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Ratio of Stagnation and Static Density Formula

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The Stagnation to Static Density ratio depends upon the Mach number and ratio of specific heats. Check FAQs

ρ r = {(1 + (\frac{γ - 1}{2}) \cdot M^{2})}^{\frac{1}{γ - 1}}

ρ_r - Stagnation to Static Density?γ - Specific Heat Ratio?M - Mach Number?

Ratio of Stagnation and Static Density Example

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Here is how the Ratio of Stagnation and Static Density equation looks like with Values.

Here is how the Ratio of Stagnation and Static Density equation looks like with Units.

Here is how the Ratio of Stagnation and Static Density equation looks like.

4.3469 = {(1 + (\frac{1.4 - 1}{2}) \cdot 2^{2})}^{\frac{1}{1.4 - 1}}

4.3469 = {(1 + (\frac{1.4 - 1}{2}) \cdot 2^{2})}^{\frac{1}{1.4 - 1}}

4.3469 = {(1 + (\frac{1.4 - 1}{2}) \cdot 2^{2})}^{\frac{1}{1.4 - 1}}

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Ratio of Stagnation and Static Density Solution

Follow our step by step solution on how to calculate Ratio of Stagnation and Static Density?

FIRST Step Consider the formula

ρ r = {(1 + (\frac{γ - 1}{2}) \cdot M^{2})}^{\frac{1}{γ - 1}}

Next Step Substitute values of Variables

∴

ρ r = {(1 + (\frac{1.4 - 1}{2}) \cdot 2^{2})}^{\frac{1}{1.4 - 1}}

Next Step Prepare to Evaluate

∴

ρ r = {(1 + (\frac{1.4 - 1}{2}) \cdot 2^{2})}^{\frac{1}{1.4 - 1}}

Next Step Evaluate

∴

ρ r = 4.34691614825959

LAST Step Rounding Answer

∴

ρ r = 4.3469

Ratio of Stagnation and Static Density Formula Elements

Variables

Stagnation to Static Density

The Stagnation to Static Density ratio depends upon the Mach number and ratio of specific heats.

Symbol: ρ_r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Stagnation to Static Density

Specific Heat Ratio

The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume of the flowing fluid for non-viscous and compressible flow.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

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

Other formulas in Governing Equations and Sound Wave category

Go Speed of Sound

a = \sqrt{γ \cdot [R-Dry-Air] \cdot T s}

Go Mach Number

M = \frac{V b}{a}

Go Mach Angle

μ = a \sin (\frac{1}{M})

Go Mayer's Formula

R = C p - C v

How to Evaluate Ratio of Stagnation and Static Density?

Ratio of Stagnation and Static Density evaluator uses Stagnation to Static Density = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1)) to evaluate the Stagnation to Static Density, Ratio of Stagnation and Static Density equation relates the ratio of stagnation density to static density to the Mach number of the flow and the specific heat ratio of the gas. It demonstrates how the density of a compressible flow changes due to the effects of compression or expansion associated with changes in flow velocity and Mach number. Stagnation to Static Density is denoted by ρ_r symbol.

How to evaluate Ratio of Stagnation and Static Density using this online evaluator? To use this online evaluator for Ratio of Stagnation and Static Density, enter Specific Heat Ratio (γ) & Mach Number (M) and hit the calculate button.

FAQs on Ratio of Stagnation and Static Density

What is the formula to find Ratio of Stagnation and Static Density?

The formula of Ratio of Stagnation and Static Density is expressed as Stagnation to Static Density = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1)). Here is an example- 4.308444 = (1+((1.4-1)/2)*2^2)^(1/(1.4-1)).

How to calculate Ratio of Stagnation and Static Density?

With Specific Heat Ratio (γ) & Mach Number (M) we can find Ratio of Stagnation and Static Density using the formula - Stagnation to Static Density = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1)).

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Ratio of Stagnation and Static Density Formula

Ratio of Stagnation and Static Density Example

Ratio of Stagnation and Static Density Solution

Ratio of Stagnation and Static Density Formula Elements

Other formulas in Governing Equations and Sound Wave category

How to Evaluate Ratio of Stagnation and Static Density?

FAQs on Ratio of Stagnation and Static Density

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