## Pressure Ratio across Expansion Fan Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
Pratio = ((1+0.5*(κ-1)*(Me1^2))/(1+0.5*(κ-1)*(Me2^2)))^((κ)/(κ-1))
This formula uses 4 Variables
Variables Used
Pressure Ratio across Expansion Fan - Pressure ratio across expansion fan is the ratio of downstream and upstream pressure across 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.
Mach Number ahead Expansion Fan - Mach number ahead expansion fan is the Mach number of the upstream flow.
Mach Number behind Expansion Fan - Mach Number behind Expansion Fan is the Mach number of downstream flow across expansion fan.
STEP 1: Convert Input(s) to Base Unit
Specific Heat Ratio Dynamic: 1.392758 --> No Conversion Required
Mach Number ahead Expansion Fan: 5 --> No Conversion Required
Mach Number behind Expansion Fan: 6 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pratio = ((1+0.5*(κ-1)*(Me1^2))/(1+0.5*(κ-1)*(Me2^2)))^((κ)/(κ-1)) --> ((1+0.5*(1.392758-1)*(5^2))/(1+0.5*(1.392758-1)*(6^2)))^((1.392758)/(1.392758-1))
Evaluating ... ...
Pratio = 0.331278800624972
STEP 3: Convert Result to Output's Unit
0.331278800624972 --> No Conversion Required
0.331278800624972 <-- Pressure Ratio across Expansion Fan
(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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PSG College of Technology (PSGCT), Coimbatore
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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)

## Pressure Ratio across Expansion Fan Formula

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))
Pratio = ((1+0.5*(κ-1)*(Me1^2))/(1+0.5*(κ-1)*(Me2^2)))^((κ)/(κ-1))

## When an expansion fan is formed?

When a flow is turned away from itself, an expansion fan is formed. The expansion through the wave takes place across a continuous succession of Mach waves and entropy change is zero for each Mach wave, hence the expansion is isentropic.

## What is forward and rearward Mach angle?

The forward Machangle is the angle formed between the forward Mach line and upstream direction of the flow. The rearward Mach angle is the angle formed between the rearward Mach line and downstream flow direction (parallel to convex corner).

## How to Calculate Pressure Ratio across Expansion Fan?

Pressure Ratio across Expansion Fan calculator uses 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)) to calculate the Pressure Ratio across Expansion Fan, Pressure Ratio across Expansion Fan formula is obtained as the ratio of static to stagnation pressure ratio downstream to upstream across the expansion fan. Pressure Ratio across Expansion Fan is denoted by Pratio symbol.

How to calculate Pressure Ratio across Expansion Fan using this online calculator? To use this online calculator for Pressure Ratio across Expansion Fan, enter Specific Heat Ratio Dynamic (κ), Mach Number ahead Expansion Fan (Me1) & Mach Number behind Expansion Fan (Me2) and hit the calculate button. Here is how the Pressure Ratio across Expansion Fan calculation can be explained with given input values -> 0.331279 = ((1+0.5*(1.392758-1)*(5^2))/(1+0.5*(1.392758-1)*(6^2)))^((1.392758)/(1.392758-1)).

### FAQ

What is Pressure Ratio across Expansion Fan?
Pressure Ratio across Expansion Fan formula is obtained as the ratio of static to stagnation pressure ratio downstream to upstream across the expansion fan and is represented as Pratio = ((1+0.5*(κ-1)*(Me1^2))/(1+0.5*(κ-1)*(Me2^2)))^((κ)/(κ-1)) or 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)). The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at constant volume, Mach number ahead expansion fan is the Mach number of the upstream flow & Mach Number behind Expansion Fan is the Mach number of downstream flow across expansion fan.
How to calculate Pressure Ratio across Expansion Fan?
Pressure Ratio across Expansion Fan formula is obtained as the ratio of static to stagnation pressure ratio downstream to upstream across the expansion fan is calculated using 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)). To calculate Pressure Ratio across Expansion Fan, you need Specific Heat Ratio Dynamic (κ), Mach Number ahead Expansion Fan (Me1) & Mach Number behind Expansion Fan (Me2). With our tool, you need to enter the respective value for Specific Heat Ratio Dynamic, Mach Number ahead Expansion Fan & Mach Number behind Expansion Fan and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. Let Others Know