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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Formula

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Inverse of Density for Hypersonic Flow using Mach Number

Formula

`"ϵ" = (2+("γ"-1)*"M"^2*sin("θ"_{"d"})^2)/(2+("γ"+1)*"M"^2*sin("θ"_{"d"})^2)`

Example

`"0.497973m³/kg"=(2+("1.1"-1)*("5.4")^2*sin("0.191986rad")^2)/(2+("1.1"+1)*("5.4")^2*sin("0.191986rad")^2)`

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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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< 17 Hypersonic Flow and Disturbances Calculators

Inverse of Density for Hypersonic Flow using Mach Number

Go 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)

Coefficient of Pressure with Slenderness Ratio and Similarity Constant

Go Pressure Coefficient = (2*Slenderness Ratio^2)/(Specific Heat Ratio*Hypersonic Similarity Parameter^2)*(Specific Heat Ratio*Hypersonic Similarity Parameter^2*Non Dimensionalized Pressure-1)

Coefficient of Pressure with Slenderness Ratio

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

Non Dimensional Pressure Equation with Slenderness Ratio

Go Non Dimensionalized Pressure = Pressure/(Specific Heat Ratio*Mach Number^2*Slenderness Ratio^2*Free Stream Pressure)

Density Ratio with Similarity Constant having Slenderness Ratio

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

Rasmussen Closed Form Expression for Shock Wave Angle

Go Wave Angle Similarity Parameter = Hypersonic Similarity Parameter*sqrt((Specific Heat Ratio+1)/2+1/Hypersonic Similarity Parameter^2)

Non Dimensional Change in Hypersonic Disturbance Velocity in y Direction

Go Non Dimensional Disturbance Y Velocity = Change in Velocity for Hypersonic Flow y direction/(Freestream Velocity Normal*Slenderness Ratio)

Non Dimensional Change in Hypersonic Disturbance Velocity in x Direction

Go Non Dimensional Disturbance X Velocity = Change in Velocity for Hypersonic Flow/(Freestream Velocity for Blast Wave*Slenderness Ratio^2)

Doty and Rasmussen- Normal Force Coefficient

Go Coefficient of Force = 2*Normal Force/(Density of Fluid*Freestream Velocity Normal^2*Area)

Constant G used for Finding Location of Perturbed Shock

Go Perturbed Shock Location Constant = Perturbed Shock Location Constant at Normal Force/Perturbed Shock Location Constant at Drag Force

Non Dimensional Velocity Disturbance in y Direction in Hypersonic Flow

Go Non Dimensional Disturbance Y Velocity = (2/(Specific Heat Ratio+1))*(1-1/Hypersonic Similarity Parameter^2)

Non Dimensionalised Time

Go Non Dimensionalized Time = Time/(Length/Freestream Velocity Normal)

Similarity Constant Equation using Wave Angle

Go Wave Angle Similarity Parameter = Mach Number*Wave Angle*180/pi

Change in Velocity for Hypersonic Flow in X Direction

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

Distance from Tip of Leading Edge to Base

Go Distance from X-Axis = Freestream Velocity for Blast Wave*Total Time Taken

Similarity Constant Equation with Slenderness Ratio

Go Hypersonic Similarity Parameter = Mach Number*Slenderness Ratio

Inverse of Density for Hypersonic Flow

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

Inverse of Density for Hypersonic Flow using Mach Number Formula

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, The Inverse of density for hypersonic flow using Mach number formula is defined as the interrelation between the Mach number, specific heat ratio, and deflection angle. 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?

The Inverse of density for hypersonic flow using Mach number formula is defined as the interrelation between the Mach number, specific heat ratio, and deflection angle 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?

The Inverse of density for hypersonic flow using Mach number formula is defined as the interrelation between the Mach number, specific heat ratio, and deflection angle 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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