Mach Number given Dynamic Pressure Calculator

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✖Dynamic Pressure, denoted as q, is a measure of the kinetic energy per unit volume of a flowing fluid.ⓘ Dynamic Pressure [q]			+10% -10%
✖Ambient Air Density refers to the density of the air surrounding an object or within a particular environment.ⓘ Ambient Air Density [ρ]			+10% -10%
✖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.ⓘ Heat Capacity Ratio [Y]			+10% -10%
✖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.ⓘ Specific Gas Constant [R]			+10% -10%
✖Static Temperature refers to the temperature of a fluid (such as air or a gas) that is not in motion.ⓘ Static Temperature [T]			+10% -10%

✖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.ⓘ Mach Number given Dynamic Pressure [M]

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Formula

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Mach Number given Dynamic Pressure

Formula

`"M" = sqrt((2*"q")/("ρ"*"Y"*"R"*"T"))`

Example

`"0.182929"=sqrt((2*"10Pa")/("1.225kg/m³"*"1.4"*"4.1J/(kg*K)"*"85K"))`

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Mach Number given Dynamic Pressure Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mach Number = sqrt((2*Dynamic Pressure)/(Ambient Air Density*Heat Capacity Ratio*Specific Gas Constant*Static Temperature))
M = sqrt((2*q)/(ρ*Y*R*T))
This formula uses 1 Functions, 6 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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.
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.
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.
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.

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
Heat Capacity Ratio: 1.4 --> No Conversion Required
Specific Gas Constant: 4.1 Joule per Kilogram per K --> 4.1 Joule per Kilogram per K No Conversion Required
Static Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = sqrt((2*q)/(ρ*Y*R*T)) --> sqrt((2*10)/(1.225*1.4*4.1*85))

Evaluating ... ...

M = 0.182928572117412

STEP 3: Convert Result to Output's Unit

0.182928572117412 --> No Conversion Required

FINAL ANSWER

0.182928572117412 ≈ 0.182929 <-- Mach Number

(Calculation completed in 00.004 seconds)

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Created by Himanshu Sharma

National Institute of Technology, Hamirpur (NITH), Himachal Pradesh

Himanshu Sharma has created this Calculator and 50+ more calculators!

Verified by Kartikay Pandit

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]

Mach Number given Dynamic Pressure Formula

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

What is mach number?

Mach number (M or Ma) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.

How to Calculate Mach Number given Dynamic Pressure?

Mach Number given Dynamic Pressure calculator uses Mach Number = sqrt((2*Dynamic Pressure)/(Ambient Air Density*Heat Capacity Ratio*Specific Gas Constant*Static Temperature)) to calculate the Mach Number, Mach Number given Dynamic Pressure formula is defined as the ratio of the speed of the sound and the object travelling in air of a given density and dynamic pressure. Mach Number is denoted by M symbol.

How to calculate Mach Number given Dynamic Pressure using this online calculator? To use this online calculator for Mach Number given Dynamic Pressure, enter Dynamic Pressure (q), Ambient Air Density (ρ), Heat Capacity Ratio (Y), Specific Gas Constant (R) & Static Temperature (T) and hit the calculate button. Here is how the Mach Number given Dynamic Pressure calculation can be explained with given input values -> 0.182929 = sqrt((2*10)/(1.225*1.4*4.1*85)).

FAQ

What is Mach Number given Dynamic Pressure?

Mach Number given Dynamic Pressure formula is defined as the ratio of the speed of the sound and the object travelling in air of a given density and dynamic pressure and is represented as M = sqrt((2*q)/(ρ*Y*R*T)) or Mach Number = sqrt((2*Dynamic Pressure)/(Ambient Air Density*Heat Capacity Ratio*Specific Gas Constant*Static Temperature)). 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, 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, 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 & Static Temperature refers to the temperature of a fluid (such as air or a gas) that is not in motion.

How to calculate Mach Number given Dynamic Pressure?

Mach Number given Dynamic Pressure formula is defined as the ratio of the speed of the sound and the object travelling in air of a given density and dynamic pressure is calculated using Mach Number = sqrt((2*Dynamic Pressure)/(Ambient Air Density*Heat Capacity Ratio*Specific Gas Constant*Static Temperature)). To calculate Mach Number given Dynamic Pressure, you need Dynamic Pressure (q), Ambient Air Density (ρ), Heat Capacity Ratio (Y), Specific Gas Constant (R) & Static Temperature (T). With our tool, you need to enter the respective value for Dynamic Pressure, Ambient Air Density, Heat Capacity Ratio, Specific Gas Constant & Static Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Mach Number?

In this formula, Mach Number uses Dynamic Pressure, Ambient Air Density, Heat Capacity Ratio, Specific Gas Constant & Static Temperature. We can use 1 other way(s) to calculate the same, which is/are as follows -

Mach Number = sqrt(2*Dynamic Pressure/(Static Pressure*Heat Capacity Ratio))

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