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Critical Pressure Formula

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Critical Pressure is defined as the pressure that will exist at a point when the flow becomes sonic at that point. Check FAQs

p cr = {(\frac{2}{γ + 1})}^{\frac{γ}{γ - 1}} \cdot P 0

p_cr - Critical Pressure?γ - Specific Heat Ratio?P₀ - Stagnation Pressure?

Critical Pressure Example

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With units

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

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

Here is how the Critical Pressure equation looks like.

2.6414 = {(\frac{2}{1.4 + 1})}^{\frac{1.4}{1.4 - 1}} \cdot 5

2.6414at = {(\frac{2}{1.4 + 1})}^{\frac{1.4}{1.4 - 1}} \cdot 5at

2.6414 = {(\frac{2}{1.4 + 1})}^{\frac{1.4}{1.4 - 1}} \cdot 5

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Critical Pressure Solution

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

FIRST Step Consider the formula

p cr = {(\frac{2}{γ + 1})}^{\frac{γ}{γ - 1}} \cdot P 0

Next Step Substitute values of Variables

∴

p cr = {(\frac{2}{1.4 + 1})}^{\frac{1.4}{1.4 - 1}} \cdot 5at

Next Step Convert Units

∴

p cr = {(\frac{2}{1.4 + 1})}^{\frac{1.4}{1.4 - 1}} \cdot 490332.5Pa

Next Step Prepare to Evaluate

∴

p cr = {(\frac{2}{1.4 + 1})}^{\frac{1.4}{1.4 - 1}} \cdot 490332.5

Next Step Evaluate

∴

p cr = 259033.729675831Pa

Next Step Convert to Output's Unit

∴

p cr = 2.64140893858587at

LAST Step Rounding Answer

∴

p cr = 2.6414at

Critical Pressure Formula Elements

Variables

Critical Pressure

Critical Pressure is defined as the pressure that will exist at a point when the flow becomes sonic at that point.

Symbol: p_cr

Measurement: PressureUnit: at

Note: Value should be greater than 0.

Formulas to find Critical Pressure

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

Stagnation Pressure

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.

Symbol: P₀

Measurement: PressureUnit: at

Note: Value can be positive or negative.

Formulas to find Stagnation Pressure

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 Pressure?

Critical Pressure evaluator uses Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure to evaluate the Critical Pressure, Critical Pressure formula is defined as the pressure at which a gas can flow through a nozzle at the speed of sound. It is essential in understanding compressible flow behavior in aerospace applications and the dynamics of sound waves. Critical Pressure is denoted by p_cr symbol.

How to evaluate Critical Pressure using this online evaluator? To use this online evaluator for Critical Pressure, enter Specific Heat Ratio (γ) & Stagnation Pressure (P₀) and hit the calculate button.

FAQs on Critical Pressure

What is the formula to find Critical Pressure?

The formula of Critical Pressure is expressed as Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure. Here is an example- 2.7E-5 = (2/(1.4+1))^(1.4/(1.4-1))*490332.5.

How to calculate Critical Pressure?

With Specific Heat Ratio (γ) & Stagnation Pressure (P₀) we can find Critical Pressure using the formula - Critical Pressure = (2/(Specific Heat Ratio+1))^(Specific Heat Ratio/(Specific Heat Ratio-1))*Stagnation Pressure.

Can the Critical Pressure be negative?

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

Which unit is used to measure Critical Pressure?

Critical Pressure is usually measured using the Atmosphere Technical[at] for Pressure. Pascal[at], Kilopascal[at], Bar[at] are the few other units in which Critical Pressure can be measured.

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