Temperature behind oblique shock for given upstream temperature and normal upstream Mach number Calculator

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✖Temperature ahead of shock wave is the upstream temperature ahead of the shock.ⓘ Temperature ahead of Shock [T_s1]			+10% -10%
✖The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio Dynamic [κ]			+10% -10%
✖Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave.ⓘ Component of upstream mach normal to oblique shock [M_n1]			+10% -10%

✖Temperature behind shock is defined as the downstream temperature across the shock.ⓘ Temperature behind oblique shock for given upstream temperature and normal upstream Mach number [T_s2]

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Formula

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Temperature behind oblique shock for given upstream temperature and normal upstream Mach number

Formula

`"T"_{"s2"} = "T"_{"s1"}*((1+((2*"κ")/("κ"+1))*(("M"_{"n1"}^2)-1))/(("κ"+1)*("M"_{"n1"}^2)/(2+(("κ"-1)*("M"_{"n1"}^2)))))`

Example

`"1322.494K"="789K"*((1+((2*"1.392758")/("1.392758"+1))*((("2")^2)-1))/(("1.392758"+1)*(("2")^2)/(2+(("1.392758"-1)*(("2")^2)))))`

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Temperature behind oblique shock for given upstream temperature and normal upstream Mach number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature behind Shock = Temperature ahead of Shock*((1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))))
T_s2 = T_s1*((1+((2*κ)/(κ+1))*((M_n1^2)-1))/((κ+1)*(M_n1^2)/(2+((κ-1)*(M_n1^2)))))
This formula uses 4 Variables

Variables Used

Temperature behind Shock - (Measured in Kelvin) - Temperature behind shock is defined as the downstream temperature across the shock.
Temperature ahead of Shock - (Measured in Kelvin) - Temperature ahead of shock wave is the upstream temperature ahead of the shock.
Specific Heat Ratio Dynamic - The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Component of upstream mach normal to oblique shock - Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave.

STEP 1: Convert Input(s) to Base Unit

Temperature ahead of Shock: 789 Kelvin --> 789 Kelvin No Conversion Required
Specific Heat Ratio Dynamic: 1.392758 --> No Conversion Required
Component of upstream mach normal to oblique shock: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_s2 = T_s1*((1+((2*κ)/(κ+1))*((M_n1^2)-1))/((κ+1)*(M_n1^2)/(2+((κ-1)*(M_n1^2))))) --> 789*((1+((2*1.392758)/(1.392758+1))*((2^2)-1))/((1.392758+1)*(2^2)/(2+((1.392758-1)*(2^2)))))

Evaluating ... ...

T_s2 = 1322.49374319858

STEP 3: Convert Result to Output's Unit

1322.49374319858 Kelvin --> No Conversion Required

FINAL ANSWER

1322.49374319858 Kelvin <-- Temperature behind Shock

(Calculation completed in 00.000 seconds)

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Home » Physics » Gas Dynamics » Oblique Shock and Expansion Waves » Temperature behind oblique shock for given upstream temperature and normal upstream Mach number

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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!

< 19 Oblique Shock and Expansion Waves Calculators

Temperature behind oblique shock for given upstream temperature and normal upstream Mach number

Go Temperature behind Shock = Temperature ahead of Shock*((1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))))

Prandtl Meyer function at upstream Mach number

Go Prandtl Meyer Function at upstream Mach no. = sqrt((Specific Heat Ratio Dynamic+1)/(Specific Heat Ratio Dynamic-1))*atan(sqrt(((Specific Heat Ratio Dynamic-1)*((Mach Number ahead of shock^2)-1))/(Specific Heat Ratio Dynamic+1)))-atan(sqrt(((Mach Number ahead of shock^2)-1)))

Prandtl Meyer function

Go Prandtl Meyer Function = sqrt((Specific Heat Ratio Dynamic+1)/(Specific Heat Ratio Dynamic-1))*atan(sqrt(((Specific Heat Ratio Dynamic-1)*((Mach Number^2)-1))/(Specific Heat Ratio Dynamic+1)))-atan(sqrt(((Mach Number^2)-1)))

Temperature Ratio across Oblique Shock

Go Temperature Ratio across Shock = (1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))

Flow deflection angle

Go Flow Deflection angle = atan((2*cot(Oblique shock angle)*(((Mach Number ahead of shock*sin(Oblique shock angle))^2)-1))/(((Mach Number ahead of shock^2)*(Specific Heat Ratio Dynamic+cos(2*Oblique shock angle)))+2))

Pressure behind expansion fan

Go Pressure behind expansion fan = Pressure ahead Expansion Fan*((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2)))^((Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic-1))

Component of downstream Mach number normal to oblique shock for given normal upstream Mach number

Go Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*((Specific Heat Ratio Dynamic-1)*Component of upstream mach normal to oblique shock^2))/(Specific Heat Ratio Dynamic*Component of upstream mach normal to oblique shock^2-0.5*(Specific Heat Ratio Dynamic-1)))

Pressure Ratio across Expansion Fan

Go Pressure Ratio across Expansion Fan = ((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2)))^((Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic-1))

Density behind oblique shock for given upstream density and normal upstream Mach number

Go Density behind Shock = Density ahead of shock*((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))

Temperature behind expansion fan

Go Temperature behind Expansion Fan = Temperature ahead Expansion Fan*((1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2)))

Density Ratio across Oblique Shock

Go Density Ratio across Shock = (Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2)))

Temperature Ratio across Expansion Fan

Go Temperature Ratio across Expansion Fan = (1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number ahead Expansion Fan^2))/(1+0.5*(Specific Heat Ratio Dynamic-1)*(Mach Number behind Expansion Fan^2))

Pressure behind oblique shock for given upstream pressure and normal upstream Mach number

Go Static pressure behind shock = Static pressure ahead of shock*(1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))

Pressure Ratio across Oblique shock

Go Pressure Ratio across Shock = 1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1)

Component of Downstream Mach normal to oblique shock

Go Downstream Mach Normal to Oblique Shock = Mach Number behind shock*sin(Oblique shock angle-Flow Deflection angle)

Component of Upstream Mach normal to oblique shock

Go Component of upstream mach normal to oblique shock = Mach Number ahead of shock*sin(Oblique shock angle)

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.

Rearward Mach Angle of Expansion Fan

Go Rearward Mach Angle = arsin(1/Mach Number behind Expansion Fan)

Forward Mach angle of expansion fan

Go Forward Mach Angle = arsin(1/Mach Number ahead Expansion Fan)

Temperature behind oblique shock for given upstream temperature and normal upstream Mach number Formula

What is the physical mechanism that creates waves in a supersonic flow?

The physical generation of waves in a supersonic flow-both shock and expansion waves-is due to the propagation of information via molecular collisions and due to the fact that such propagation cannot work its way into certain regions of the supersonic flow.

Which component of flow velocity describe changes of flow properties across oblique shock?

By applying continuity, momentum and energy equation across oblique we obtain that the tangential component of the flow velocity does not appear in governing equations and it is constant across an oblique shock and changes across an oblique shock wave are governed only by the component of velocity normal to the wave.

How to Calculate Temperature behind oblique shock for given upstream temperature and normal upstream Mach number?

Temperature behind oblique shock for given upstream temperature and normal upstream Mach number calculator uses Temperature behind Shock = Temperature ahead of Shock*((1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))) to calculate the Temperature behind Shock, The Temperature behind oblique shock for given upstream temperature and normal upstream Mach number formula is obtained by multiplying the temperature ahead of an oblique shock to temperature ratio across the oblique shock. Temperature behind Shock is denoted by T_s2 symbol.

How to calculate Temperature behind oblique shock for given upstream temperature and normal upstream Mach number using this online calculator? To use this online calculator for Temperature behind oblique shock for given upstream temperature and normal upstream Mach number, enter Temperature ahead of Shock (T_s1), Specific Heat Ratio Dynamic (κ) & Component of upstream mach normal to oblique shock (M_n1) and hit the calculate button. Here is how the Temperature behind oblique shock for given upstream temperature and normal upstream Mach number calculation can be explained with given input values -> 2380.489 = 789*((1+((2*1.392758)/(1.392758+1))*((2^2)-1))/((1.392758+1)*(2^2)/(2+((1.392758-1)*(2^2))))).

FAQ

What is Temperature behind oblique shock for given upstream temperature and normal upstream Mach number?

The Temperature behind oblique shock for given upstream temperature and normal upstream Mach number formula is obtained by multiplying the temperature ahead of an oblique shock to temperature ratio across the oblique shock and is represented as T_s2 = T_s1*((1+((2*κ)/(κ+1))*((M_n1^2)-1))/((κ+1)*(M_n1^2)/(2+((κ-1)*(M_n1^2))))) or Temperature behind Shock = Temperature ahead of Shock*((1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))). Temperature ahead of shock wave is the upstream temperature ahead of the shock, The Specific Heat Ratio Dynamic is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave.

How to calculate Temperature behind oblique shock for given upstream temperature and normal upstream Mach number?

The Temperature behind oblique shock for given upstream temperature and normal upstream Mach number formula is obtained by multiplying the temperature ahead of an oblique shock to temperature ratio across the oblique shock is calculated using Temperature behind Shock = Temperature ahead of Shock*((1+((2*Specific Heat Ratio Dynamic)/(Specific Heat Ratio Dynamic+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific Heat Ratio Dynamic+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific Heat Ratio Dynamic-1)*(Component of upstream mach normal to oblique shock^2))))). To calculate Temperature behind oblique shock for given upstream temperature and normal upstream Mach number, you need Temperature ahead of Shock (T_s1), Specific Heat Ratio Dynamic (κ) & Component of upstream mach normal to oblique shock (M_n1). With our tool, you need to enter the respective value for Temperature ahead of Shock, Specific Heat Ratio Dynamic & Component of upstream mach normal to oblique 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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