Pressure Ratio across Expansion Fan Solution

STEP 0: Pre-Calculation Summary
Formula Used
Pressure Ratio Across Expansion Fan = ((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))
Pe,r = ((1+0.5*(γe-1)*Me1^2)/(1+0.5*(γe-1)*Me2^2))^((γe)/(γe-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 expansion fan.
Specific Heat Ratio Expansion Wave - The Specific Heat Ratio Expansion Wave is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Mach Number Ahead of Expansion Fan - Mach Number Ahead of 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 Expansion Wave: 1.41 --> No Conversion Required
Mach Number Ahead of Expansion Fan: 5 --> No Conversion Required
Mach Number Behind Expansion Fan: 6 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pe,r = ((1+0.5*(γe-1)*Me1^2)/(1+0.5*(γe-1)*Me2^2))^((γe)/(γe-1)) --> ((1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2))^((1.41)/(1.41-1))
Evaluating ... ...
Pe,r = 0.340265841483963
STEP 3: Convert Result to Output's Unit
0.340265841483963 --> No Conversion Required
FINAL ANSWER
0.340265841483963 0.340266 <-- Pressure Ratio Across Expansion Fan
(Calculation completed in 00.004 seconds)

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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10+ Expansion Waves Calculators

Flow Deflection Angle due to Expansion Wave
Go Flow Deflection angle = (sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Behind Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Behind Expansion Fan^2-1)))- (sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Ahead of Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Ahead of Expansion Fan^2-1)))
Prandtl Meyer Function at Upstream Mach Number
Go Prandtl Meyer Function at Upstream Mach no. = sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Ahead of Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Ahead of Expansion Fan^2-1))
Prandtl Meyer Function
Go Prandtl Meyer Function = sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number^2-1))
Pressure behind Expansion Fan
Go Pressure Behind Expansion Fan = Pressure Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))
Pressure Ratio across Expansion Fan
Go Pressure Ratio Across Expansion Fan = ((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))
Temperature behind Expansion Fan
Go Temperature Behind Expansion Fan = Temperature Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))
Temperature Ratio across Expansion Fan
Go Temperature Ratio Across Expansion Fan = (1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2)
Flow Deflection Angle using Prandtl Meyer Function
Go Flow Deflection angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.
Forward Mach Angle of Expansion Fan
Go Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan)
Rearward Mach Angle of Expansion Fan
Go Rearward Mach Angle = arsin(1/Mach Number Behind Expansion Fan)

Pressure Ratio across Expansion Fan Formula

Pressure Ratio Across Expansion Fan = ((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))
Pe,r = ((1+0.5*(γe-1)*Me1^2)/(1+0.5*(γe-1)*Me2^2))^((γe)/(γe-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 Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1)) to calculate the Pressure Ratio Across Expansion Fan, The pressure ratio across expansion fan is a measure of the change in pressure experienced by a fluid as it passes through the fan. Expansion fans are regions in a fluid flow where the flow velocity decreases and pressure increases due to an expansion in the flow area. Pressure Ratio Across Expansion Fan is denoted by Pe,r 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 Expansion Wave e), Mach Number Ahead of 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 -> 0.335105 = ((1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2))^((1.41)/(1.41-1)).

FAQ

What is Pressure Ratio across Expansion Fan?
The pressure ratio across expansion fan is a measure of the change in pressure experienced by a fluid as it passes through the fan. Expansion fans are regions in a fluid flow where the flow velocity decreases and pressure increases due to an expansion in the flow area and is represented as Pe,r = ((1+0.5*(γe-1)*Me1^2)/(1+0.5*(γe-1)*Me2^2))^((γe)/(γe-1)) or Pressure Ratio Across Expansion Fan = ((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1)). The Specific Heat Ratio Expansion Wave is the ratio of the heat capacity at constant pressure to heat capacity at constant volume, Mach Number Ahead of 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?
The pressure ratio across expansion fan is a measure of the change in pressure experienced by a fluid as it passes through the fan. Expansion fans are regions in a fluid flow where the flow velocity decreases and pressure increases due to an expansion in the flow area is calculated using Pressure Ratio Across Expansion Fan = ((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1)). To calculate Pressure Ratio across Expansion Fan, you need Specific Heat Ratio Expansion Wave e), Mach Number Ahead of Expansion Fan (Me1) & Mach Number Behind Expansion Fan (Me2). With our tool, you need to enter the respective value for Specific Heat Ratio Expansion Wave, Mach Number Ahead of 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.
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