Temperature Ratio across Expansion Fan Calculator

✖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 Ratio Across Expansion Fan is the ratio of downstream temperature to upstream temperature across the expansion fan.ⓘ Temperature Ratio across Expansion Fan [T_e,r]

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Temperature Ratio across Expansion Fan Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
T_e,r = (1+0.5*(γ_e-1)*M_e1^2)/(1+0.5*(γ_e-1)*M_e2^2)
This formula uses 4 Variables

Variables Used

Temperature Ratio Across Expansion Fan - Temperature Ratio Across Expansion Fan is the ratio of downstream temperature to upstream temperature across 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

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

T_e,r = (1+0.5*(γ_e-1)*M_e1^2)/(1+0.5*(γ_e-1)*M_e2^2) --> (1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2)

Evaluating ... ...

T_e,r = 0.73090692124105

STEP 3: Convert Result to Output's Unit

0.73090692124105 --> No Conversion Required

FINAL ANSWER

0.73090692124105 ≈ 0.730907 <-- Temperature Ratio Across Expansion Fan

(Calculation completed in 00.004 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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< Expansion Waves Calculators

Pressure behind Expansion Fan

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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)

Temperature Ratio across Expansion Fan Formula

LaTeX Go

Do you know who developed the centered expansion wave theory?

The centered expansion wave theory was developed by Ludwig Prandtl and his student Theodor Meyerin 1907-1908. It is commonly denoted as Prandtl-Meyer expansion waves.

How to Calculate Temperature Ratio across Expansion Fan?

Temperature Ratio across Expansion Fan calculator uses 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) to calculate the Temperature Ratio Across Expansion Fan, The Temperature Ratio across Expansion Fan formula is defined as the ratio of static to stagnation temperature downstream of the expansion fan to the static to stagnation temperature upstream of the expansion fan. Temperature Ratio Across Expansion Fan is denoted by T_e,r symbol.

How to calculate Temperature Ratio across Expansion Fan using this online calculator? To use this online calculator for Temperature Ratio across Expansion Fan, enter 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 Ratio across Expansion Fan calculation can be explained with given input values -> 0.731707 = (1+0.5*(1.41-1)*5^2)/(1+0.5*(1.41-1)*6^2).

FAQ

What is Temperature Ratio across Expansion Fan?

The Temperature Ratio across Expansion Fan formula is defined as the ratio of static to stagnation temperature downstream of the expansion fan to the static to stagnation temperature upstream of the expansion fan and is represented as T_e,r = (1+0.5*(γ_e-1)*M_e1^2)/(1+0.5*(γ_e-1)*M_e2^2) or 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). 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 Ratio across Expansion Fan?

The Temperature Ratio across Expansion Fan formula is defined as the ratio of static to stagnation temperature downstream of the expansion fan to the static to stagnation temperature upstream of the expansion fan is calculated using 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). To calculate Temperature Ratio across Expansion Fan, you need 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 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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