Density behind Normal Shock given Upstream Density and Mach Number Calculator

✖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%
✖The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio [γ]			+10% -10%
✖Mach Number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.ⓘ Mach Number [M]			+10% -10%

✖Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave.ⓘ Density behind Normal Shock given Upstream Density and Mach Number [ρ₂]

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Density behind Normal Shock given Upstream Density and Mach Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density Behind Normal Shock = Density Ahead of Normal Shock*(((Specific Heat Ratio+1)*Mach Number^2)/(2+(Specific Heat Ratio-1)*Mach Number^2))
ρ₂ = ρ₁*(((γ+1)*M^2)/(2+(γ-1)*M^2))
This formula uses 4 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.
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.
Specific Heat Ratio - The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Mach Number - Mach Number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.

STEP 1: Convert Input(s) to Base Unit

Density Ahead of Normal Shock: 5.4 Kilogram per Cubic Meter --> 5.4 Kilogram per Cubic Meter No Conversion Required
Specific Heat Ratio: 1.4 --> No Conversion Required
Mach Number: 1.03 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ₂ = ρ₁*(((γ+1)*M^2)/(2+(γ-1)*M^2)) --> 5.4*(((1.4+1)*1.03^2)/(2+(1.4-1)*1.03^2))

Evaluating ... ...

ρ₂ = 5.67129634212741

STEP 3: Convert Result to Output's Unit

5.67129634212741 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

5.67129634212741 ≈ 5.671296 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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< 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 given Upstream Density and Mach Number Formula

LaTeX Go

Density Behind Normal Shock = Density Ahead of Normal Shock*(((Specific Heat Ratio+1)*Mach Number^2)/(2+(Specific Heat Ratio-1)*Mach Number^2))
ρ₂ = ρ₁*(((γ+1)*M^2)/(2+(γ-1)*M^2))

How to obtain density ratio across normal shock?

Density ratio across the normal shock is obtained by rearranging the continuity equation and using Prandtl relation.

How to Calculate Density behind Normal Shock given Upstream Density and Mach Number?

Density behind Normal Shock given Upstream Density and Mach Number calculator uses Density Behind Normal Shock = Density Ahead of Normal Shock*(((Specific Heat Ratio+1)*Mach Number^2)/(2+(Specific Heat Ratio-1)*Mach Number^2)) to calculate the Density Behind Normal Shock, Density behind Normal Shock given Upstream Density and Mach Number formula is defined as a relationship that describes how the density of a gas changes across a normal shock wave, influenced by the upstream density and the Mach number of the flow. Density Behind Normal Shock is denoted by ρ₂ symbol.

How to calculate Density behind Normal Shock given Upstream Density and Mach Number using this online calculator? To use this online calculator for Density behind Normal Shock given Upstream Density and Mach Number, enter Density Ahead of Normal Shock (ρ₁), Specific Heat Ratio (γ) & Mach Number (M) and hit the calculate button. Here is how the Density behind Normal Shock given Upstream Density and Mach Number calculation can be explained with given input values -> 5.671296 = 5.4*(((1.4+1)*1.03^2)/(2+(1.4-1)*1.03^2)).

FAQ

What is Density behind Normal Shock given Upstream Density and Mach Number?

Density behind Normal Shock given Upstream Density and Mach Number formula is defined as a relationship that describes how the density of a gas changes across a normal shock wave, influenced by the upstream density and the Mach number of the flow and is represented as ρ₂ = ρ₁*(((γ+1)*M^2)/(2+(γ-1)*M^2)) or 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 Ahead of Normal Shock refers to the density of a fluid before encountering a normal shock wave, The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Mach Number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.

How to calculate Density behind Normal Shock given Upstream Density and Mach Number?

Density behind Normal Shock given Upstream Density and Mach Number formula is defined as a relationship that describes how the density of a gas changes across a normal shock wave, influenced by the upstream density and the Mach number of the flow is calculated using Density Behind Normal Shock = Density Ahead of Normal Shock*(((Specific Heat Ratio+1)*Mach Number^2)/(2+(Specific Heat Ratio-1)*Mach Number^2)). To calculate Density behind Normal Shock given Upstream Density and Mach Number, you need Density Ahead of Normal Shock (ρ₁), Specific Heat Ratio (γ) & Mach Number (M). With our tool, you need to enter the respective value for Density Ahead of Normal Shock, Specific Heat Ratio & Mach Number 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 Density Ahead of Normal Shock, Specific Heat Ratio & Mach Number. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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