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Inverse of Density for Hypersonic Flow using Mach Number Formula

GoInverse of Density for Hypersonic Flow Formula

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Inverse of Density is the variable used for simplifying the equation. Check FAQs

ϵ = \frac{2 + (γ - 1) \cdot M^{2} \cdot {\sin (θ d)}^{2}}{2 + (γ + 1) \cdot M^{2} \cdot {\sin (θ d)}^{2}}

ϵ - Inverse of Density?γ - Specific Heat Ratio?M - Mach Number?θ_d - Deflection Angle?

Inverse of Density for Hypersonic Flow using Mach Number Example

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Here is how the Inverse of Density for Hypersonic Flow using Mach Number equation looks like with Values.

Here is how the Inverse of Density for Hypersonic Flow using Mach Number equation looks like with Units.

Here is how the Inverse of Density for Hypersonic Flow using Mach Number equation looks like.

0.498 = \frac{2 + (1.1 - 1) \cdot {5.4}^{2} \cdot {\sin (0.192)}^{2}}{2 + (1.1 + 1) \cdot {5.4}^{2} \cdot {\sin (0.192)}^{2}}

0.498m³/kg = \frac{2 + (1.1 - 1) \cdot {5.4}^{2} \cdot {\sin (0.192rad)}^{2}}{2 + (1.1 + 1) \cdot {5.4}^{2} \cdot {\sin (0.192rad)}^{2}}

0.498 = \frac{2 + (1.1 - 1) \cdot {5.4}^{2} \cdot {\sin (0.192)}^{2}}{2 + (1.1 + 1) \cdot {5.4}^{2} \cdot {\sin (0.192)}^{2}}

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Inverse of Density for Hypersonic Flow using Mach Number Solution

Follow our step by step solution on how to calculate Inverse of Density for Hypersonic Flow using Mach Number?

FIRST Step Consider the formula

ϵ = \frac{2 + (γ - 1) \cdot M^{2} \cdot {\sin (θ d)}^{2}}{2 + (γ + 1) \cdot M^{2} \cdot {\sin (θ d)}^{2}}

Next Step Substitute values of Variables

∴

ϵ = \frac{2 + (1.1 - 1) \cdot {5.4}^{2} \cdot {\sin (0.192rad)}^{2}}{2 + (1.1 + 1) \cdot {5.4}^{2} \cdot {\sin (0.192rad)}^{2}}

Next Step Prepare to Evaluate

∴

ϵ = \frac{2 + (1.1 - 1) \cdot {5.4}^{2} \cdot {\sin (0.192)}^{2}}{2 + (1.1 + 1) \cdot {5.4}^{2} \cdot {\sin (0.192)}^{2}}

Next Step Evaluate

∴

ϵ = 0.497972759875935m³/kg

LAST Step Rounding Answer

∴

ϵ = 0.498m³/kg

Inverse of Density for Hypersonic Flow using Mach Number Formula Elements

Variables

Functions

Inverse of Density

Inverse of Density is the variable used for simplifying the equation.

Symbol: ϵ

Measurement: Specific VolumeUnit: m³/kg

Note: Value should be greater than 0.

Formulas to find Inverse of Density

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.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Specific Heat Ratio

Mach Number

Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number

Deflection Angle

A Deflection angle is the angle between the onward extension of the previous leg and the line ahead.

Symbol: θ_d

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Deflection Angle

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.

Syntax: sin(Angle)

Other Formulas to find Inverse of Density

Go Inverse of Density for Hypersonic Flow

ϵ = \frac{1}{ρ \cdot β}

Other formulas in Hypersonic Flow and Disturbances category

Go Change in Velocity for Hypersonic Flow in X Direction

u' = v fluid - U ∞

Go Similarity Constant Equation with Slenderness Ratio

K = M \cdot λ

Go Density Ratio with Similarity Constant having Slenderness Ratio

ρ ratio = (\frac{γ + 1}{γ - 1}) \cdot (\frac{1}{1 + \frac{2}{(γ - 1) \cdot K^{2}}})

Go Coefficient of Pressure with Slenderness Ratio

C p = \frac{2}{γ} \cdot M^{2} \cdot (p - \cdot γ \cdot M^{2} \cdot λ^{2} - 1)

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

Inverse of Density for Hypersonic Flow using Mach Number evaluator 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 evaluate 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 evaluate Inverse of Density for Hypersonic Flow using Mach Number using this online evaluator? To use this online evaluator 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.

FAQs on Inverse of Density for Hypersonic Flow using Mach Number

What is the formula to find Inverse of Density for Hypersonic Flow using Mach Number?

The formula of Inverse of Density for Hypersonic Flow using Mach Number is expressed as 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). Here is an example- 0.497973 = (2+(1.1-1)*5.4^2*sin(0.191986)^2)/(2+(1.1+1)*5.4^2*sin(0.191986)^2).

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

With Specific Heat Ratio (γ), Mach Number (M) & Deflection Angle (θ_d) we can find Inverse of Density for Hypersonic Flow using Mach Number using the formula - 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). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Inverse of Density?

Here are the different ways to Calculate Inverse of Density-

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

Can the Inverse of Density for Hypersonic Flow using Mach Number be negative?

No, the Inverse of Density for Hypersonic Flow using Mach Number, measured in Specific Volume cannot be negative.

Which unit is used to measure Inverse of Density for Hypersonic Flow using Mach Number?

Inverse of Density for Hypersonic Flow using Mach Number is usually measured using the Cubic Meter per Kilogram[m³/kg] for Specific Volume. Cubic Centimeter per Gram[m³/kg], Liter per Kilogram[m³/kg], Liter per Gram[m³/kg] are the few other units in which Inverse of Density for Hypersonic Flow using Mach Number can be measured.

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Inverse of Density for Hypersonic Flow using Mach Number Formula

​GoInverse of Density for Hypersonic Flow Formula

Inverse of Density for Hypersonic Flow using Mach Number Example

Inverse of Density for Hypersonic Flow using Mach Number Solution

Inverse of Density for Hypersonic Flow using Mach Number Formula Elements

Other Formulas to find Inverse of Density

Other formulas in Hypersonic Flow and Disturbances category

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

FAQs on Inverse of Density for Hypersonic Flow using Mach Number

Variable Name

GoInverse of Density for Hypersonic Flow Formula