Critical Temperature 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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Governing Equations and Sound Wave

Normal Shock Wave

Oblique Shock and Expansion Waves

✖Stagnation Temperature is defined as the temperature that would exist if the flow were slowed down isentropically to zero velocity.ⓘ Stagnation Temperature [T₀]			+10% -10%
✖The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume of the flowing fluid for non-viscous and compressible flow.ⓘ Specific Heat Ratio [γ]			+10% -10%

✖Critical Temperature is defined as the temperature that will exist at a point when the flow becomes sonic at that point.ⓘ Critical Temperature [T_cr]

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Formula

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Critical Temperature

Formula

`"T"_{"cr"} = (2*"T"_{"0"})/("γ"+1)`

Example

`"250K"=(2*"300K")/("1.4"+1)`

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Critical Temperature Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1)
T_cr = (2*T₀)/(γ+1)
This formula uses 3 Variables

Variables Used

Critical Temperature - (Measured in Kelvin) - Critical Temperature is defined as the temperature that will exist at a point when the flow becomes sonic at that point.
Stagnation Temperature - (Measured in Kelvin) - Stagnation Temperature is defined as the temperature that would exist if the flow were slowed down isentropically to zero velocity.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume of the flowing fluid for non-viscous and compressible flow.

STEP 1: Convert Input(s) to Base Unit

Stagnation Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Specific Heat Ratio: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_cr = (2*T₀)/(γ+1) --> (2*300)/(1.4+1)

Evaluating ... ...

T_cr = 250

STEP 3: Convert Result to Output's Unit

250 Kelvin --> No Conversion Required

FINAL ANSWER

250 Kelvin <-- Critical Temperature

(Calculation completed in 00.004 seconds)

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Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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

Verified by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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< 18 Governing Equations and Sound Wave Calculators

Speed of Sound Downstream of Sound Wave

Go Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1)))

Speed of Sound Upstream of Sound Wave

Go Sound Speed Upstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Downstream of Sound^2-Flow Velocity Upstream of Sound^2)/2+Sound Speed Downstream^2/(Specific Heat Ratio-1)))

Flow Velocity Downstream of Sound Wave

Go Flow Velocity Downstream of Sound = sqrt(2*((Sound Speed Upstream^2-Sound Speed Downstream^2)/(Specific Heat Ratio-1)+Flow Velocity Upstream of Sound^2/2))

Flow Velocity Upstream of Sound Wave

Go Flow Velocity Upstream of Sound = sqrt(2*((Sound Speed Downstream^2-Sound Speed Upstream^2)/(Specific Heat Ratio-1)+Flow Velocity Downstream of Sound^2/2))

Ratio of Stagnation and Static Pressure

Go Stagnation to Static Pressure = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(Specific Heat Ratio/(Specific Heat Ratio-1))

Critical Pressure

Go Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure

Stagnation Temperature

Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)

Speed of Sound

Go Speed of Sound = sqrt(Specific Heat Ratio*[R-Dry-Air]*Static Temperature)

Ratio of Stagnation and Static Density

Go Stagnation to Static Density = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1))

Critical Density

Go Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1))

Mayer's Formula

Go Specific Gas Constant = Specific Heat Capacity at Constant Pressure-Specific Heat Capacity at Constant Volume

Ratio of Stagnation and Static Temperature

Go Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2

Critical Temperature

Go Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1)

Isentropic Compressibility for given Density and Speed of Sound

Go Isentropic Compressibility = 1/(Density*Speed of Sound^2)

Mach Number

Go Mach Number = Speed of Object/Speed of Sound

Speed of Sound given Isentropic Change

Go Speed of Sound = sqrt(Isentropic Change)

Mach Angle

Go Mach Angle = asin(1/Mach Number)

Isentropic Change across Sound Wave

Go Isentropic Change = Speed of Sound^2

Critical Temperature Formula

Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1)
T_cr = (2*T₀)/(γ+1)

What is the critical temperature?

The Critical Temperature is defined as the temperature at a point in a fluid flow when the flow is accelerated or decelerated to sonic condition isentropically.

How to Calculate Critical Temperature?

Critical Temperature calculator uses Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1) to calculate the Critical Temperature, The Critical Temperature at a point in a fluid flow is defined as the temperature that would exist if the flow became sonic at that point. Critical Temperature is denoted by T_cr symbol.

How to calculate Critical Temperature using this online calculator? To use this online calculator for Critical Temperature, enter Stagnation Temperature (T₀) & Specific Heat Ratio (γ) and hit the calculate button. Here is how the Critical Temperature calculation can be explained with given input values -> 248.9627 = (2*300)/(1.4+1).

FAQ

What is Critical Temperature?

The Critical Temperature at a point in a fluid flow is defined as the temperature that would exist if the flow became sonic at that point and is represented as T_cr = (2*T₀)/(γ+1) or Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1). Stagnation Temperature is defined as the temperature that would exist if the flow were slowed down isentropically to zero velocity & The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume of the flowing fluid for non-viscous and compressible flow.

How to calculate Critical Temperature?

The Critical Temperature at a point in a fluid flow is defined as the temperature that would exist if the flow became sonic at that point is calculated using Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1). To calculate Critical Temperature, you need Stagnation Temperature (T₀) & Specific Heat Ratio (γ). With our tool, you need to enter the respective value for Stagnation Temperature & Specific Heat Ratio 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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