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)
ρr = (γo+1)*(Mn1^2)/(2+(γo-1)*Mn1^2)
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
ρr = (γo+1)*(Mn1^2)/(2+(γo-1)*Mn1^2) --> (1.4+1)*(1.606^2)/(2+(1.4-1)*1.606^2)
Evaluating ... ...
ρr = 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)

Credits

Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
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PSG College of Technology (PSGCT), Coimbatore
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10+ Oblique Shock Calculators

Temperature behind Oblique Shock for given Upstream Temperature and Normal Upstream Mach Number
Go Temperature Behind Oblique Shock = Temperature Ahead of Oblique Shock*((1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((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)))
Flow Deflection Angle due to Oblique Shock
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))
Temperature Ratio across Oblique Shock
Go Temperature Ratio Across Oblique Shock = (1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))/((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 Number Normal to Oblique Shock for given Normal Upstream Mach Number
Go Downstream Mach Normal to Oblique Shock = sqrt((1+0.5*(Specific Heat Ratio Oblique Shock-1)*Upstream Mach Normal to Oblique Shock^2)/(Specific Heat Ratio Oblique Shock*Upstream Mach Normal to Oblique Shock^2-0.5*(Specific Heat Ratio Oblique Shock-1)))
Density behind Oblique Shock for given Upstream Density and Normal Upstream Mach Number
Go Density Behind Oblique Shock = Density Ahead of 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))
Pressure behind Oblique Shock for given Upstream Pressure and Normal Upstream Mach Number
Go Static Pressure Behind Oblique Shock = Static Pressure Ahead of Oblique Shock*(1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1))
Density Ratio across Oblique Shock
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
Go Downstream Mach Normal to Oblique Shock = Mach Number Behind Oblique Shock*sin(Oblique Shock Angle-Flow Deflection Angle Oblique Shock)
Pressure Ratio across Oblique Shock
Go Pressure Ratio Across Oblique Shock = 1+((2*Specific Heat Ratio Oblique Shock)/(Specific Heat Ratio Oblique Shock+1))*(Upstream Mach Normal to Oblique Shock^2-1)
Component of Upstream Mach Normal to Oblique Shock
Go Upstream Mach Normal to Oblique Shock = Mach Number Ahead of Oblique Shock*sin(Oblique Shock Angle)

Density Ratio across Oblique Shock 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)
ρr = (γo+1)*(Mn1^2)/(2+(γo-1)*Mn1^2)

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 ρr 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 o) & Upstream Mach Normal to Oblique Shock (Mn1) 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 ρr = (γo+1)*(Mn1^2)/(2+(γo-1)*Mn1^2) 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 o) & Upstream Mach Normal to Oblique Shock (Mn1). 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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