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
Tr = 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
Tr = 1+((γ-1)/2)*M^2 --> 1+((1.4-1)/2)*2^2
Evaluating ... ...
Tr = 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)

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
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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

Ratio of Stagnation and Static Temperature Formula

Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2
Tr = 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 depends upon the Mach number and ratio of specific heats. Stagnation to Static Temperature is denoted by Tr 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 depends upon the Mach number and ratio of specific heats and is represented as Tr = 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 depends upon the Mach number and ratio of specific heats 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.
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