Critical Density Calculator

✖Stagnation Density is defined as the density of fluid at a stagnation point in a fluid flow.ⓘ Stagnation Density [ρ_o]			+10% -10%
✖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%

✖Critical Density is defined as the density of the fluid at sonic conditions, when Mach number is one.ⓘ Critical Density [ρ_cr]

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Formula

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Critical Density

Formula

ρ cr = ρ o \cdot {(\frac{2}{γ + 1})}^{\frac{1}{γ - 1}}

Example

0.773405 kg/m³ = 1.22 kg/m³ \cdot {(\frac{2}{1.4 + 1})}^{\frac{1}{1.4 - 1}}

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Critical Density Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1))
ρ_cr = ρ_o*(2/(γ+1))^(1/(γ-1))
This formula uses 3 Variables

Variables Used

Critical Density - (Measured in Kilogram per Cubic Meter) - Critical Density is defined as the density of the fluid at sonic conditions, when Mach number is one.
Stagnation Density - (Measured in Kilogram per Cubic Meter) - Stagnation Density is defined as the density of fluid at a stagnation point in a fluid flow.
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.

STEP 1: Convert Input(s) to Base Unit

Stagnation Density: 1.22 Kilogram per Cubic Meter --> 1.22 Kilogram per Cubic Meter No Conversion Required
Specific Heat Ratio: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ_cr = ρ_o*(2/(γ+1))^(1/(γ-1)) --> 1.22*(2/(1.4+1))^(1/(1.4-1))

Evaluating ... ...

ρ_cr = 0.773404537217943

STEP 3: Convert Result to Output's Unit

0.773404537217943 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

0.773404537217943 ≈ 0.773405 Kilogram per Cubic Meter <-- Critical Density

(Calculation completed in 00.020 seconds)

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Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Vinay Mishra

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

Vinay Mishra has verified this Calculator and 100+ more calculators!

< Governing Equations and Sound Wave Calculators

Speed of Sound

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

Mayer's Formula

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

Mach Number

Go Mach Number = Speed of Object/Speed of Sound

Mach Angle

Go Mach Angle = asin(1/Mach Number)

Critical Density Formula

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

What is Critical Density?

In terminology of compressible flows, critical density refers to the mass per unit volume of the fluid at sonic conditions, i.e. when Mach number is 1.

How to Calculate Critical Density?

Critical Density calculator uses Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1)) to calculate the Critical Density, The Critical Density at a point in a fluid flow is defined as the density that would exist if the flow became sonic at that point. Critical Density is denoted by ρ_cr symbol.

How to calculate Critical Density using this online calculator? To use this online calculator for Critical Density, enter Stagnation Density (ρ_o) & Specific Heat Ratio (γ) and hit the calculate button. Here is how the Critical Density calculation can be explained with given input values -> 0.77416 = 1.22*(2/(1.4+1))^(1/(1.4-1)).

FAQ

What is Critical Density?

The Critical Density at a point in a fluid flow is defined as the density that would exist if the flow became sonic at that point and is represented as ρ_cr = ρ_o*(2/(γ+1))^(1/(γ-1)) or Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1)). Stagnation Density is defined as the density of fluid at a stagnation point in a fluid flow & 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.

How to calculate Critical Density?

The Critical Density at a point in a fluid flow is defined as the density that would exist if the flow became sonic at that point is calculated using Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1)). To calculate Critical Density, you need Stagnation Density (ρ_o) & Specific Heat Ratio (γ). With our tool, you need to enter the respective value for Stagnation Density & Specific Heat Ratio 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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