Inverse of Density for Hypersonic Flow using Mach Number Calculator

✖The Specific Heat Ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.ⓘ 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%
✖A Deflection angle is the angle between the onward extension of the previous leg and the line ahead.ⓘ Deflection Angle [θ_d]			+10% -10%

✖Inverse of Density is the variable used for simplifying the equation.ⓘ Inverse of Density for Hypersonic Flow using Mach Number [ϵ]

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Inverse of Density for Hypersonic Flow using Mach Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inverse of Density = (2+(Specific Heat Ratio-1)*Mach Number^2*sin(Deflection Angle)^2)/(2+(Specific Heat Ratio+1)*Mach Number^2*sin(Deflection Angle)^2)
ϵ = (2+(γ-1)*M^2*sin(θ_d)^2)/(2+(γ+1)*M^2*sin(θ_d)^2)
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Inverse of Density - (Measured in Cubic Meter per Kilogram) - Inverse of Density is the variable used for simplifying the equation.
Specific Heat Ratio - The Specific Heat Ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.
Mach Number - Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.
Deflection Angle - (Measured in Radian) - A Deflection angle is the angle between the onward extension of the previous leg and the line ahead.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.1 --> No Conversion Required
Mach Number: 5.4 --> No Conversion Required
Deflection Angle: 0.191986 Radian --> 0.191986 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϵ = (2+(γ-1)*M^2*sin(θ_d)^2)/(2+(γ+1)*M^2*sin(θ_d)^2) --> (2+(1.1-1)*5.4^2*sin(0.191986)^2)/(2+(1.1+1)*5.4^2*sin(0.191986)^2)

Evaluating ... ...

ϵ = 0.497972759875935

STEP 3: Convert Result to Output's Unit

0.497972759875935 Cubic Meter per Kilogram --> No Conversion Required

FINAL ANSWER

0.497972759875935 ≈ 0.497973 Cubic Meter per Kilogram <-- Inverse of Density

(Calculation completed in 00.004 seconds)

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< Hypersonic Flow and Disturbances Calculators

Coefficient of Pressure with Slenderness Ratio

LaTeX Go Pressure Coefficient = 2/Specific Heat Ratio*Mach Number^2*(Non Dimensionalized Pressure*Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2-1)

Density Ratio with Similarity Constant having Slenderness Ratio

LaTeX Go Density Ratio = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1))*(1/(1+2/((Specific Heat Ratio-1)*Hypersonic Similarity Parameter^2)))

Change in Velocity for Hypersonic Flow in X Direction

LaTeX Go Change in Velocity for Hypersonic Flow = Fluid Velocity-Freestream Velocity Normal

Similarity Constant Equation with Slenderness Ratio

LaTeX Go Hypersonic Similarity Parameter = Mach Number*Slenderness Ratio

Inverse of Density for Hypersonic Flow using Mach Number Formula

LaTeX Go

What is Mach angle?

Mach Angle. As an object moves through a gas, the gas molecules are deflected around the object. If the speed of the object is much less than the speed of sound of the gas, the density of the gas remains constant and the flow of gas can be described by conserving momentum, and energy in the flow

How to Calculate Inverse of Density for Hypersonic Flow using Mach Number?

Inverse of Density for Hypersonic Flow using Mach Number calculator uses Inverse of Density = (2+(Specific Heat Ratio-1)*Mach Number^2*sin(Deflection Angle)^2)/(2+(Specific Heat Ratio+1)*Mach Number^2*sin(Deflection Angle)^2) to calculate the Inverse of Density, Inverse of Density for Hypersonic Flow using Mach Number formula is defined as a dimensionless quantity that characterizes the compressibility of a fluid in hypersonic flow, providing a measure of the fluid's ability to be compressed in response to changes in pressure. Inverse of Density is denoted by ϵ symbol.

How to calculate Inverse of Density for Hypersonic Flow using Mach Number using this online calculator? To use this online calculator for Inverse of Density for Hypersonic Flow using Mach Number, enter Specific Heat Ratio (γ), Mach Number (M) & Deflection Angle (θ_d) and hit the calculate button. Here is how the Inverse of Density for Hypersonic Flow using Mach Number calculation can be explained with given input values -> 0.497973 = (2+(1.1-1)*5.4^2*sin(0.191986)^2)/(2+(1.1+1)*5.4^2*sin(0.191986)^2).

FAQ

What is Inverse of Density for Hypersonic Flow using Mach Number?

Inverse of Density for Hypersonic Flow using Mach Number formula is defined as a dimensionless quantity that characterizes the compressibility of a fluid in hypersonic flow, providing a measure of the fluid's ability to be compressed in response to changes in pressure and is represented as ϵ = (2+(γ-1)*M^2*sin(θ_d)^2)/(2+(γ+1)*M^2*sin(θ_d)^2) or Inverse of Density = (2+(Specific Heat Ratio-1)*Mach Number^2*sin(Deflection Angle)^2)/(2+(Specific Heat Ratio+1)*Mach Number^2*sin(Deflection Angle)^2). The Specific Heat Ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume, Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound & A Deflection angle is the angle between the onward extension of the previous leg and the line ahead.

How to calculate Inverse of Density for Hypersonic Flow using Mach Number?

Inverse of Density for Hypersonic Flow using Mach Number formula is defined as a dimensionless quantity that characterizes the compressibility of a fluid in hypersonic flow, providing a measure of the fluid's ability to be compressed in response to changes in pressure is calculated using Inverse of Density = (2+(Specific Heat Ratio-1)*Mach Number^2*sin(Deflection Angle)^2)/(2+(Specific Heat Ratio+1)*Mach Number^2*sin(Deflection Angle)^2). To calculate Inverse of Density for Hypersonic Flow using Mach Number, you need Specific Heat Ratio (γ), Mach Number (M) & Deflection Angle (θ_d). With our tool, you need to enter the respective value for Specific Heat Ratio, Mach Number & Deflection Angle 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 Inverse of Density?

In this formula, Inverse of Density uses Specific Heat Ratio, Mach Number & Deflection Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -

Inverse of Density = 1/(Density*Wave Angle)

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