Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Temperature Behind Normal Shock = Temperature Ahead of 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)))
T2 = T1*((1+((2*γ)/(γ+1))*(M1^2-1))/((γ+1)*(M1^2)/(2+(γ-1)*M1^2)))
This formula uses 4 Variables
Variables Used
Temperature Behind Normal Shock - (Measured in Kelvin) - Temperature Behind Normal Shock is defined as the downstream temperature across the shock.
Temperature Ahead of Normal Shock - (Measured in Kelvin) - Temperature Ahead of Normal Shock signifies the temperature of a fluid before encountering a normal 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
Temperature Ahead of Normal Shock: 298.15 Kelvin --> 298.15 Kelvin No Conversion Required
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
T2 = T1*((1+((2*γ)/(γ+1))*(M1^2-1))/((γ+1)*(M1^2)/(2+(γ-1)*M1^2))) --> 298.15*((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 ... ...
T2 = 391.641137299502
STEP 3: Convert Result to Output's Unit
391.641137299502 Kelvin --> No Conversion Required
FINAL ANSWER
391.641137299502 391.6411 Kelvin <-- Temperature Behind Normal Shock
(Calculation completed in 00.004 seconds)

Credits

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Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
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Verified by Maiarutselvan V
PSG College of Technology (PSGCT), Coimbatore
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Downstream Shock Waves Calculators

Mach Number behind Shock
​ LaTeX ​ Go Mach Number Behind Normal Shock = ((2+Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Mach Number Ahead of Normal Shock^2)/(2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Specific Heat Ratio+1))^(1/2)
Static Pressure behind Normal Shock using Normal Shock Momentum Equation
​ LaTeX ​ Go Static pressure Behind Normal shock = Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Density Behind Normal Shock*Velocity Downstream of Shock^2
Velocity behind Normal Shock
​ LaTeX ​ Go Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))
Characteristic Mach Number behind Shock
​ LaTeX ​ Go Characteristic Mach Number Behind Shock = 1/Characteristic Mach Number Ahead of Shock

Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number Formula

​LaTeX ​Go
Temperature Behind Normal Shock = Temperature Ahead of 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)))
T2 = T1*((1+((2*γ)/(γ+1))*(M1^2-1))/((γ+1)*(M1^2)/(2+(γ-1)*M1^2)))

How to obtain temperature ratio across normal shock?

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

How to Calculate Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number?

Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number calculator uses Temperature Behind Normal Shock = Temperature Ahead of 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 Behind Normal Shock, Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number formula is defined as a method to determine the temperature of a gas after it passes through a normal shock wave, considering the upstream conditions and Mach number. Temperature Behind Normal Shock is denoted by T2 symbol.

How to calculate Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number using this online calculator? To use this online calculator for Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number, enter Temperature Ahead of Normal Shock (T1), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M1) and hit the calculate button. Here is how the Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number calculation can be explained with given input values -> 391.6411 = 298.15*((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 Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number?
Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number formula is defined as a method to determine the temperature of a gas after it passes through a normal shock wave, considering the upstream conditions and Mach number and is represented as T2 = T1*((1+((2*γ)/(γ+1))*(M1^2-1))/((γ+1)*(M1^2)/(2+(γ-1)*M1^2))) or Temperature Behind Normal Shock = Temperature Ahead of 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))). Temperature Ahead of Normal Shock signifies the temperature of a fluid before encountering a normal shock wave, 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 Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number?
Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number formula is defined as a method to determine the temperature of a gas after it passes through a normal shock wave, considering the upstream conditions and Mach number is calculated using Temperature Behind Normal Shock = Temperature Ahead of 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 Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number, you need Temperature Ahead of Normal Shock (T1), Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M1). With our tool, you need to enter the respective value for Temperature Ahead of Normal Shock, 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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