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

Governing Equations and Sound Wave

Oblique Shock and Expansion Waves

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Downstream Shock Waves

Normal Shock Relations

Property Change Across Shock Waves

Upstream Shock Waves

✖Temperature Ahead of Normal Shock signifies the temperature of a fluid before encountering a normal shock wave.ⓘ Temperature Ahead of Normal Shock [T₁]			+10% -10%
✖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 Behind Normal Shock is defined as the downstream temperature across the shock.ⓘ Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number [T₂]

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Formula

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

Formula

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

Example

`"391.6411K"="298.15K"*((1+((2*"1.4")/("1.4"+1))*(("1.49")^2-1))/(("1.4"+1)*(("1.49")^2)/(2+("1.4"-1)*("1.49")^2)))`

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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)

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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

Maiarutselvan V has verified this Calculator and 300+ more calculators!

< 15 Downstream Shock Waves Calculators

Stagnation Pressure behind Normal Shock by Rayleigh Pitot Tube formula

Go Stagnation Pressure Behind Normal Shock = Static Pressure Ahead of Normal Shock*((1-Specific Heat Ratio+2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2)/(Specific Heat Ratio+1))*(((Specific Heat Ratio+1)^2*Mach Number Ahead of Normal Shock^2)/(4*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-2*(Specific Heat Ratio-1)))^((Specific Heat Ratio)/(Specific Heat Ratio-1))

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

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)))

Static Enthalpy behind Normal Shock for given Upstream Enthalpy and Mach Number

Go Enthalpy Behind Normal Shock = Enthalpy 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))

Mach Number behind Shock

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)

Velocity behind Normal Shock by Normal Shock Momentum Equation

Go Velocity Downstream of Shock = sqrt((Static Pressure Ahead of Normal Shock-Static pressure Behind Normal shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2)/Density Behind Normal Shock)

Density behind Normal Shock using Normal Shock Momentum Equation

Go Density Behind Normal Shock = (Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Static pressure Behind Normal shock)/(Velocity Downstream of Shock^2)

Static Pressure behind Normal Shock using Normal Shock Momentum Equation

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

Density behind Normal Shock given Upstream Density and Mach Number

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

Static Pressure behind Normal Shock for given Upstream Pressure and Mach Number

Go Static pressure Behind Normal shock = Static Pressure Ahead of Normal Shock*(1+((2*Specific Heat Ratio)/(Specific Heat Ratio+1))*(Mach Number Ahead of Normal Shock^2-1))

Velocity behind Normal Shock from Normal Shock Energy Equation

Go Velocity Downstream of Shock = sqrt(2*(Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2)/2-Enthalpy Behind Normal Shock))

Velocity behind Normal Shock

Go Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))

Enthalpy behind Normal Shock from Normal Shock Energy Equation

Go Enthalpy Behind Normal Shock = Enthalpy Ahead of Normal Shock+(Velocity Upstream of Shock^2-Velocity Downstream of Shock^2)/2

Flow Velocity Downstream of Shock Wave using Continuity Equation

Go Velocity Downstream of Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Density Behind Normal Shock

Density Downstream of Shock Wave using Continuity Equation

Go Density Behind Normal Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Velocity Downstream of Shock

Characteristic Mach Number behind Shock

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

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, The Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number computes the temperature of a fluid behind a normal shock wave based on the provided upstream temperature and Mach number. This formula incorporates the ratio of specific heats for the fluid and accounts for the change in temperature resulting from the shock wave passage. 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?

The Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number computes the temperature of a fluid behind a normal shock wave based on the provided upstream temperature and Mach number. This formula incorporates the ratio of specific heats for the fluid and accounts for the change in temperature resulting from the shock wave passage 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?

The Static Temperature behind Normal Shock for given Upstream Temperature and Mach Number computes the temperature of a fluid behind a normal shock wave based on the provided upstream temperature and Mach number. This formula incorporates the ratio of specific heats for the fluid and accounts for the change in temperature resulting from the shock wave passage 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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