Ratio of Stagnation and Static Density Calculator

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

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Governing Equations and Sound Wave

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✖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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Formula

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Ratio of Stagnation and Static Density

Formula

`"ρ"_{"r"} = (1+(("γ"-1)/2)*"M"^2)^(1/("γ"-1))`

Example

`"4.346916"=(1+(("1.4"-1)/2)*("2")^2)^(1/("1.4"-1))`

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Ratio of Stagnation and Static Density Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stagnation to Static Density = (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 - 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

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Compressible Flow » Governing Equations and Sound Wave » Ratio of Stagnation and Static Density

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Created by Vinay Mishra

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

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Amrita School of Engineering (ASE), Vallikavu

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< 18 Governing Equations and Sound Wave Calculators

Speed of Sound Downstream of Sound Wave

Go Sound Speed Downstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Upstream of Sound^2-Flow Velocity Downstream of Sound^2)/2+Sound Speed Upstream^2/(Specific Heat Ratio-1)))

Speed of Sound Upstream of Sound Wave

Go Sound Speed Upstream = sqrt((Specific Heat Ratio-1)*((Flow Velocity Downstream of Sound^2-Flow Velocity Upstream of Sound^2)/2+Sound Speed Downstream^2/(Specific Heat Ratio-1)))

Flow Velocity Downstream of Sound Wave

Go Flow Velocity Downstream of Sound = sqrt(2*((Sound Speed Upstream^2-Sound Speed Downstream^2)/(Specific Heat Ratio-1)+Flow Velocity Upstream of Sound^2/2))

Flow Velocity Upstream of Sound Wave

Go Flow Velocity Upstream of Sound = sqrt(2*((Sound Speed Downstream^2-Sound Speed Upstream^2)/(Specific Heat Ratio-1)+Flow Velocity Downstream of Sound^2/2))

Ratio of Stagnation and Static Pressure

Go Stagnation to Static Pressure = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(Specific Heat Ratio/(Specific Heat Ratio-1))

Critical Pressure

Go Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure

Stagnation Temperature

Go Stagnation Temperature = Static Temperature+(Flow Velocity Downstream of Sound^2)/(2*Specific Heat Capacity at Constant Pressure)

Speed of Sound

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

Ratio of Stagnation and Static Density

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

Critical Density

Go Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1))

Mayer's Formula

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

Ratio of Stagnation and Static Temperature

Go Stagnation to Static Temperature = 1+((Specific Heat Ratio-1)/2)*Mach Number^2

Critical Temperature

Go Critical Temperature = (2*Stagnation Temperature)/(Specific Heat Ratio+1)

Isentropic Compressibility for given Density and Speed of Sound

Go Isentropic Compressibility = 1/(Density*Speed of Sound^2)

Mach Number

Go Mach Number = Speed of Object/Speed of Sound

Speed of Sound given Isentropic Change

Go Speed of Sound = sqrt(Isentropic Change)

Mach Angle

Go Mach Angle = asin(1/Mach Number)

Isentropic Change across Sound Wave

Go Isentropic Change = Speed of Sound^2

Ratio of Stagnation and Static Density Formula

Stagnation to Static Density = (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 = (1+((Specific Heat Ratio-1)/2)*Mach Number^2)^(1/(Specific Heat Ratio-1)) to calculate 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 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 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 and is represented as ρ_r = (1+((γ-1)/2)*M^2)^(1/(γ-1)) or Stagnation to Static Density = (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 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 is calculated using Stagnation to Static Density = (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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