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Density behind Normal Shock given Upstream Density and Mach Number Formula

GoDensity behind Normal Shock using Normal Shock Momentum Equation Formula

GoDensity Downstream of Shock Wave using Continuity Equation Formula

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Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave. Check FAQs

ρ 2 = ρ 1 \cdot (\frac{(γ + 1) \cdot M^{2}}{2 + (γ - 1) \cdot M^{2}})

ρ₂ - Density Behind Normal Shock?ρ₁ - Density Ahead of Normal Shock?γ - Specific Heat Ratio?M - Mach Number?

Density behind Normal Shock given Upstream Density and Mach Number Example

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Here is how the Density behind Normal Shock given Upstream Density and Mach Number equation looks like with Values.

Here is how the Density behind Normal Shock given Upstream Density and Mach Number equation looks like with Units.

Here is how the Density behind Normal Shock given Upstream Density and Mach Number equation looks like.

5.6713 = 5.4 \cdot (\frac{(1.4 + 1) \cdot {1.03}^{2}}{2 + (1.4 - 1) \cdot {1.03}^{2}})

5.6713kg/m³ = 5.4kg/m³ \cdot (\frac{(1.4 + 1) \cdot {1.03}^{2}}{2 + (1.4 - 1) \cdot {1.03}^{2}})

5.6713 = 5.4 \cdot (\frac{(1.4 + 1) \cdot {1.03}^{2}}{2 + (1.4 - 1) \cdot {1.03}^{2}})

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Density behind Normal Shock given Upstream Density and Mach Number Solution

Follow our step by step solution on how to calculate Density behind Normal Shock given Upstream Density and Mach Number?

FIRST Step Consider the formula

ρ 2 = ρ 1 \cdot (\frac{(γ + 1) \cdot M^{2}}{2 + (γ - 1) \cdot M^{2}})

Next Step Substitute values of Variables

∴

ρ 2 = 5.4kg/m³ \cdot (\frac{(1.4 + 1) \cdot {1.03}^{2}}{2 + (1.4 - 1) \cdot {1.03}^{2}})

Next Step Prepare to Evaluate

∴

ρ 2 = 5.4 \cdot (\frac{(1.4 + 1) \cdot {1.03}^{2}}{2 + (1.4 - 1) \cdot {1.03}^{2}})

Next Step Evaluate

∴

ρ 2 = 5.67129634212741kg/m³

LAST Step Rounding Answer

∴

ρ 2 = 5.6713kg/m³

Density behind Normal Shock given Upstream Density and Mach Number Formula Elements

Variables

Density Behind Normal Shock

Density Behind Normal Shock represents the density of a fluid after passing through a normal shock wave.

Symbol: ρ₂

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Behind Normal Shock

Density Ahead of Normal Shock

Density Ahead of Normal Shock refers to the density of a fluid before encountering a normal shock wave.

Symbol: ρ₁

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Ahead of Normal Shock

Specific Heat Ratio

The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value should be between 1 to 2.

Formulas to find Specific Heat Ratio

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.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number

Other Formulas to find Density Behind Normal Shock

Go Density behind Normal Shock using Normal Shock Momentum Equation

ρ 2 = \frac{P 1 + ρ 1 \cdot {V 1}^{2} - P 2}{{V 2}^{2}}

Go Density Downstream of Shock Wave using Continuity Equation

ρ 2 = \frac{ρ 1 \cdot V 1}{V 2}

Other formulas in Downstream Shock Waves category

Go Characteristic Mach Number behind Shock

M2 cr = \frac{1}{M1 cr}

Go Mach Number behind Shock

M 2 = {(\frac{2 + γ \cdot {M 1}^{2} - {M 1}^{2}}{2 \cdot γ \cdot {M 1}^{2} - γ + 1})}^{\frac{1}{2}}

Go Velocity behind Normal Shock

V 2 = \frac{V 1}{\frac{γ + 1}{(γ - 1) + \frac{2}{M^{2}}}}

Go Static Pressure behind Normal Shock using Normal Shock Momentum Equation

P 2 = P 1 + ρ 1 \cdot {V 1}^{2} - ρ 2 \cdot {V 2}^{2}

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

Density behind Normal Shock given Upstream Density and Mach Number evaluator 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 evaluate the Density Behind Normal Shock, The Density behind Normal Shock given Upstream Density and Mach Number, calculates the density of a fluid after passing through a normal shock wave, crucial in understanding compressible flow behavior. It reveals how shock waves alter density, impacting aerodynamics, combustion, and propulsion systems, vital in aerospace and engineering applications. Density Behind Normal Shock is denoted by ρ₂ symbol.

How to evaluate Density behind Normal Shock given Upstream Density and Mach Number using this online evaluator? To use this online evaluator 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.

FAQs on Density behind Normal Shock given Upstream Density and Mach Number

What is the formula to find Density behind Normal Shock given Upstream Density and Mach Number?

The formula of Density behind Normal Shock given Upstream Density and Mach Number is expressed as Density Behind Normal Shock = Density Ahead of Normal Shock*(((Specific Heat Ratio+1)*Mach Number^2)/(2+(Specific Heat Ratio-1)*Mach Number^2)). Here is an example- 5.671296 = 5.4*(((1.4+1)*1.03^2)/(2+(1.4-1)*1.03^2)).

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

With Density Ahead of Normal Shock (ρ₁), Specific Heat Ratio (γ) & Mach Number (M) we can find Density behind Normal Shock given Upstream Density and Mach Number using the formula - Density Behind Normal Shock = Density Ahead of Normal Shock*(((Specific Heat Ratio+1)*Mach Number^2)/(2+(Specific Heat Ratio-1)*Mach Number^2)).

What are the other ways to Calculate Density Behind Normal Shock?

Here are the different ways to Calculate Density Behind Normal Shock-

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

Can the Density behind Normal Shock given Upstream Density and Mach Number be negative?

No, the Density behind Normal Shock given Upstream Density and Mach Number, measured in Density cannot be negative.

Which unit is used to measure Density behind Normal Shock given Upstream Density and Mach Number?

Density behind Normal Shock given Upstream Density and Mach Number is usually measured using the Kilogram per Cubic Meter[kg/m³] for Density. Kilogram per Cubic Centimeter[kg/m³], Gram per Cubic Meter[kg/m³], Gram per Cubic Centimeter[kg/m³] are the few other units in which Density behind Normal Shock given Upstream Density and Mach Number can be measured.

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Density behind Normal Shock given Upstream Density and Mach Number Formula

​GoDensity behind Normal Shock using Normal Shock Momentum Equation Formula

​GoDensity Downstream of Shock Wave using Continuity Equation Formula

Density behind Normal Shock given Upstream Density and Mach Number Example

Density behind Normal Shock given Upstream Density and Mach Number Solution

Density behind Normal Shock given Upstream Density and Mach Number Formula Elements

Other Formulas to find Density Behind Normal Shock

Other formulas in Downstream Shock Waves category

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

FAQs on Density behind Normal Shock given Upstream Density and Mach Number

Variable Name

GoDensity behind Normal Shock using Normal Shock Momentum Equation Formula

GoDensity Downstream of Shock Wave using Continuity Equation Formula