Density Ratio across Oblique Shock Calculator

✖The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific Heat Ratio Oblique Shock [γ_o]			+10% -10%
✖Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.ⓘ Upstream Mach Normal to Oblique Shock [M_n1]			+10% -10%

✖Density Ratio Across Oblique Shock is the ratio of the downstream density to the upstream density across the oblique shock.ⓘ Density Ratio across Oblique Shock [ρ_r]

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Density Ratio across Oblique Shock Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
ρ_r = (γ_o+1)*(M_n1^2)/(2+(γ_o-1)*M_n1^2)
This formula uses 3 Variables

Variables Used

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio Oblique Shock: 1.4 --> No Conversion Required
Upstream Mach Normal to Oblique Shock: 1.606 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ_r = (γ_o+1)*(M_n1^2)/(2+(γ_o-1)*M_n1^2) --> (1.4+1)*(1.606^2)/(2+(1.4-1)*1.606^2)

Evaluating ... ...

ρ_r = 2.04181740745373

STEP 3: Convert Result to Output's Unit

2.04181740745373 --> No Conversion Required

FINAL ANSWER

2.04181740745373 ≈ 2.041817 <-- Density Ratio Across Oblique 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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< Oblique Shock Calculators

Flow Deflection Angle due to Oblique Shock

LaTeX Go Flow Deflection Angle Oblique Shock = atan((2*cot(Oblique Shock Angle)*((Mach Number Ahead of Oblique Shock*sin(Oblique Shock Angle))^2-1))/(Mach Number Ahead of Oblique Shock^2*(Specific Heat Ratio Oblique Shock+cos(2*Oblique Shock Angle))+2))

Density Ratio across Oblique Shock

LaTeX Go 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)

Component of Downstream Mach Normal to Oblique Shock

LaTeX Go Downstream Mach Normal to Oblique Shock = Mach Number Behind Oblique Shock*sin(Oblique Shock Angle-Flow Deflection Angle Oblique Shock)

Component of Upstream Mach Normal to Oblique Shock

LaTeX Go Upstream Mach Normal to Oblique Shock = Mach Number Ahead of Oblique Shock*sin(Oblique Shock Angle)

Density Ratio across Oblique Shock Formula

LaTeX Go

What is oblique shock?

A shock wave that makes an oblique angle with the upstream flow, is called oblique shock. A normal shock wave is a special case of a general family of oblique shock, where the wave angle is 90°.

What is Wave angle and Mach angle?

Wave angle is the angle that oblique shock makes with the upstream direction of flow. Mach angle is the angle formed between the Mach wave (an envelope of disturbance) and freestream direction of flow. Mach wave is the limiting case for the oblique shock (i.e., it is an infinitely weak oblique shock).

How to Calculate Density Ratio across Oblique Shock?

Density Ratio across Oblique Shock calculator 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 calculate 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 calculate Density Ratio across Oblique Shock using this online calculator? To use this online calculator 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. Here is how the Density Ratio across Oblique Shock calculation can be explained with given input values -> 2.041817 = (1.4+1)*(1.606^2)/(2+(1.4-1)*1.606^2).

FAQ

What is 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 and is represented as ρ_r = (γ_o+1)*(M_n1^2)/(2+(γ_o-1)*M_n1^2) or 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). The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume & Upstream Mach Normal to Oblique Shock represents the Mach number's component aligned with the shock wave's normal direction.

How to calculate 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 is calculated using 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 calculate Density Ratio across Oblique Shock, you need Specific Heat Ratio Oblique Shock (γ_o) & Upstream Mach Normal to Oblique Shock (M_n1). With our tool, you need to enter the respective value for Specific Heat Ratio Oblique Shock & Upstream Mach Normal to Oblique Shock and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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