Temperature given Dynamic Pressure and Mach Number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Static Temperature = (2*Dynamic Pressure)/(Ambient Air Density*Mach Number^2*Specific Gas Constant*Heat Capacity Ratio)
T = (2*q)/(ρ*M^2*R*Y)
This formula uses 6 Variables
Variables Used
Static Temperature - (Measured in Kelvin) - Static Temperature refers to the temperature of a fluid (such as air or a gas) that is not in motion.
Dynamic Pressure - (Measured in Pascal) - Dynamic Pressure, denoted as q, is a measure of the kinetic energy per unit volume of a flowing fluid.
Ambient Air Density - (Measured in Kilogram per Cubic Meter) - Ambient Air Density refers to the density of the air surrounding an object or within a particular environment.
Mach Number - Mach Number (Ma) is a dimensionless quantity that represents the ratio of the speed of an object (such as an aircraft or projectile) to the speed of sound in the surrounding medium.
Specific Gas Constant - (Measured in Joule per Kilogram per K) - Specific Gas Constant (R) is the constant for a particular gas, representing the amount of energy required to raise the temperature of one unit of the gas by one degree Kelvin (or Celsius) per mole.
Heat Capacity Ratio - The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
STEP 1: Convert Input(s) to Base Unit
Dynamic Pressure: 10 Pascal --> 10 Pascal No Conversion Required
Ambient Air Density: 1.225 Kilogram per Cubic Meter --> 1.225 Kilogram per Cubic Meter No Conversion Required
Mach Number: 8 --> No Conversion Required
Specific Gas Constant: 4.1 Joule per Kilogram per K --> 4.1 Joule per Kilogram per K No Conversion Required
Heat Capacity Ratio: 1.4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T = (2*q)/(ρ*M^2*R*Y) --> (2*10)/(1.225*8^2*4.1*1.4)
Evaluating ... ...
T = 0.0444428642537154
STEP 3: Convert Result to Output's Unit
0.0444428642537154 Kelvin --> No Conversion Required
FINAL ANSWER
0.0444428642537154 0.044443 Kelvin <-- Static Temperature
(Calculation completed in 00.004 seconds)

Credits

Created by Himanshu Sharma
National Institute of Technology, Hamirpur (NITH), Himachal Pradesh
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National Institute Of Technology (NIT), Hamirpur
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14 Atmosphere and Gas Properties Calculators

Mach Number given Dynamic Pressure
Go Mach Number = sqrt((2*Dynamic Pressure)/(Ambient Air Density*Heat Capacity Ratio*Specific Gas Constant*Static Temperature))
Ambient Air Density given Mach Number and Temperature
Go Ambient Air Density = (2*Dynamic Pressure)/(Mach Number^2*Heat Capacity Ratio*Specific Gas Constant*Static Temperature)
Temperature given Dynamic Pressure and Mach Number
Go Static Temperature = (2*Dynamic Pressure)/(Ambient Air Density*Mach Number^2*Specific Gas Constant*Heat Capacity Ratio)
Gas constant given dynamic pressure
Go Specific Gas Constant = (2*Dynamic Pressure)/(Ambient Air Density*Mach Number^2*Heat Capacity Ratio*Static Temperature)
Equivalent Airspeed given Static Pressure
Go Equivalent Airspeed = Sonic Speed at Sea Level*Mach Number*(Static Pressure*6894.7573/Static Sea Level Pressure)^(0.5)
Geometric altitude for given geopotential altitude
Go Geometric Altitude = [Earth-R]*Geopotential altitude/([Earth-R]-Geopotential altitude)
Geopotential altitude
Go Geopotential altitude = [Earth-R]*Geometric Altitude/([Earth-R]+Geometric Altitude)
Mach Number given Static and Dynamic Pressure
Go Mach Number = sqrt(2*Dynamic Pressure/(Static Pressure*Heat Capacity Ratio))
Ambient Pressure given Dynamic Pressure and Mach Number
Go Static Pressure = (2*Dynamic Pressure)/(Heat Capacity Ratio*Mach Number^2)
Ambient air density given mach number
Go Ambient Air Density = 2*Dynamic Pressure/(Mach Number*Sonic Speed)^2
Ambient air density given dynamic pressure
Go Ambient Air Density = 2*Dynamic Pressure/(Flight Speed^2)
Lapse rate
Go Lapse Rate = Change in Temperature/Altitude difference
Geometric altitude
Go Geometric Altitude = Absolute Altitude-[Earth-R]
Absolute altitude
Go Absolute Altitude = Geometric Altitude+[Earth-R]

Temperature given Dynamic Pressure and Mach Number Formula

Static Temperature = (2*Dynamic Pressure)/(Ambient Air Density*Mach Number^2*Specific Gas Constant*Heat Capacity Ratio)
T = (2*q)/(ρ*M^2*R*Y)

What is specific heat of air?

Specific heat, the quantity of heat required to raise the temperature of one gram of a substance by one Celsius degree. The units of specific heat are usually calories or joules per gram per Celsius degree.

How to Calculate Temperature given Dynamic Pressure and Mach Number?

Temperature given Dynamic Pressure and Mach Number calculator uses Static Temperature = (2*Dynamic Pressure)/(Ambient Air Density*Mach Number^2*Specific Gas Constant*Heat Capacity Ratio) to calculate the Static Temperature, Temperature given Dynamic Pressure and Mach Number is a formula used in aerodynamics to determine the temperature of a gas under specific condition. Static Temperature is denoted by T symbol.

How to calculate Temperature given Dynamic Pressure and Mach Number using this online calculator? To use this online calculator for Temperature given Dynamic Pressure and Mach Number, enter Dynamic Pressure (q), Ambient Air Density (ρ), Mach Number (M), Specific Gas Constant (R) & Heat Capacity Ratio (Y) and hit the calculate button. Here is how the Temperature given Dynamic Pressure and Mach Number calculation can be explained with given input values -> 0.044443 = (2*10)/(1.225*8^2*4.1*1.4).

FAQ

What is Temperature given Dynamic Pressure and Mach Number?
Temperature given Dynamic Pressure and Mach Number is a formula used in aerodynamics to determine the temperature of a gas under specific condition and is represented as T = (2*q)/(ρ*M^2*R*Y) or Static Temperature = (2*Dynamic Pressure)/(Ambient Air Density*Mach Number^2*Specific Gas Constant*Heat Capacity Ratio). Dynamic Pressure, denoted as q, is a measure of the kinetic energy per unit volume of a flowing fluid, Ambient Air Density refers to the density of the air surrounding an object or within a particular environment, Mach Number (Ma) is a dimensionless quantity that represents the ratio of the speed of an object (such as an aircraft or projectile) to the speed of sound in the surrounding medium, Specific Gas Constant (R) is the constant for a particular gas, representing the amount of energy required to raise the temperature of one unit of the gas by one degree Kelvin (or Celsius) per mole & The Heat Capacity Ratio also known as the adiabatic index is the ratio of specific heats i.e. the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
How to calculate Temperature given Dynamic Pressure and Mach Number?
Temperature given Dynamic Pressure and Mach Number is a formula used in aerodynamics to determine the temperature of a gas under specific condition is calculated using Static Temperature = (2*Dynamic Pressure)/(Ambient Air Density*Mach Number^2*Specific Gas Constant*Heat Capacity Ratio). To calculate Temperature given Dynamic Pressure and Mach Number, you need Dynamic Pressure (q), Ambient Air Density (ρ), Mach Number (M), Specific Gas Constant (R) & Heat Capacity Ratio (Y). With our tool, you need to enter the respective value for Dynamic Pressure, Ambient Air Density, Mach Number, Specific Gas Constant & Heat Capacity 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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