Critical Pressure 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

✖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%
✖Stagnation Pressure at point in fluid flow is defined as the pressure that would exist if the flow were slowed down isentropically to zero velocity.ⓘ Stagnation Pressure [P₀]			+10% -10%

✖Critical Pressure is defined as the pressure that will exist at a point when the flow becomes sonic at that point.ⓘ Critical Pressure [p_cr]

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Formula

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Critical Pressure

Formula

`"p"_{"cr"} = (2/("γ"+1))^("γ"/("γ"-1))*"P"_{"0"}`

Example

`"2.641409at"=(2/("1.4"+1))^("1.4"/("1.4"-1))*"5at"`

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Critical Pressure Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure
p_cr = (2/(γ+1))^(γ/(γ-1))*P₀
This formula uses 3 Variables

Variables Used

Critical Pressure - (Measured in Pascal) - Critical Pressure is defined as the pressure that will exist at a point when the flow becomes sonic at that point.
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.
Stagnation Pressure - (Measured in Pascal) - Stagnation Pressure at point in fluid flow is defined as the pressure that would exist if the flow were slowed down isentropically to zero velocity.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.4 --> No Conversion Required
Stagnation Pressure: 5 Atmosphere Technical --> 490332.5 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

p_cr = (2/(γ+1))^(γ/(γ-1))*P₀ --> (2/(1.4+1))^(1.4/(1.4-1))*490332.5

Evaluating ... ...

p_cr = 259033.729675831

STEP 3: Convert Result to Output's Unit

259033.729675831 Pascal -->2.64140893858587 Atmosphere Technical (Check conversion here)

FINAL ANSWER

2.64140893858587 ≈ 2.641409 Atmosphere Technical <-- Critical Pressure

(Calculation completed in 00.004 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

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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 Pressure Formula

Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure
p_cr = (2/(γ+1))^(γ/(γ-1))*P₀

What is Critical Pressure?

The Critical Pressure is defined as the pressure at a point in a fluid flow when the flow is accelerated or decelerated to sonic condition isentropically.

How to Calculate Critical Pressure?

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

How to calculate Critical Pressure using this online calculator? To use this online calculator for Critical Pressure, enter Specific Heat Ratio (γ) & Stagnation Pressure (P₀) and hit the calculate button. Here is how the Critical Pressure calculation can be explained with given input values -> 2.7E-5 = (2/(1.4+1))^(1.4/(1.4-1))*490332.5.

FAQ

What is Critical Pressure?

The Critical Pressure at a point in a fluid flow is defined as the pressure that would exist if the flow became sonic at that point and is represented as p_cr = (2/(γ+1))^(γ/(γ-1))*P₀ or Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure. 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 & Stagnation Pressure at point in fluid flow is defined as the pressure that would exist if the flow were slowed down isentropically to zero velocity.

How to calculate Critical Pressure?

The Critical Pressure at a point in a fluid flow is defined as the pressure that would exist if the flow became sonic at that point is calculated using Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure. To calculate Critical Pressure, you need Specific Heat Ratio (γ) & Stagnation Pressure (P₀). With our tool, you need to enter the respective value for Specific Heat Ratio & Stagnation Pressure 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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