Stagnation Temperature Solution

STEP 0: Pre-Calculation Summary
Formula Used
Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)
T0 = Ts+(u2^2)/(2*Cp)
This formula uses 4 Variables
Variables Used
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.
Static Temperature - (Measured in Kelvin) - The Static Temperature is defined as the temperature measured by a thermometer placed within the fluid without affecting the fluid's velocity or pressure.
Flow Velocity Downstream of Sound - (Measured in Meter per Second) - Flow Velocity Downstream of Sound represents the velocity of a fluid flow or airflow after being influenced by a sound wave.
Specific Heat Capacity at Constant Pressure - (Measured in Joule per Kilogram per K) - Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure.
STEP 1: Convert Input(s) to Base Unit
Static Temperature: 296 Kelvin --> 296 Kelvin No Conversion Required
Flow Velocity Downstream of Sound: 45 Meter per Second --> 45 Meter per Second No Conversion Required
Specific Heat Capacity at Constant Pressure: 1005 Joule per Kilogram per K --> 1005 Joule per Kilogram per K No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T0 = Ts+(u2^2)/(2*Cp) --> 296+(45^2)/(2*1005)
Evaluating ... ...
T0 = 297.007462686567
STEP 3: Convert Result to Output's Unit
297.007462686567 Kelvin --> No Conversion Required
FINAL ANSWER
297.007462686567 297.0075 Kelvin <-- Stagnation Temperature
(Calculation completed in 00.004 seconds)

Credits

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Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune
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19 Thermodynamics and Governing Equations Calculators

Max work output in Brayton cycle
Go Maximum Work done in Brayton Cycle = (1005*1/Compressor Efficiency)*Temperature at Inlet of Compressor in Brayton*(sqrt(Temperature at Inlet to Turbine in Brayton Cycle/Temperature at Inlet of Compressor in Brayton*Compressor Efficiency*Turbine Efficiency)-1)^2
Choked Mass Flow Rate given specific heat ratio
Go Choked Mass Flow Rate = (Heat Capacity Ratio/(sqrt(Heat Capacity Ratio-1)))*((Heat Capacity Ratio+1)/2)^(-((Heat Capacity Ratio+1)/(2*Heat Capacity Ratio-2)))
Choked Mass Flow Rate
Go Choked Mass Flow Rate = (Mass Flow Rate*sqrt(Specific Heat Capacity at Constant Pressure*Temperature))/(Nozzle Throat Area*Throat Pressure)
Stagnation Velocity of Sound given Specific Heat at Constant Pressure
Go Stagnation Velocity of Sound = sqrt((Heat Capacity Ratio-1)*Specific Heat Capacity at Constant Pressure*Stagnation Temperature)
Specific Heat of mixed out gas
Go Specific Heat of Mixed Gas = (Specific Heat of Core Gas+Bypass Ratio*Specific Heat of Bypass Air)/(1+Bypass Ratio)
Stagnation Temperature
Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)
Stagnation Velocity of Sound
Go Stagnation Velocity of Sound = sqrt(Heat Capacity Ratio*[R]*Stagnation Temperature)
Speed of Sound
Go Speed of Sound = sqrt(Heat Capacity Ratio*[R-Dry-Air]*Static Temperature)
Stagnation Velocity of Sound given Stagnation Enthalpy
Go Stagnation Velocity of Sound = sqrt((Heat Capacity Ratio-1)*Stagnation Enthalpy)
Heat Capacity Ratio
Go Heat Capacity Ratio = Specific Heat Capacity at Constant Pressure/Specific Heat Capacity at Constant Volume
Efficiency of cycle
Go Efficiency of Cycle = (Turbine Work-Compressor Work)/Heat
Internal Energy of Perfect Gas at given Temperature
Go Internal Energy = Specific Heat Capacity at Constant Volume*Temperature
Enthalpy of Ideal Gas at given Temperature
Go Enthalpy = Specific Heat Capacity at Constant Pressure*Temperature
Stagnation enthalpy
Go Stagnation Enthalpy = Enthalpy+(Velocity of Fluid Flow^2)/2
Efficiency of Joule cycle
Go Efficiency of Joule Cycle = Net Work Output/Heat
Pressure Ratio
Go Pressure Ratio = Final Pressure/Initial Pressure
Work ratio in practical cycle
Go Work Ratio = 1-(Compressor Work/Turbine Work)
Mach Number
Go Mach Number = Speed of Object/Speed of Sound
Mach Angle
Go Mach Angle = asin(1/Mach Number)

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(Heat Capacity 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

Stagnation Temperature Formula

Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)
T0 = Ts+(u2^2)/(2*Cp)

What is a Stagnation Point?

In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero.

Why is stagnation temperature important?

The stagnation temperature is important because it is the temperature that occurs at a stagnation point on the object.

How to Calculate Stagnation Temperature?

Stagnation Temperature calculator uses Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure) to calculate the Stagnation Temperature, The Stagnation Temperature is defined as the total temperature at all points on the streamline leading to the stagnation point and depends upon the velocity at the point of interest along the stagnation streamline. Stagnation Temperature is denoted by T0 symbol.

How to calculate Stagnation Temperature using this online calculator? To use this online calculator for Stagnation Temperature, enter Static Temperature (Ts), Flow Velocity Downstream of Sound (u2) & Specific Heat Capacity at Constant Pressure (Cp) and hit the calculate button. Here is how the Stagnation Temperature calculation can be explained with given input values -> 297.0075 = 296+(45^2)/(2*1005).

FAQ

What is Stagnation Temperature?
The Stagnation Temperature is defined as the total temperature at all points on the streamline leading to the stagnation point and depends upon the velocity at the point of interest along the stagnation streamline and is represented as T0 = Ts+(u2^2)/(2*Cp) or Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure). The Static Temperature is defined as the temperature measured by a thermometer placed within the fluid without affecting the fluid's velocity or pressure, Flow Velocity Downstream of Sound represents the velocity of a fluid flow or airflow after being influenced by a sound wave & Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure.
How to calculate Stagnation Temperature?
The Stagnation Temperature is defined as the total temperature at all points on the streamline leading to the stagnation point and depends upon the velocity at the point of interest along the stagnation streamline is calculated using Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure). To calculate Stagnation Temperature, you need Static Temperature (Ts), Flow Velocity Downstream of Sound (u2) & Specific Heat Capacity at Constant Pressure (Cp). With our tool, you need to enter the respective value for Static Temperature, Flow Velocity Downstream of Sound & Specific Heat Capacity at Constant Pressure 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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