Temperature Ratio across Normal Shock Calculator

✖The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.ⓘ Mach Number Ahead of Normal Shock [M₁]			+10% -10%

✖Temperature Ratio Across Normal Shock is the ratio of downstream temperature to upstream temperature across the shock wave.ⓘ Temperature Ratio across Normal Shock [T_r]

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Temperature Ratio across Normal Shock Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature Ratio Across Normal Shock = (1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+((Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)))
T_r = (1+((2*γ)/(γ+1))*(M₁^2-1))/((γ+1)*(M₁^2)/(2+((γ-1)*M₁^2)))
This formula uses 3 Variables

Variables Used

Temperature Ratio Across Normal Shock - Temperature Ratio Across Normal Shock is the ratio of downstream temperature to upstream temperature across the shock wave.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Mach Number Ahead of Normal Shock - Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number Ahead of Normal Shock: 1.49 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_r = (1+((2*γ)/(γ+1))*(M₁^2-1))/((γ+1)*(M₁^2)/(2+((γ-1)*M₁^2))) --> (1+((2*1.4)/(1.4+1))*(1.49^2-1))/((1.4+1)*(1.49^2)/(2+((1.4-1)*1.49^2)))

Evaluating ... ...

T_r = 1.3135708109995

STEP 3: Convert Result to Output's Unit

1.3135708109995 --> No Conversion Required

FINAL ANSWER

1.3135708109995 ≈ 1.313571 <-- Temperature Ratio Across Normal Shock

(Calculation completed in 00.020 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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< Property Change Across Shock Waves Calculators

Density Ratio across Normal Shock

LaTeX Go Density Ratio Across Normal Shock = (Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2)

Entropy Change across Normal Shock

LaTeX Go Entropy Change = Specific Gas Constant*ln(Stagnation Pressure Ahead of Normal Shock/Stagnation Pressure Behind Normal Shock)

Pressure Ratio across Normal Shock

LaTeX Go Pressure Ratio Across Normal Shock = 1+(2*Specific Heat Ratio)/(Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2-1)

Shock Strength

LaTeX Go Shock Strength = ((2*Specific Heat Ratio)/(1+Specific Heat Ratio))*(Mach Number Ahead of Normal Shock^2-1)

Temperature Ratio across Normal Shock Formula

LaTeX Go

How to obtain temperature ratio across normal shock?

the temperature ratio across normal shock is obtained by multiplying the pressure ratio and inverse of density ratio across the shock. The temperature increases downstream of the normal shock.

How to Calculate Temperature Ratio across Normal Shock?

Temperature Ratio across Normal Shock calculator uses Temperature Ratio Across Normal Shock = (1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+((Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2))) to calculate the Temperature Ratio Across Normal Shock, The Temperature Ratio across Normal Shock formula is defined as the ratio of downstream to upstream temperature across the shock. It is a function of specific heat ratio and upstream Mach number. Temperature Ratio Across Normal Shock is denoted by T_r symbol.

How to calculate Temperature Ratio across Normal Shock using this online calculator? To use this online calculator for Temperature Ratio across Normal Shock, enter Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) and hit the calculate button. Here is how the Temperature Ratio across Normal Shock calculation can be explained with given input values -> 1.000666 = (1+((2*1.4)/(1.4+1))*(1.49^2-1))/((1.4+1)*(1.49^2)/(2+((1.4-1)*1.49^2))).

FAQ

What is Temperature Ratio across Normal Shock?

The Temperature Ratio across Normal Shock formula is defined as the ratio of downstream to upstream temperature across the shock. It is a function of specific heat ratio and upstream Mach number and is represented as T_r = (1+((2*γ)/(γ+1))*(M₁^2-1))/((γ+1)*(M₁^2)/(2+((γ-1)*M₁^2))) or Temperature Ratio Across Normal Shock = (1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+((Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2))). The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.

How to calculate Temperature Ratio across Normal Shock?

The Temperature Ratio across Normal Shock formula is defined as the ratio of downstream to upstream temperature across the shock. It is a function of specific heat ratio and upstream Mach number is calculated using Temperature Ratio Across Normal Shock = (1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))/((Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+((Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2))). To calculate Temperature Ratio across Normal Shock, you need Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁). With our tool, you need to enter the respective value for Specific Heat Ratio & Mach Number Ahead of Normal Shock 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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