Critical Speed of Sound from Prandtl Relation 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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Normal Shock Wave

Governing Equations and Sound Wave

Oblique Shock and Expansion Waves

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Normal Shock Relations

Downstream Shock Waves

Property Change Across Shock Waves

Upstream Shock Waves

✖Velocity Downstream of Shock is the velocity of flow behind the shock wave.ⓘ Velocity Downstream of Shock [V₂]			+10% -10%
✖Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.ⓘ Velocity Upstream of Shock [V₁]			+10% -10%

✖The Critical Speed of Sound is defined as the speed of sound at critical conditions in fluid flow.ⓘ Critical Speed of Sound from Prandtl Relation [a_cr]

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Formula

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Critical Speed of Sound from Prandtl Relation

Formula

`"a"_{"cr"} = sqrt("V"_{"2"}*"V"_{"1"})`

Example

`"79.74154m/s"=sqrt("79.351m/s"*"80.134m/s")`

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Critical Speed of Sound from Prandtl Relation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Speed of Sound = sqrt(Velocity Downstream of Shock*Velocity Upstream of Shock)
a_cr = sqrt(V₂*V₁)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Critical Speed of Sound - (Measured in Meter per Second) - The Critical Speed of Sound is defined as the speed of sound at critical conditions in fluid flow.
Velocity Downstream of Shock - (Measured in Meter per Second) - Velocity Downstream of Shock is the velocity of flow behind the shock wave.
Velocity Upstream of Shock - (Measured in Meter per Second) - Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.

STEP 1: Convert Input(s) to Base Unit

Velocity Downstream of Shock: 79.351 Meter per Second --> 79.351 Meter per Second No Conversion Required
Velocity Upstream of Shock: 80.134 Meter per Second --> 80.134 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_cr = sqrt(V₂*V₁) --> sqrt(79.351*80.134)

Evaluating ... ...

a_cr = 79.7415389492829

STEP 3: Convert Result to Output's Unit

79.7415389492829 Meter per Second --> No Conversion Required

FINAL ANSWER

79.7415389492829 ≈ 79.74154 Meter per Second <-- Critical Speed of Sound

(Calculation completed in 00.004 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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Amrita School of Engineering (ASE), Vallikavu

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< 7 Normal Shock Relations Calculators

Enthalpy Difference using Hugoniot Equation

Go Enthalpy Change = 0.5*(Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock)*((Density Ahead of Normal Shock+Density Behind Normal Shock)/(Density Behind Normal Shock*Density Ahead of Normal Shock))

Relation between Mach Number and Characteristic Mach Number

Go Characteristic Mach Number = ((Specific Heat Ratio+1)/(Specific Heat Ratio-1+2/(Mach Number^2)))^0.5

Critical Speed of Sound from Prandtl Relation

Go Critical Speed of Sound = sqrt(Velocity Downstream of Shock*Velocity Upstream of Shock)

Downstream Velocity using Prandtl Relation

Go Velocity Downstream of Shock = (Critical Speed of Sound^2)/Velocity Upstream of Shock

Upstream Velocity using Prandtl Relation

Go Velocity Upstream of Shock = (Critical Speed of Sound^2)/Velocity Downstream of Shock

Mach Number given Impact and Static Pressure

Go Mach Number = (5*((Impact Pressure/Static Pressure+1)^(2/7)-1))^(0.5)

Characteristic Mach Number

Go Characteristic Mach Number = Fluid Velocity/Critical Speed of Sound

Critical Speed of Sound from Prandtl Relation Formula

Critical Speed of Sound = sqrt(Velocity Downstream of Shock*Velocity Upstream of Shock)
a_cr = sqrt(V₂*V₁)

What is Prandtl relation?

Prandtl relation is an intermediate relation for normal shocks. It relates the velocity ahead of a shock to the downstream velocity after the shock, which in turn help to obtain downstream Mach number of the flow.

How to Calculate Critical Speed of Sound from Prandtl Relation?

Critical Speed of Sound from Prandtl Relation calculator uses Critical Speed of Sound = sqrt(Velocity Downstream of Shock*Velocity Upstream of Shock) to calculate the Critical Speed of Sound, Critical speed of sound from Prandtl relation formula is defined as the square root of product of upstream and downstream velocities across the normal shock. Critical Speed of Sound is denoted by a_cr symbol.

How to calculate Critical Speed of Sound from Prandtl Relation using this online calculator? To use this online calculator for Critical Speed of Sound from Prandtl Relation, enter Velocity Downstream of Shock (V₂) & Velocity Upstream of Shock (V₁) and hit the calculate button. Here is how the Critical Speed of Sound from Prandtl Relation calculation can be explained with given input values -> 107.2655 = sqrt(79.351*80.134).

FAQ

What is Critical Speed of Sound from Prandtl Relation?

Critical speed of sound from Prandtl relation formula is defined as the square root of product of upstream and downstream velocities across the normal shock and is represented as a_cr = sqrt(V₂*V₁) or Critical Speed of Sound = sqrt(Velocity Downstream of Shock*Velocity Upstream of Shock). Velocity Downstream of Shock is the velocity of flow behind the shock wave & Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.

How to calculate Critical Speed of Sound from Prandtl Relation?

Critical speed of sound from Prandtl relation formula is defined as the square root of product of upstream and downstream velocities across the normal shock is calculated using Critical Speed of Sound = sqrt(Velocity Downstream of Shock*Velocity Upstream of Shock). To calculate Critical Speed of Sound from Prandtl Relation, you need Velocity Downstream of Shock (V₂) & Velocity Upstream of Shock (V₁). With our tool, you need to enter the respective value for Velocity Downstream of Shock & Velocity Upstream of Shock 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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