mach number normal to oblique shock for given normal upstream Mach number, 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.
How many ways are there to calculate Downstream Mach Normal to Oblique Shock?
In this formula, Downstream Mach Normal to Oblique Shock uses Specific Heat Ratio Dynamic & Component of upstream mach normal to oblique shock. We can use 1 other way(s) to calculate the same, which is/are as follows -
• Downstream Mach Normal to Oblique Shock = Mach Number behind shock*sin(Oblique shock angle-Flow Deflection angle) Let Others Know