Ratio of Stagnation and Static Density Calculator

✖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.ⓘ 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%

✖The Stagnation to Static Density ratio depends upon the Mach number and ratio of specific heats.ⓘ Ratio of Stagnation and Static Density [ρ_r]

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Ratio of Stagnation and Static Density Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stagnation to Static Density Ratio = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1))
ρ_r = (1+((γ-1)/2)*M^2)^(1/(γ-1))
This formula uses 3 Variables

Variables Used

Stagnation to Static Density Ratio - The Stagnation to Static Density ratio depends upon the Mach number and ratio of specific heats.
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.
Mach Number - Mach Number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ_r = (1+((γ-1)/2)*M^2)^(1/(γ-1)) --> (1+((1.4-1)/2)*2^2)^(1/(1.4-1))

Evaluating ... ...

ρ_r = 4.34691614825959

STEP 3: Convert Result to Output's Unit

4.34691614825959 --> No Conversion Required

FINAL ANSWER

4.34691614825959 ≈ 4.346916 <-- Stagnation to Static Density Ratio

(Calculation completed in 00.005 seconds)

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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Verified by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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< Governing Equations and Sound Wave Calculators

Speed of Sound

LaTeX Go Speed of Sound = sqrt(Specific Heat Ratio*[R-Dry-Air]*Static Temperature)

Mayer's Formula

LaTeX Go Specific Gas Constant = Specific Heat Capacity at Constant Pressure-Specific Heat Capacity at Constant Volume

Mach Number

LaTeX Go Mach Number = Speed of Object/Speed of Sound

Mach Angle

LaTeX Go Mach Angle = asin(1/Mach Number)

Ratio of Stagnation and Static Density Formula

LaTeX Go

Stagnation to Static Density Ratio = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1))
ρ_r = (1+((γ-1)/2)*M^2)^(1/(γ-1))

What is Stagnation Density?

The point at which the resultant velocity of the fluid becomes zero will be termed as the stagnation point. The value of density of compressible fluid at the stagnation point will be called stagnation density.

How to Calculate Ratio of Stagnation and Static Density?

Ratio of Stagnation and Static Density calculator uses Stagnation to Static Density Ratio = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1)) to calculate the Stagnation to Static Density Ratio, Ratio of Stagnation and Static Density formula is defined as a relationship that describes the variation between stagnation density and static density in compressible flow, highlighting the effects of Mach number and specific heat ratio on fluid dynamics. Stagnation to Static Density Ratio is denoted by ρ_r symbol.

How to calculate Ratio of Stagnation and Static Density using this online calculator? To use this online calculator for Ratio of Stagnation and Static Density, enter Specific Heat Ratio (γ) & Mach Number (M) and hit the calculate button. Here is how the Ratio of Stagnation and Static Density calculation can be explained with given input values -> 4.308444 = (1+((1.4-1)/2)*2^2)^(1/(1.4-1)).

FAQ

What is Ratio of Stagnation and Static Density?

Ratio of Stagnation and Static Density formula is defined as a relationship that describes the variation between stagnation density and static density in compressible flow, highlighting the effects of Mach number and specific heat ratio on fluid dynamics and is represented as ρ_r = (1+((γ-1)/2)*M^2)^(1/(γ-1)) or Stagnation to Static Density Ratio = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1)). 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 & Mach Number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

How to calculate Ratio of Stagnation and Static Density?

Ratio of Stagnation and Static Density formula is defined as a relationship that describes the variation between stagnation density and static density in compressible flow, highlighting the effects of Mach number and specific heat ratio on fluid dynamics is calculated using Stagnation to Static Density Ratio = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1)). To calculate Ratio of Stagnation and Static Density, you need Specific Heat Ratio (γ) & Mach Number (M). With our tool, you need to enter the respective value for Specific Heat Ratio & Mach Number and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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