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Density Ratio across Normal Shock Formula

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Density Ratio Across Normal Shock indicates the ratio of densities before and after passing through a normal shock wave. Check FAQs

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

ρ_r - Density Ratio Across Normal Shock?γ - Specific Heat Ratio?M₁ - Mach Number Ahead of Normal Shock?

Density Ratio across Normal Shock Example

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Here is how the Density Ratio across Normal Shock equation looks like with Values.

Here is how the Density Ratio across Normal Shock equation looks like with Units.

Here is how the Density Ratio across Normal Shock equation looks like.

1.8449 = (1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}

1.8449 = (1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}

1.8449 = (1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}

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Density Ratio across Normal Shock Solution

Follow our step by step solution on how to calculate Density Ratio across Normal Shock?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ρ r = (1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}

Next Step Prepare to Evaluate

∴

ρ r = (1.4 + 1) \cdot \frac{{1.49}^{2}}{2 + (1.4 - 1) \cdot {1.49}^{2}}

Next Step Evaluate

∴

ρ r = 1.84493289566627

LAST Step Rounding Answer

∴

ρ r = 1.8449

Density Ratio across Normal Shock Formula Elements

Variables

Density Ratio Across Normal Shock

Density Ratio Across Normal Shock indicates the ratio of densities before and after passing through a normal shock wave.

Symbol: ρ_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Density Ratio Across 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 Ahead of Normal Shock

Mach Number Ahead of Normal Shock represents the velocity of a fluid or airflow relative to the speed of sound before encountering a normal shock wave.

Symbol: M₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number Ahead of Normal Shock

Other formulas in Property Change Across Shock Waves category

Go Shock Strength

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

Go Entropy Change across Normal Shock

ΔS = R \cdot \ln (\frac{p 01}{p 02})

Go Pressure Ratio across Normal Shock

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

Go Temperature Ratio across Normal Shock

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

How to Evaluate Density Ratio across Normal Shock?

Density Ratio across Normal Shock evaluator uses Density Ratio Across Normal Shock = (Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2) to evaluate the Density Ratio Across Normal Shock, The Density Ratio across Normal Shock calculates the ratio of densities across a normal shock wave. This formula incorporates the ratio of specific heats for the fluid and the Mach number ahead of the shock to determine the density ratio. It provides insight into the change in density across the shock wave, aiding in the analysis of compressible flow behavior. Density Ratio Across Normal Shock is denoted by ρ_r symbol.

How to evaluate Density Ratio across Normal Shock using this online evaluator? To use this online evaluator for Density Ratio across Normal Shock, enter Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) and hit the calculate button.

FAQs on Density Ratio across Normal Shock

What is the formula to find Density Ratio across Normal Shock?

The formula of Density Ratio across Normal Shock is expressed as Density Ratio Across Normal Shock = (Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2). Here is an example- 1.844933 = (1.4+1)*(1.49^2)/(2+(1.4-1)*1.49^2).

How to calculate Density Ratio across Normal Shock?

With Specific Heat Ratio (γ) & Mach Number Ahead of Normal Shock (M₁) we can find Density Ratio across Normal Shock using the formula - Density Ratio Across Normal Shock = (Specific Heat Ratio+1)*(Mach Number Ahead of Normal Shock^2)/(2+(Specific Heat Ratio-1)*Mach Number Ahead of Normal Shock^2).

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Density Ratio across Normal Shock Formula

Density Ratio across Normal Shock Example

Density Ratio across Normal Shock Solution

Density Ratio across Normal Shock Formula Elements

Other formulas in Property Change Across Shock Waves category

How to Evaluate Density Ratio across Normal Shock?

FAQs on Density Ratio across Normal Shock

Variable Name