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Critical Density Formula

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Critical Density is defined as the density of the fluid at sonic conditions, when Mach number is one. Check FAQs

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

ρ_cr - Critical Density?ρ_o - Stagnation Density?γ - Specific Heat Ratio?

Critical Density Example

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Here is how the Critical Density equation looks like with Values.

Here is how the Critical Density equation looks like with Units.

Here is how the Critical Density equation looks like.

0.7734 = 1.22 \cdot {(\frac{2}{1.4 + 1})}^{\frac{1}{1.4 - 1}}

0.7734kg/m³ = 1.22kg/m³ \cdot {(\frac{2}{1.4 + 1})}^{\frac{1}{1.4 - 1}}

0.7734 = 1.22 \cdot {(\frac{2}{1.4 + 1})}^{\frac{1}{1.4 - 1}}

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Critical Density Solution

Follow our step by step solution on how to calculate Critical Density?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

ρ cr = 1.22 \cdot {(\frac{2}{1.4 + 1})}^{\frac{1}{1.4 - 1}}

Next Step Evaluate

∴

ρ cr = 0.773404537217943kg/m³

LAST Step Rounding Answer

∴

ρ cr = 0.7734kg/m³

Critical Density Formula Elements

Variables

Critical Density

Critical Density is defined as the density of the fluid at sonic conditions, when Mach number is one.

Symbol: ρ_cr

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Critical Density

Stagnation Density

Stagnation Density is defined as the density of fluid at a stagnation point in a fluid flow.

Symbol: ρ_o

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Stagnation Density

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.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Specific Heat Ratio

Other formulas in Governing Equations and Sound Wave category

Go Speed of Sound

a = \sqrt{γ \cdot [R-Dry-Air] \cdot T s}

Go Mach Number

M = \frac{V b}{a}

Go Mach Angle

μ = a \sin (\frac{1}{M})

Go Mayer's Formula

R = C p - C v

How to Evaluate Critical Density?

Critical Density evaluator uses Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1)) to evaluate the Critical Density, Critical Density formula is defined as the density at which a gas transitions from subsonic to supersonic flow, playing a crucial role in understanding compressible flow dynamics and the behavior of sound waves in various aerospace applications. Critical Density is denoted by ρ_cr symbol.

How to evaluate Critical Density using this online evaluator? To use this online evaluator for Critical Density, enter Stagnation Density (ρ_o) & Specific Heat Ratio (γ) and hit the calculate button.

FAQs on Critical Density

What is the formula to find Critical Density?

The formula of Critical Density is expressed as Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1)). Here is an example- 0.77416 = 1.22*(2/(1.4+1))^(1/(1.4-1)).

How to calculate Critical Density?

With Stagnation Density (ρ_o) & Specific Heat Ratio (γ) we can find Critical Density using the formula - Critical Density = Stagnation Density*(2/(Specific Heat Ratio+1))^(1/(Specific Heat Ratio-1)).

Can the Critical Density be negative?

No, the Critical Density, measured in Density cannot be negative.

Which unit is used to measure Critical Density?

Critical Density is usually measured using the Kilogram per Cubic Meter[kg/m³] for Density. Kilogram per Cubic Centimeter[kg/m³], Gram per Cubic Meter[kg/m³], Gram per Cubic Centimeter[kg/m³] are the few other units in which Critical Density can be measured.

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Critical Density Formula

Critical Density Example

Critical Density Solution

Critical Density Formula Elements

Other formulas in Governing Equations and Sound Wave category

How to Evaluate Critical Density?

FAQs on Critical Density

Variable Name