Oblique Shock Wave Relations Formula - Fluid Mechanics

Formula:

Pressure Ratio
P2 / P1 = 1 + ((2 * γ) / (γ + 1)) * (M12 * sin2β - 1)


Where,

P2 / P1 = Pressure Ratio of Oblique Shock Wave
P2 = Downstream Pressure
P1 = Upstream Pressure
β = Oblique Shock Angle
γ = Heat Capacity Ratio
M1 = Mach Number of Upstream
sin = Sine


Formula:

Density Ratio
ρ2 / ρ1 = [(γ + 1) * M12 * sin2β] / [(γ + 1) * M12 * sin2β + 2]


Where,

ρ2 / ρ1 = Density Ratio of Oblique Shock Wave
ρ2 = Downstream Density
ρ1 = Upstream Ambient Density


Formula:

Temperature Ratio
T2 / T1 = [((2 * γ) * (γ - 1)) / (γ+1)2] * [M12 * sin2β]


Where,

T2 / T1 = Temperature Ratio of Oblique Shock Wave
T2 = Post Normal Temperature
T1 = Upstream Ambient Temperature


Formula:

Stagnation Pressure Ratio
Pt1 / Pt0 = [((γ + 1) * M12 * sin2β) / ((γ - 1) * M12 * sin2β + 2)](γ/(γ-1)) * [(γ + 1) / ((2 * γ) * M12 * sin2β - (γ - 1))](1/(γ-1)


Where,

Pt1 / Pt0 = Stagnation Pressure Ratio of Oblique Shock Wave
Pt1 = Post Normal Total Pressure
Pt0 = Upstream Ambient Total Pressure

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