Pressure behind Expansion Fan Calculator

↳

⤿

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

⤿

Oblique Shock and Expansion Waves

Governing Equations and Sound Wave

Normal Shock Wave

⤿

Expansion Waves

Oblique Shock

✖Pressure Ahead of Expansion Fan is the pressure in the upstream direction of the expansion fan.ⓘ Pressure Ahead of Expansion Fan [P₁]			+10% -10%
✖The Specific Heat Ratio Expansion Wave is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio Expansion Wave [γ_e]			+10% -10%
✖Mach Number Ahead of Expansion Fan is the Mach number of the upstream flow.ⓘ Mach Number Ahead of Expansion Fan [M_e1]			+10% -10%
✖Mach Number Behind Expansion Fan is the Mach number of downstream flow across the expansion fan.ⓘ Mach Number Behind Expansion Fan [M_e2]			+10% -10%

✖Pressure Behind Expansion Fan is the pressure in the downstream direction of the expansion fan.ⓘ Pressure behind Expansion Fan [P₂]

⎘ Copy

👎

Formula

✖

Pressure behind Expansion Fan

Formula

`"P"_{"2"} = "P"_{"1"}*((1+0.5*("γ"_{"e"}-1)*"M"_{"e1"}^2)/(1+0.5*("γ"_{"e"}-1)*"M"_{"e2"}^2))^(("γ"_{"e"})/("γ"_{"e"}-1))`

Example

`"13.61063Pa"="40Pa"*((1+0.5*("1.41"-1)*("5")^2)/(1+0.5*("1.41"-1)*("6")^2))^(("1.41")/("1.41"-1))`

Calculator

LaTeX

Reset

👍

Download Oblique Shock and Expansion Waves Formulas PDF

Pressure behind Expansion Fan Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
P₂ = P₁*((1+0.5*(γ_e-1)*M_e1^2)/(1+0.5*(γ_e-1)*M_e2^2))^((γ_e)/(γ_e-1))
This formula uses 5 Variables

Variables Used

Pressure Behind Expansion Fan - (Measured in Pascal) - Pressure Behind Expansion Fan is the pressure in the downstream direction of the expansion fan.
Pressure Ahead of Expansion Fan - (Measured in Pascal) - Pressure Ahead of Expansion Fan is the pressure in the upstream direction of the 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 the expansion fan.

STEP 1: Convert Input(s) to Base Unit

Pressure Ahead of Expansion Fan: 40 Pascal --> 40 Pascal No Conversion Required
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

P₂ = P₁*((1+0.5*(γ_e-1)*M_e1^2)/(1+0.5*(γ_e-1)*M_e2^2))^((γ_e)/(γ_e-1)) --> 40*((1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2))^((1.41)/(1.41-1))

Evaluating ... ...

P₂ = 13.6106336593585

STEP 3: Convert Result to Output's Unit

13.6106336593585 Pascal --> No Conversion Required

FINAL ANSWER

13.6106336593585 ≈ 13.61063 Pascal <-- Pressure Behind Expansion Fan

(Calculation completed in 00.020 seconds)

You are here -

Home » Physics » Aerodynamics » Compressible Flow » Oblique Shock and Expansion Waves » Expansion Waves » Pressure behind Expansion Fan

Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has verified this Calculator and 100+ more calculators!

< 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 behind Expansion Fan Formula

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 behind Expansion Fan?

Pressure behind Expansion Fan calculator uses 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)) to calculate the Pressure Behind Expansion Fan, The Pressure behind Expansion Fan formula is defined as the product of upstream static pressure ahead of expansion fan to the ratio of static to stagnation pressure ratio downstream to upstream across the expansion fan. Pressure Behind Expansion Fan is denoted by P₂ symbol.

How to calculate Pressure behind Expansion Fan using this online calculator? To use this online calculator for Pressure behind Expansion Fan, enter Pressure Ahead of Expansion Fan (P₁), Specific Heat Ratio Expansion Wave (γ_e), Mach Number Ahead of Expansion Fan (M_e1) & Mach Number Behind Expansion Fan (M_e2) and hit the calculate button. Here is how the Pressure behind Expansion Fan calculation can be explained with given input values -> 13.4042 = 40*((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 behind Expansion Fan?

The Pressure behind Expansion Fan formula is defined as the product of upstream static pressure ahead of expansion fan to the ratio of static to stagnation pressure ratio downstream to upstream across the expansion fan and is represented as P₂ = P₁*((1+0.5*(γ_e-1)*M_e1^2)/(1+0.5*(γ_e-1)*M_e2^2))^((γ_e)/(γ_e-1)) or 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 Ahead of Expansion Fan is the pressure in the upstream direction of the expansion fan, 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 the expansion fan.

How to calculate Pressure behind Expansion Fan?

The Pressure behind Expansion Fan formula is defined as the product of upstream static pressure ahead of expansion fan to the ratio of static to stagnation pressure ratio downstream to upstream across the expansion fan is calculated using 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)). To calculate Pressure behind Expansion Fan, you need Pressure Ahead of Expansion Fan (P₁), Specific Heat Ratio Expansion Wave (γ_e), Mach Number Ahead of Expansion Fan (M_e1) & Mach Number Behind Expansion Fan (M_e2). With our tool, you need to enter the respective value for Pressure Ahead of Expansion Fan, 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.

Home

FREE PDFs

🔍 Search