Upstream Velocity using 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

✖The Critical Speed of Sound is defined as the speed of sound at critical conditions in fluid flow.ⓘ Critical Speed of Sound [a_cr]			+10% -10%
✖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.ⓘ Upstream Velocity using Prandtl Relation [V₁]

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Formula

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Upstream Velocity using Prandtl Relation

Formula

`"V"_{"1"} = ("a"_{"cr"}^2)/"V"_{"2"}`

Example

`"80.13292m/s"=(("79.741m/s")^2)/"79.351m/s"`

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Upstream Velocity using Prandtl Relation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity Upstream of Shock = (Critical Speed of Sound^2)/Velocity Downstream of Shock
V₁ = (a_cr^2)/V₂
This formula uses 3 Variables

Variables Used

Velocity Upstream of Shock - (Measured in Meter per Second) - Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.
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.

STEP 1: Convert Input(s) to Base Unit

Critical Speed of Sound: 79.741 Meter per Second --> 79.741 Meter per Second No Conversion Required
Velocity Downstream of Shock: 79.351 Meter per Second --> 79.351 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V₁ = (a_cr^2)/V₂ --> (79.741^2)/79.351

Evaluating ... ...

V₁ = 80.1329168000403

STEP 3: Convert Result to Output's Unit

80.1329168000403 Meter per Second --> No Conversion Required

FINAL ANSWER

80.1329168000403 ≈ 80.13292 Meter per Second <-- Velocity Upstream of Shock

(Calculation completed in 00.004 seconds)

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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 Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has verified this Calculator and 200+ more calculators!

< 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

Upstream Velocity using Prandtl Relation Formula

Velocity Upstream of Shock = (Critical Speed of Sound^2)/Velocity Downstream of Shock
V₁ = (a_cr^2)/V₂

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 in terms of upstream Mach number.

How to Calculate Upstream Velocity using Prandtl Relation?

Upstream Velocity using Prandtl Relation calculator uses Velocity Upstream of Shock = (Critical Speed of Sound^2)/Velocity Downstream of Shock to calculate the Velocity Upstream of Shock, The Upstream Velocity using Prandtl Relation computes the velocity of a fluid upstream of a normal shock wave based on the Prandtl relation. This formula utilizes the critical speed of sound and the downstream velocity of the fluid to determine the upstream velocity. It provides insight into the flow conditions upstream of the shock wave, aiding in the analysis of compressible flow phenomena. Velocity Upstream of Shock is denoted by V₁ symbol.

How to calculate Upstream Velocity using Prandtl Relation using this online calculator? To use this online calculator for Upstream Velocity using Prandtl Relation, enter Critical Speed of Sound (a_cr) & Velocity Downstream of Shock (V₂) and hit the calculate button. Here is how the Upstream Velocity using Prandtl Relation calculation can be explained with given input values -> 80.13292 = (79.741^2)/79.351.

FAQ

What is Upstream Velocity using Prandtl Relation?

The Upstream Velocity using Prandtl Relation computes the velocity of a fluid upstream of a normal shock wave based on the Prandtl relation. This formula utilizes the critical speed of sound and the downstream velocity of the fluid to determine the upstream velocity. It provides insight into the flow conditions upstream of the shock wave, aiding in the analysis of compressible flow phenomena and is represented as V₁ = (a_cr^2)/V₂ or Velocity Upstream of Shock = (Critical Speed of Sound^2)/Velocity Downstream of Shock. The Critical Speed of Sound is defined as the speed of sound at critical conditions in fluid flow & Velocity Downstream of Shock is the velocity of flow behind the shock wave.

How to calculate Upstream Velocity using Prandtl Relation?

The Upstream Velocity using Prandtl Relation computes the velocity of a fluid upstream of a normal shock wave based on the Prandtl relation. This formula utilizes the critical speed of sound and the downstream velocity of the fluid to determine the upstream velocity. It provides insight into the flow conditions upstream of the shock wave, aiding in the analysis of compressible flow phenomena is calculated using Velocity Upstream of Shock = (Critical Speed of Sound^2)/Velocity Downstream of Shock. To calculate Upstream Velocity using Prandtl Relation, you need Critical Speed of Sound (a_cr) & Velocity Downstream of Shock (V₂). With our tool, you need to enter the respective value for Critical Speed of Sound & Velocity Downstream 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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