Ratio of Stagnation and Static Density Calculator

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✖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 00.001 seconds)

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< 6 Basic Compressible Flow Calculators

Critical Pressure

sonic_pressure = (2/(Specific heat ratio+1))^(Specific heat ratio/(Specific heat ratio-1))*(Stagnation pressure at a point in fluid flow) 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

Ratio of Stagnation and Static Density

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

Critical Density

sonic_density = Stagnation density*(2/(Specific heat ratio+1))^(1/(Specific heat ratio-1)) Go

Ratio of Stagnation and Static Temperature

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

Critical Temperature

sonic_temp = (2/(Specific heat ratio+1))*(Stagnation Temperature) 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.

How many ways are there to calculate Stagnation to Static Density?

In this formula, Stagnation to Static Density uses Specific Heat Ratio and Mach Number. We can use 6 other way(s) to calculate the same, which is/are as follows -

stagnation_to_static_temp = 1+(((Specific Heat Ratio-1)/2)*(Mach Number^2))
stagnation_to_static_density = (1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)))^(1/(Specific Heat Ratio-1))
stagnation_to_static_pressure = (1+(((Specific Heat Ratio-1)/2)*(Mach Number^2)))^(Specific Heat Ratio/(Specific Heat Ratio-1))
sonic_density = Stagnation density*(2/(Specific heat ratio+1))^(1/(Specific heat ratio-1))
sonic_pressure = (2/(Specific heat ratio+1))^(Specific heat ratio/(Specific heat ratio-1))*(Stagnation pressure at a point in fluid flow)
sonic_temp = (2/(Specific heat ratio+1))*(Stagnation Temperature)

Where is the Ratio of Stagnation and Static Density calculator used?

Among many, Ratio of Stagnation and Static Density calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}

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