Ratio of Stagnation and Static Density Calculator

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Physics	Gas Dynamics ↺
Gas Dynamics	Basic Compressible Flow ↺

✖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%

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

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Credits

Vinay Mishra

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

Vinay Mishra has created this Calculator and 300+ more calculators!

Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has verified this Calculator and 200+ more calculators!

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))
ρo/ρ = (1+(((γ-1)/2)*(M^2)))^(1/(γ-1))
This formula uses 2 Variables

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.6 --> No Conversion Required
Mach Number: 1 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρo/ρ = (1+(((γ-1)/2)*(M^2)))^(1/(γ-1)) --> (1+(((1.6-1)/2)*(1^2)))^(1/(1.6-1))

Evaluating ... ...

ρo/ρ = 1.54847995275536

STEP 3: Convert Result to Output's Unit

1.54847995275536 --> No Conversion Required

FINAL ANSWER

1.54847995275536 <-- Stagnation to Static Density

(Calculation completed in 00.016 seconds)

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< 11 Other formulas that you can solve using the same Inputs

Exact Density Ratio

density_ratio = ((Specific Heat Ratio+1)*((Mach Number*(sin(Wave angle)))^2))/((Specific Heat Ratio-1)*((Mach Number*(sin(Wave angle)))^2)+2) Go

Exact pressure ratio

pressure_ratio = 1+(2*Specific Heat Ratio/(Specific Heat Ratio+1))*(((Mach Number*sin(Wave angle))^2)-1) Go

Pressure ratio when Mach becomes infinite

pressure_ratio = (2*Specific Heat Ratio/(Specific Heat Ratio+1))*((Mach Number*sin(Wave angle))^2) Go

Ratio of stagnation and static pressure

stagnation_to_static_pressure = (1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)))^(Specific Heat Ratio/(Specific Heat Ratio-1)) Go

Mach number

mach_no = Fluid Velocity/(sqrt(Specific Heat Ratio*Universal Gas Constant*Final Temp.)) Go

Deflection angle

deflection_angle = (2/(Specific Heat Ratio-1))*((1/Mach Number ahead of shock)-(1/Mach Number behind shock)) Go

Relation between Characteristic Mach number and Mach number

characteristic_mach_number = ((Specific heat ratio+1)/((Specific heat ratio-1)+(2/(Mach Number^2))))^0.5 Go

Speed of Sound

speed_sound = sqrt(Specific Heat Ratio*[R-Dry-Air]*Temperature of Gas) Go

Ratio of Stagnation and Static Temperature

stagnation_to_static_temp = 1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)) Go

Density ratio when Mach become infinite

density_ratio = (Specific Heat Ratio+1)/(Specific Heat Ratio-1) Go

Mach Angle

mach_angle = asin(1/Mach Number) Go

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))
ρo/ρ = (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, The Ratio of Stagnation and Static Density is dependent upon the Mach number and ratio of specific heats. Stagnation to Static Density and is denoted by ρo/ρ 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) and 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 -> 1.54848 = (1+(((1.6-1)/2)*(1^2)))^(1/(1.6-1)).

FAQ

What is Ratio of Stagnation and Static Density?

The Ratio of Stagnation and Static Density is dependent upon the Mach number and ratio of specific heats and is represented as ρo/ρ = (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 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 and 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?

The Ratio of Stagnation and Static Density is dependent upon the Mach number and ratio of specific heats 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) and Mach Number (M). With our tool, you need to enter the respective value for Specific Heat Ratio and 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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