Ratio of Stagnation and Static Temperature Calculator

✖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%
✖Mach Number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.ⓘ Mach Number [M]			+10% -10%

✖The Stagnation to Static Temperature ratio depends upon the Mach number and ratio of specific heats.ⓘ Ratio of Stagnation and Static Temperature [T_r]

⎘ Copy

👎

Formula

✖

Ratio of Stagnation and Static Temperature

Formula

T r = 1 + (\frac{γ - 1}{2}) \cdot M^{2}

Example

1.8 = 1 + (\frac{1.4 - 1}{2}) \cdot 2^{2}

Calculator

LaTeX

Reset

👍

Download Governing Equations and Sound Wave Formulas PDF PDF Image

Ratio of Stagnation and Static Temperature Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2
T_r = 1+((γ-1)/2)*M^2
This formula uses 3 Variables

Variables Used

Stagnation to Static Temperature - The Stagnation to Static Temperature ratio depends upon the Mach number and ratio of specific heats.
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.
Mach Number - Mach Number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

T_r = 1.8

STEP 3: Convert Result to Output's Unit

1.8 --> No Conversion Required

FINAL ANSWER

1.8 <-- Stagnation to Static Temperature

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Aerodynamics » Compressible Flow » Aerospace » Governing Equations and Sound Wave » Ratio of Stagnation and Static Temperature

Credits

Created by Vinay Mishra

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

Vinay Mishra has created this Calculator and 300+ more calculators!

Verified by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has verified this Calculator and 200+ more calculators!

< Governing Equations and Sound Wave Calculators

Speed of Sound

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

Mayer's Formula

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

Mach Number

Go Mach Number = Speed of Object/Speed of Sound

Mach Angle

Go Mach Angle = asin(1/Mach Number)

Ratio of Stagnation and Static Temperature Formula

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

Why is Stagnation Temperature important?

Stagnation or Total air temperature is an essential input to an air data computer in order to enable computation of static air temperature and hence true airspeed.

How to Calculate Ratio of Stagnation and Static Temperature?

Ratio of Stagnation and Static Temperature calculator uses Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2 to calculate the Stagnation to Static Temperature, The Ratio of Stagnation and Static temperature, this equation demonstrates how the ratio of stagnation temperature to static temperature varies with the Mach number of the flow. It indicates the temperature rise due to compression or temperature drop due to expansion associated with changes in flow velocity and Mach number in a compressible flow. Stagnation to Static Temperature is denoted by T_r symbol.

How to calculate Ratio of Stagnation and Static Temperature using this online calculator? To use this online calculator for Ratio of Stagnation and Static Temperature, enter Specific Heat Ratio (γ) & Mach Number (M) and hit the calculate button. Here is how the Ratio of Stagnation and Static Temperature calculation can be explained with given input values -> 1.82 = 1+((1.4-1)/2)*2^2.

FAQ

What is Ratio of Stagnation and Static Temperature?

The Ratio of Stagnation and Static temperature, this equation demonstrates how the ratio of stagnation temperature to static temperature varies with the Mach number of the flow. It indicates the temperature rise due to compression or temperature drop due to expansion associated with changes in flow velocity and Mach number in a compressible flow and is represented as T_r = 1+((γ-1)/2)*M^2 or Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2. 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 & Mach Number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

How to calculate Ratio of Stagnation and Static Temperature?

The Ratio of Stagnation and Static temperature, this equation demonstrates how the ratio of stagnation temperature to static temperature varies with the Mach number of the flow. It indicates the temperature rise due to compression or temperature drop due to expansion associated with changes in flow velocity and Mach number in a compressible flow is calculated using Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2. To calculate Ratio of Stagnation and Static Temperature, you need Specific Heat Ratio (γ) & Mach Number (M). With our tool, you need to enter the respective value for Specific Heat Ratio & Mach Number and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search