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Density Ratio across Oblique Shock Formula

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Density Ratio Across Oblique Shock is the ratio of the downstream density to the upstream density across the oblique shock. Check FAQs

ρ r = (γ o + 1) \cdot \frac{{M n1}^{2}}{2 + (γ o - 1) \cdot {M n1}^{2}}

ρ_r - Density Ratio Across Oblique Shock?γ_o - Specific Heat Ratio Oblique Shock?M_n1 - Upstream Mach Normal to Oblique Shock?

Density Ratio across Oblique Shock Example

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

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

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

2.0418 = (1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}

2.0418 = (1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}

2.0418 = (1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}

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Density Ratio across Oblique Shock Solution

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

FIRST Step Consider the formula

ρ r = (γ o + 1) \cdot \frac{{M n1}^{2}}{2 + (γ o - 1) \cdot {M n1}^{2}}

Next Step Substitute values of Variables

∴

ρ r = (1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}

Next Step Prepare to Evaluate

∴

ρ r = (1.4 + 1) \cdot \frac{{1.606}^{2}}{2 + (1.4 - 1) \cdot {1.606}^{2}}

Next Step Evaluate

∴

ρ r = 2.04181740745373

LAST Step Rounding Answer

∴

ρ r = 2.0418

Density Ratio across Oblique Shock Formula Elements

Variables

Density Ratio Across Oblique Shock

Density Ratio Across Oblique Shock is the ratio of the downstream density to the upstream density across the oblique shock.

Symbol: ρ_r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Density Ratio Across Oblique Shock

Specific Heat Ratio Oblique Shock

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

Symbol: γ_o

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Specific Heat Ratio Oblique Shock

Upstream Mach Normal to Oblique Shock

Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.

Symbol: M_n1

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Upstream Mach Normal to Oblique Shock

Other formulas in Oblique Shock category

Go Component of Upstream Mach Normal to Oblique Shock

M n1 = M 1 \cdot \sin (β)

Go Component of Downstream Mach Normal to Oblique Shock

M n2 = M 2 \cdot \sin (β - θ)

Go Flow Deflection Angle due to Oblique Shock

θ = a \tan (\frac{2 \cdot \cot (β) \cdot ({(M 1 \cdot \sin (β))}^{2} - 1)}{{M 1}^{2} \cdot (γ o + \cos (2 \cdot β)) + 2})

Go Pressure Ratio across Oblique Shock

P r = 1 + (\frac{2 \cdot γ o}{γ o + 1}) \cdot ({M n1}^{2} - 1)

How to Evaluate Density Ratio across Oblique Shock?

Density Ratio across Oblique Shock evaluator uses Density Ratio Across Oblique Shock = (Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2) to evaluate the Density Ratio Across Oblique Shock, The Density Ratio across Oblique Shock formula defines the ratio of the density of the fluid immediately behind an oblique shock wave to the density of the fluid ahead of the shock wave, considering parameters such as the upstream density, Mach number, and shock wave angle. Density Ratio Across Oblique Shock is denoted by ρ_r symbol.

How to evaluate Density Ratio across Oblique Shock using this online evaluator? To use this online evaluator for Density Ratio across Oblique Shock, enter Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1) and hit the calculate button.

FAQs on Density Ratio across Oblique Shock

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

The formula of Density Ratio across Oblique Shock is expressed as Density Ratio Across Oblique Shock = (Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2). Here is an example- 2.041817 = (1.4+1)*(1.606^2)/(2+(1.4-1)*1.606^2).

How to calculate Density Ratio across Oblique Shock?

With Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1) we can find Density Ratio across Oblique Shock using the formula - Density Ratio Across Oblique Shock = (Specific Heat Ratio Oblique Shock+1)*(Upstream Mach Normal to Oblique Shock^2)/(2+(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2).

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Density Ratio across Oblique Shock Formula

Density Ratio across Oblique Shock Example

Density Ratio across Oblique Shock Solution

Density Ratio across Oblique Shock Formula Elements

Other formulas in Oblique Shock category

How to Evaluate Density Ratio across Oblique Shock?

FAQs on Density Ratio across Oblique Shock

Variable Name