Velocity ahead of Normal Shock by Normal Shock Momentum Equation 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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Upstream Shock Waves

Downstream Shock Waves

Normal Shock Relations

Property Change Across Shock Waves

✖Static Pressure Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave.ⓘ Static pressure Behind Normal shock [P₂]			+10% -10%
✖Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock.ⓘ Static Pressure Ahead of Normal Shock [P₁]			+10% -10%
✖Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave.ⓘ Density Behind Normal Shock [ρ₂]			+10% -10%
✖Velocity Downstream of Shock is the velocity of flow behind the shock wave.ⓘ Velocity Downstream of Shock [V₂]			+10% -10%
✖Density Ahead of Normal Shock refers to the density of a fluid before encountering a normal shock wave.ⓘ Density Ahead of Normal Shock [ρ₁]			+10% -10%

✖Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.ⓘ Velocity ahead of Normal Shock by Normal Shock Momentum Equation [V₁]

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Formula

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Velocity ahead of Normal Shock by Normal Shock Momentum Equation

Formula

`"V"_{"1"} = sqrt(("P"_{"2"}-"P"_{"1"}+"ρ"_{"2"}*"V"_{"2"}^2)/"ρ"_{"1"})`

Example

`"80.13394m/s"=sqrt(("110Pa"-"65.374Pa"+"5.5kg/m³"*("79.351m/s")^2)/"5.4kg/m³")`

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Velocity ahead of Normal Shock by Normal Shock Momentum Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity Upstream of Shock = sqrt((Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock+Density Behind Normal Shock*Velocity Downstream of Shock^2)/Density Ahead of Normal Shock)
V₁ = sqrt((P₂-P₁+ρ₂*V₂^2)/ρ₁)
This formula uses 1 Functions, 6 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

Velocity Upstream of Shock - (Measured in Meter per Second) - Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.
Static pressure Behind Normal shock - (Measured in Pascal) - Static Pressure Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave.
Static Pressure Ahead of Normal Shock - (Measured in Pascal) - Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock.
Density Behind Normal Shock - (Measured in Kilogram per Cubic Meter) - Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave.
Velocity Downstream of Shock - (Measured in Meter per Second) - Velocity Downstream of Shock is the velocity of flow behind the shock wave.
Density Ahead of Normal Shock - (Measured in Kilogram per Cubic Meter) - Density Ahead of Normal Shock refers to the density of a fluid before encountering a normal shock wave.

STEP 1: Convert Input(s) to Base Unit

Static pressure Behind Normal shock: 110 Pascal --> 110 Pascal No Conversion Required
Static Pressure Ahead of Normal Shock: 65.374 Pascal --> 65.374 Pascal No Conversion Required
Density Behind Normal Shock: 5.5 Kilogram per Cubic Meter --> 5.5 Kilogram per Cubic Meter No Conversion Required
Velocity Downstream of Shock: 79.351 Meter per Second --> 79.351 Meter per Second No Conversion Required
Density Ahead of Normal Shock: 5.4 Kilogram per Cubic Meter --> 5.4 Kilogram per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V₁ = sqrt((P₂-P₁+ρ₂*V₂^2)/ρ₁) --> sqrt((110-65.374+5.5*79.351^2)/5.4)

Evaluating ... ...

V₁ = 80.1339418139913

STEP 3: Convert Result to Output's Unit

80.1339418139913 Meter per Second --> No Conversion Required

FINAL ANSWER

80.1339418139913 ≈ 80.13394 Meter per Second <-- Velocity Upstream of Shock

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Compressible Flow » Normal Shock Wave » Upstream Shock Waves » Velocity ahead of Normal Shock by Normal Shock Momentum Equation

Credits

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 Upstream Shock Waves Calculators

Velocity ahead of Normal Shock by Normal Shock Momentum Equation

Go Velocity Upstream of Shock = sqrt((Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock+Density Behind Normal Shock*Velocity Downstream of Shock^2)/Density Ahead of Normal Shock)

Density ahead of Normal Shock using Normal Shock Momentum Equation

Go Density Ahead of Normal Shock = (Static pressure Behind Normal shock+Density Behind Normal Shock*Velocity Downstream of Shock^2-Static Pressure Ahead of Normal Shock)/(Velocity Upstream of Shock^2)

Static Pressure ahead of Normal Shock using Normal Shock Momentum Equation

Go Static Pressure Ahead of Normal Shock = Static pressure Behind Normal shock+Density Behind Normal Shock*Velocity Downstream of Shock^2-Density Ahead of Normal Shock*Velocity Upstream of Shock^2

Velocity ahead of Normal Shock from Normal Shock Energy Equation

Go Velocity Upstream of Shock = sqrt(2*(Enthalpy Behind Normal Shock+(Velocity Downstream of Shock^2)/2-Enthalpy Ahead of Normal Shock))

Enthalpy ahead of Normal Shock from Normal Shock Energy Equation

Go Enthalpy Ahead of Normal Shock = Enthalpy Behind Normal Shock+(Velocity Downstream of Shock^2-Velocity Upstream of Shock^2)/2

Flow Velocity Upstream of Shock Wave using Continuity Equation

Go Velocity Upstream of Shock = (Density Behind Normal Shock*Velocity Downstream of Shock)/Density Ahead of Normal Shock

Density Upstream of Shock Wave using Continuity Equation

Go Density Ahead of Normal Shock = (Density Behind Normal Shock*Velocity Downstream of Shock)/Velocity Upstream of Shock

Velocity ahead of Normal Shock by Normal Shock Momentum Equation Formula

Which parameter govern the changes of flow properties across normal shock?

Continuity, momentum and energy equations across normal shock lead to relations for changes across a normal shock as a function of upstream Mach number only.

How to Calculate Velocity ahead of Normal Shock by Normal Shock Momentum Equation?

Velocity ahead of Normal Shock by Normal Shock Momentum Equation calculator uses Velocity Upstream of Shock = sqrt((Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock+Density Behind Normal Shock*Velocity Downstream of Shock^2)/Density Ahead of Normal Shock) to calculate the Velocity Upstream of Shock, The Velocity ahead of Normal Shock by Normal Shock Momentum Equation calculates the velocity of a fluid ahead of a normal shock wave using the Normal Shock Momentum Equation. This formula considers parameters such as the static pressures ahead and behind the shock, the density behind the shock, and the velocity downstream of the shock. It provides crucial information about the fluid velocity before encountering the shock wave, aiding in the analysis of compressible flow behavior. Velocity Upstream of Shock is denoted by V₁ symbol.

How to calculate Velocity ahead of Normal Shock by Normal Shock Momentum Equation using this online calculator? To use this online calculator for Velocity ahead of Normal Shock by Normal Shock Momentum Equation, enter Static pressure Behind Normal shock (P₂), Static Pressure Ahead of Normal Shock (P₁), Density Behind Normal Shock (ρ₂), Velocity Downstream of Shock (V₂) & Density Ahead of Normal Shock (ρ₁) and hit the calculate button. Here is how the Velocity ahead of Normal Shock by Normal Shock Momentum Equation calculation can be explained with given input values -> 80.13394 = sqrt((110-65.374+5.5*79.351^2)/5.4).

FAQ

What is Velocity ahead of Normal Shock by Normal Shock Momentum Equation?

The Velocity ahead of Normal Shock by Normal Shock Momentum Equation calculates the velocity of a fluid ahead of a normal shock wave using the Normal Shock Momentum Equation. This formula considers parameters such as the static pressures ahead and behind the shock, the density behind the shock, and the velocity downstream of the shock. It provides crucial information about the fluid velocity before encountering the shock wave, aiding in the analysis of compressible flow behavior and is represented as V₁ = sqrt((P₂-P₁+ρ₂*V₂^2)/ρ₁) or Velocity Upstream of Shock = sqrt((Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock+Density Behind Normal Shock*Velocity Downstream of Shock^2)/Density Ahead of Normal Shock). Static Pressure Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave, Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock, Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave, Velocity Downstream of Shock is the velocity of flow behind the shock wave & Density Ahead of Normal Shock refers to the density of a fluid before encountering a normal shock wave.

How to calculate Velocity ahead of Normal Shock by Normal Shock Momentum Equation?

The Velocity ahead of Normal Shock by Normal Shock Momentum Equation calculates the velocity of a fluid ahead of a normal shock wave using the Normal Shock Momentum Equation. This formula considers parameters such as the static pressures ahead and behind the shock, the density behind the shock, and the velocity downstream of the shock. It provides crucial information about the fluid velocity before encountering the shock wave, aiding in the analysis of compressible flow behavior is calculated using Velocity Upstream of Shock = sqrt((Static pressure Behind Normal shock-Static Pressure Ahead of Normal Shock+Density Behind Normal Shock*Velocity Downstream of Shock^2)/Density Ahead of Normal Shock). To calculate Velocity ahead of Normal Shock by Normal Shock Momentum Equation, you need Static pressure Behind Normal shock (P₂), Static Pressure Ahead of Normal Shock (P₁), Density Behind Normal Shock (ρ₂), Velocity Downstream of Shock (V₂) & Density Ahead of Normal Shock (ρ₁). With our tool, you need to enter the respective value for Static pressure Behind Normal shock, Static Pressure Ahead of Normal Shock, Density Behind Normal Shock, Velocity Downstream of Shock & Density Ahead of Normal Shock and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Velocity Upstream of Shock?

In this formula, Velocity Upstream of Shock uses Static pressure Behind Normal shock, Static Pressure Ahead of Normal Shock, Density Behind Normal Shock, Velocity Downstream of Shock & Density Ahead of Normal Shock. We can use 2 other way(s) to calculate the same, which is/are as follows -

Velocity Upstream of Shock = sqrt(2*(Enthalpy Behind Normal Shock+(Velocity Downstream of Shock^2)/2-Enthalpy Ahead of Normal Shock))
Velocity Upstream of Shock = (Density Behind Normal Shock*Velocity Downstream of Shock)/Density Ahead of Normal Shock

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