Density ahead of Normal Shock using Normal Shock Momentum Equation Calculator

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Compressible Flow

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Normal Shock Wave

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Upstream Shock Waves

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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%
✖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%
✖Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock.ⓘ Static Pressure Ahead of Normal Shock [P₁]			+10% -10%
✖Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.ⓘ Velocity Upstream of Shock [V₁]			+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 using Normal Shock Momentum Equation [ρ₁]

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Formula

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Density ahead of Normal Shock using Normal Shock Momentum Equation

Formula

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

Example

`"5.399992kg/m³"=("110Pa"+"5.5kg/m³"*("79.351m/s")^2-"65.374Pa")/(("80.134m/s")^2)`

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Density ahead of Normal Shock using Normal Shock Momentum Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
ρ₁ = (P₂+ρ₂*V₂^2-P₁)/(V₁^2)
This formula uses 6 Variables

Variables Used

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.
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.
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.
Static Pressure Ahead of Normal Shock - (Measured in Pascal) - Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock.
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

Static pressure Behind Normal shock: 110 Pascal --> 110 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
Static Pressure Ahead of Normal Shock: 65.374 Pascal --> 65.374 Pascal 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

ρ₁ = (P₂+ρ₂*V₂^2-P₁)/(V₁^2) --> (110+5.5*79.351^2-65.374)/(80.134^2)

Evaluating ... ...

ρ₁ = 5.39999215802699

STEP 3: Convert Result to Output's Unit

5.39999215802699 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

5.39999215802699 ≈ 5.399992 Kilogram per Cubic Meter <-- Density Ahead of Normal 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 Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has verified this Calculator and 100+ 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

Density ahead of Normal Shock using Normal Shock Momentum Equation Formula

Which properties changes across normal shock and which remains same?

The normal Shock wave is a very thin region in a supersonic flow across which the pressure, density, temperature, and entropy increases; the Mach number, flow velocity, and total pressure decreases; and the total enthalpy stays the same.

How to Calculate Density ahead of Normal Shock using Normal Shock Momentum Equation?

Density ahead of Normal Shock using Normal Shock Momentum Equation calculator uses 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) to calculate the Density Ahead of Normal Shock, The Density ahead of Normal Shock using Normal Shock Momentum Equation computes the density of a fluid ahead of a normal shock wave by utilizing the Normal Shock Momentum Equation. This formula incorporates parameters such as the static pressures ahead and behind the shock, the density behind the shock, and the velocities upstream and downstream of the shock. Density Ahead of Normal Shock is denoted by ρ₁ symbol.

How to calculate Density ahead of Normal Shock using Normal Shock Momentum Equation using this online calculator? To use this online calculator for Density ahead of Normal Shock using Normal Shock Momentum Equation, enter Static pressure Behind Normal shock (P₂), Density Behind Normal Shock (ρ₂), Velocity Downstream of Shock (V₂), Static Pressure Ahead of Normal Shock (P₁) & Velocity Upstream of Shock (V₁) and hit the calculate button. Here is how the Density ahead of Normal Shock using Normal Shock Momentum Equation calculation can be explained with given input values -> 1.649266 = (110+5.5*79.351^2-65.374)/(80.134^2).

FAQ

What is Density ahead of Normal Shock using Normal Shock Momentum Equation?

The Density ahead of Normal Shock using Normal Shock Momentum Equation computes the density of a fluid ahead of a normal shock wave by utilizing the Normal Shock Momentum Equation. This formula incorporates parameters such as the static pressures ahead and behind the shock, the density behind the shock, and the velocities upstream and downstream of the shock and is represented as ρ₁ = (P₂+ρ₂*V₂^2-P₁)/(V₁^2) or 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 Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave, 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, Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock & Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.

How to calculate Density ahead of Normal Shock using Normal Shock Momentum Equation?

The Density ahead of Normal Shock using Normal Shock Momentum Equation computes the density of a fluid ahead of a normal shock wave by utilizing the Normal Shock Momentum Equation. This formula incorporates parameters such as the static pressures ahead and behind the shock, the density behind the shock, and the velocities upstream and downstream of the shock is calculated using 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). To calculate Density ahead of Normal Shock using Normal Shock Momentum Equation, you need Static pressure Behind Normal shock (P₂), Density Behind Normal Shock (ρ₂), Velocity Downstream of Shock (V₂), Static Pressure Ahead of Normal Shock (P₁) & Velocity Upstream of Shock (V₁). With our tool, you need to enter the respective value for Static pressure Behind Normal shock, Density Behind Normal Shock, Velocity Downstream of Shock, Static Pressure Ahead of Normal 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.

How many ways are there to calculate Density Ahead of Normal Shock?

In this formula, Density Ahead of Normal Shock uses Static pressure Behind Normal shock, Density Behind Normal Shock, Velocity Downstream of Shock, Static Pressure Ahead of Normal Shock & Velocity Upstream of Shock. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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