Critical Density Calculator

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

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Governing Equations and Sound Wave

Normal Shock Wave

Oblique Shock and Expansion Waves

✖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"}*(2/("γ"+1))^(1/("γ"-1))`

Example

`"0.773405kg/m³"="1.22kg/m³"*(2/("1.4"+1))^(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 00.004 seconds)

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Home » Physics » Aerodynamics » Compressible Flow » Governing Equations and Sound Wave » Critical Density

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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

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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

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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