Density Upstream of Shock Wave using Continuity 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

✖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%
✖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 Upstream of Shock Wave using Continuity Equation [ρ₁]

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Formula

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Density Upstream of Shock Wave using Continuity Equation

Formula

`"ρ"_{"1"} = ("ρ"_{"2"}*"V"_{"2"})/"V"_{"1"}`

Example

`"5.446259kg/m³"=("5.5kg/m³"*"79.351m/s")/"80.134m/s"`

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Density Upstream of Shock Wave using Continuity Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density Ahead of Normal Shock = (Density Behind Normal Shock*Velocity Downstream of Shock)/Velocity Upstream of Shock
ρ₁ = (ρ₂*V₂)/V₁
This formula uses 4 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.
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.
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

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
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 = (ρ₂*V₂)/V₁ --> (5.5*79.351)/80.134

Evaluating ... ...

ρ₁ = 5.446258766566

STEP 3: Convert Result to Output's Unit

5.446258766566 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

5.446258766566 ≈ 5.446259 Kilogram per Cubic Meter <-- Density Ahead of Normal Shock

(Calculation completed in 00.020 seconds)

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< 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 Upstream of Shock Wave using Continuity Equation Formula

Density Ahead of Normal Shock = (Density Behind Normal Shock*Velocity Downstream of Shock)/Velocity Upstream of Shock
ρ₁ = (ρ₂*V₂)/V₁

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 increase, the Mach number, flow velocity, and total pressure decreases, and the total enthalpy stays the same.

How to Calculate Density Upstream of Shock Wave using Continuity Equation?

Density Upstream of Shock Wave using Continuity Equation calculator uses Density Ahead of Normal Shock = (Density Behind Normal Shock*Velocity Downstream of Shock)/Velocity Upstream of Shock to calculate the Density Ahead of Normal Shock, The Density Upstream of Shock Wave using Continuity Equation calculates the density of a fluid ahead of a shock wave based on the continuity equation. This formula considers parameters such as the density behind the shock, the velocity downstream of the shock, and the velocity upstream of the shock. Density Ahead of Normal Shock is denoted by ρ₁ symbol.

How to calculate Density Upstream of Shock Wave using Continuity Equation using this online calculator? To use this online calculator for Density Upstream of Shock Wave using Continuity Equation, enter Density Behind Normal Shock (ρ₂), Velocity Downstream of Shock (V₂) & Velocity Upstream of Shock (V₁) and hit the calculate button. Here is how the Density Upstream of Shock Wave using Continuity Equation calculation can be explained with given input values -> 3.009866 = (5.5*79.351)/80.134.

FAQ

What is Density Upstream of Shock Wave using Continuity Equation?

The Density Upstream of Shock Wave using Continuity Equation calculates the density of a fluid ahead of a shock wave based on the continuity equation. This formula considers parameters such as the density behind the shock, the velocity downstream of the shock, and the velocity upstream of the shock and is represented as ρ₁ = (ρ₂*V₂)/V₁ or Density Ahead of Normal Shock = (Density Behind Normal Shock*Velocity Downstream of Shock)/Velocity Upstream 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 & Velocity Upstream of Shock is the velocity of flow ahead of the shock wave.

How to calculate Density Upstream of Shock Wave using Continuity Equation?

The Density Upstream of Shock Wave using Continuity Equation calculates the density of a fluid ahead of a shock wave based on the continuity equation. This formula considers parameters such as the density behind the shock, the velocity downstream of the shock, and the velocity upstream of the shock is calculated using Density Ahead of Normal Shock = (Density Behind Normal Shock*Velocity Downstream of Shock)/Velocity Upstream of Shock. To calculate Density Upstream of Shock Wave using Continuity Equation, you need Density Behind Normal Shock (ρ₂), Velocity Downstream of Shock (V₂) & Velocity Upstream of Shock (V₁). With our tool, you need to enter the respective value for Density Behind Normal Shock, 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.

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

In this formula, Density Ahead of Normal Shock uses Density Behind Normal Shock, Velocity Downstream of 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 = (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)

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