Density behind Normal Shock using Normal Shock Momentum Equation Calculator

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

✖Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave.ⓘ Density behind Normal Shock using Normal Shock Momentum Equation [ρ₂]

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Density behind Normal Shock using Normal Shock Momentum Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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 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.
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.
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

Static Pressure Ahead of Normal Shock: 65.374 Pascal --> 65.374 Pascal No Conversion Required
Density Ahead of Normal Shock: 5.4 Kilogram per Cubic Meter --> 5.4 Kilogram per Cubic Meter No Conversion Required
Velocity Upstream of Shock: 80.134 Meter per Second --> 80.134 Meter per Second No Conversion Required
Static pressure Behind Normal shock: 110 Pascal --> 110 Pascal 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

ρ₂ = (P₁+ρ₁*V₁^2-P₂)/(V₂^2) --> (65.374+5.4*80.134^2-110)/(79.351^2)

Evaluating ... ...

ρ₂ = 5.50000799749871

STEP 3: Convert Result to Output's Unit

5.50000799749871 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

5.50000799749871 ≈ 5.500008 Kilogram per Cubic Meter <-- Density Behind Normal Shock

(Calculation completed in 00.004 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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

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< Downstream Shock Waves Calculators

Mach Number behind Shock

LaTeX Go Mach Number Behind Normal Shock = ((2+Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Mach Number Ahead of Normal Shock^2)/(2*Specific Heat Ratio*Mach Number Ahead of Normal Shock^2-Specific Heat Ratio+1))^(1/2)

Static Pressure behind Normal Shock using Normal Shock Momentum Equation

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

Velocity behind Normal Shock

LaTeX Go Velocity Downstream of Shock = Velocity Upstream of Shock/((Specific Heat Ratio+1)/((Specific Heat Ratio-1)+2/(Mach Number^2)))

Characteristic Mach Number behind Shock

LaTeX Go Characteristic Mach Number Behind Shock = 1/Characteristic Mach Number Ahead of Shock

Density behind Normal Shock using Normal Shock Momentum Equation Formula

LaTeX Go

What are qualitative changes across the shock waves?

Shock waves are very thin regions 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 stay the same.

Why total enthalpy remains same across the normal shock wave?

The flow across a shock wave is adiabatic, and for steady, inviscid, adiabatic flow, total enthalpy constant, is a statement of the energy equation, hence the total enthalpy remains same before and after the normal shock wave.

How to Calculate Density behind Normal Shock using Normal Shock Momentum Equation?

Density behind Normal Shock using Normal Shock Momentum Equation calculator uses Density Behind Normal Shock = (Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Static pressure Behind Normal shock)/(Velocity Downstream of Shock^2) to calculate the Density Behind Normal Shock, Density behind Normal Shock using Normal Shock Momentum Equation formula is defined as a method to determine the density of a fluid after it passes through a normal shock wave, reflecting changes in pressure and velocity across the shock. Density Behind Normal Shock is denoted by ρ₂ symbol.

How to calculate Density behind Normal Shock using Normal Shock Momentum Equation using this online calculator? To use this online calculator for Density behind Normal Shock using Normal Shock Momentum Equation, enter Static Pressure Ahead of Normal Shock (P₁), Density Ahead of Normal Shock (ρ₁), Velocity Upstream of Shock (V₁), Static pressure Behind Normal shock (P₂) & Velocity Downstream of Shock (V₂) and hit the calculate button. Here is how the Density behind Normal Shock using Normal Shock Momentum Equation calculation can be explained with given input values -> 18.02413 = (65.374+5.4*80.134^2-110)/(79.351^2).

FAQ

What is Density behind Normal Shock using Normal Shock Momentum Equation?

Density behind Normal Shock using Normal Shock Momentum Equation formula is defined as a method to determine the density of a fluid after it passes through a normal shock wave, reflecting changes in pressure and velocity across the shock and is represented as ρ₂ = (P₁+ρ₁*V₁^2-P₂)/(V₂^2) or Density Behind Normal Shock = (Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Static pressure Behind Normal shock)/(Velocity Downstream of Shock^2). Static Pressure Ahead of Normal Shock is the pressure in the upstream direction of shock, Density Ahead of Normal Shock refers to the density of a fluid before encountering a normal shock wave, Velocity Upstream of Shock is the velocity of flow ahead of the shock wave, Static Pressure Behind Normal Shock denotes the pressure of a fluid after passing through a normal shock wave & Velocity Downstream of Shock is the velocity of flow behind the shock wave.

How to calculate Density behind Normal Shock using Normal Shock Momentum Equation?

Density behind Normal Shock using Normal Shock Momentum Equation formula is defined as a method to determine the density of a fluid after it passes through a normal shock wave, reflecting changes in pressure and velocity across the shock is calculated using Density Behind Normal Shock = (Static Pressure Ahead of Normal Shock+Density Ahead of Normal Shock*Velocity Upstream of Shock^2-Static pressure Behind Normal shock)/(Velocity Downstream of Shock^2). To calculate Density behind Normal Shock using Normal Shock Momentum Equation, you need Static Pressure Ahead of Normal Shock (P₁), Density Ahead of Normal Shock (ρ₁), Velocity Upstream of Shock (V₁), Static pressure Behind Normal shock (P₂) & Velocity Downstream of Shock (V₂). With our tool, you need to enter the respective value for Static Pressure Ahead of Normal Shock, Density Ahead of Normal Shock, Velocity Upstream of Shock, Static pressure Behind Normal shock & 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.

How many ways are there to calculate Density Behind Normal Shock?

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

Density Behind Normal Shock = Density Ahead of Normal Shock*(((Specific Heat Ratio+1)*Mach Number^2)/(2+(Specific Heat Ratio-1)*Mach Number^2))
Density Behind Normal Shock = (Density Ahead of Normal Shock*Velocity Upstream of Shock)/Velocity Downstream of Shock

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