Temperature behind Expansion Fan Calculator

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

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Oblique Shock and Expansion Waves

Governing Equations and Sound Wave

Normal Shock Wave

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Expansion Waves

Oblique Shock

✖Temperature ahead of expansion fan is the temperature in the upstream direction of the expansion fan.ⓘ Temperature Ahead of Expansion Fan [T₁]			+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%

✖Temperature behind expansion fan is the temperature in the downstream direction of the expansion fan.ⓘ Temperature behind Expansion Fan [T₂]

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Formula

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Temperature behind Expansion Fan

Formula

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

Example

`"288.065K"="394.12K"*((1+0.5*("1.41"-1)*("5")^2)/(1+0.5*("1.41"-1)*("6")^2))`

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Temperature behind Expansion Fan Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
T₂ = T₁*((1+0.5*(γ_e-1)*M_e1^2)/(1+0.5*(γ_e-1)*M_e2^2))
This formula uses 5 Variables

Variables Used

Temperature Behind Expansion Fan - (Measured in Kelvin) - Temperature behind expansion fan is the temperature in the downstream direction of the expansion fan.
Temperature Ahead of Expansion Fan - (Measured in Kelvin) - Temperature ahead of expansion fan is the temperature 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

Temperature Ahead of Expansion Fan: 394.12 Kelvin --> 394.12 Kelvin 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

T₂ = T₁*((1+0.5*(γ_e-1)*M_e1^2)/(1+0.5*(γ_e-1)*M_e2^2)) --> 394.12*((1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2))

Evaluating ... ...

T₂ = 288.065035799523

STEP 3: Convert Result to Output's Unit

288.065035799523 Kelvin --> No Conversion Required

FINAL ANSWER

288.065035799523 ≈ 288.065 Kelvin <-- Temperature Behind Expansion Fan

(Calculation completed in 00.020 seconds)

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Home » Physics » Aerodynamics » Compressible Flow » Oblique Shock and Expansion Waves » Expansion Waves » Temperature 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)

Temperature behind Expansion Fan Formula

Why expansion wave is direct antithesis of shock wave?

Across the expansion wave, the Mach number increases, pressure, temperature and density decreases and the flow is isentropic. Hence, an expansion wave is the direct antithesis of a shock wave.

How to Calculate Temperature behind Expansion Fan?

Temperature behind Expansion Fan calculator uses 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)) to calculate the Temperature Behind Expansion Fan, The Temperature behind Expansion Fan formula is derived from the ideal gas law and the concept of isentropic flow. It relates the temperature change to the Mach number through the specific heat ratio. Temperature Behind Expansion Fan is denoted by T₂ symbol.

How to calculate Temperature behind Expansion Fan using this online calculator? To use this online calculator for Temperature behind Expansion Fan, enter Temperature Ahead of Expansion Fan (T₁), 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 Temperature behind Expansion Fan calculation can be explained with given input values -> 288.3805 = 394.12*((1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2)).

FAQ

What is Temperature behind Expansion Fan?

The Temperature behind Expansion Fan formula is derived from the ideal gas law and the concept of isentropic flow. It relates the temperature change to the Mach number through the specific heat ratio and is represented as T₂ = T₁*((1+0.5*(γ_e-1)*M_e1^2)/(1+0.5*(γ_e-1)*M_e2^2)) or 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 ahead of expansion fan is the temperature 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 Temperature behind Expansion Fan?

The Temperature behind Expansion Fan formula is derived from the ideal gas law and the concept of isentropic flow. It relates the temperature change to the Mach number through the specific heat ratio is calculated using 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)). To calculate Temperature behind Expansion Fan, you need Temperature Ahead of Expansion Fan (T₁), 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 Temperature 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.

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