Flow Deflection Angle due to Oblique Shock Calculator

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Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

Two-Dimensional Incompressible Flow

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Oblique Shock and Expansion Waves

Governing Equations and Sound Wave

Normal Shock Wave

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Oblique Shock

Expansion Waves

✖Oblique Shock Angle signifies the angle formed by the direction of an incoming airflow or fluid with respect to the oblique shock wave.ⓘ Oblique Shock Angle [β]			+10% -10%
✖Mach Number Ahead of Oblique Shock signifies the velocity of a fluid or airflow relative to the speed of sound before encountering an oblique shock wave.ⓘ Mach Number Ahead of Oblique Shock [M₁]			+10% -10%
✖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%

✖Flow Deflection Angle Oblique Shock is defined as the angle by which the flow turns towards the oblique shock.ⓘ Flow Deflection Angle due to Oblique Shock [θ]

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Formula

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Flow Deflection Angle due to Oblique Shock

Formula

`"θ" = atan((2*cot("β")*(("M"_{"1"}*sin("β"))^2-1))/("M"_{"1"}^2*("γ"_{"o"}+cos(2*"β"))+2))`

Example

`"19.98876°"=atan((2*cot("53.4°")*(("2"*sin("53.4°"))^2-1))/(("2")^2*("1.4"+cos(2*"53.4°"))+2))`

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Flow Deflection Angle due to Oblique Shock Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
θ = atan((2*cot(β)*((M₁*sin(β))^2-1))/(M₁^2*(γ_o+cos(2*β))+2))
This formula uses 5 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Flow Deflection Angle Oblique Shock - (Measured in Radian) - Flow Deflection Angle Oblique Shock is defined as the angle by which the flow turns towards the oblique shock.
Oblique Shock Angle - (Measured in Radian) - Oblique Shock Angle signifies the angle formed by the direction of an incoming airflow or fluid with respect to the oblique shock wave.
Mach Number Ahead of Oblique Shock - Mach Number Ahead of Oblique Shock signifies the velocity of a fluid or airflow relative to the speed of sound before encountering an oblique shock wave.
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.

STEP 1: Convert Input(s) to Base Unit

Oblique Shock Angle: 53.4 Degree --> 0.932005820564797 Radian (Check conversion here)
Mach Number Ahead of Oblique Shock: 2 --> No Conversion Required
Specific Heat Ratio Oblique Shock: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = atan((2*cot(β)*((M₁*sin(β))^2-1))/(M₁^2*(γ_o+cos(2*β))+2)) --> atan((2*cot(0.932005820564797)*((2*sin(0.932005820564797))^2-1))/(2^2*(1.4+cos(2*0.932005820564797))+2))

Evaluating ... ...

θ = 0.348869743776527

STEP 3: Convert Result to Output's Unit

0.348869743776527 Radian -->19.9887639182092 Degree (Check conversion here)

FINAL ANSWER

19.9887639182092 ≈ 19.98876 Degree <-- Flow Deflection Angle Oblique Shock

(Calculation completed in 00.020 seconds)

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Home » Physics » Aerodynamics » Compressible Flow » Oblique Shock and Expansion Waves » Oblique Shock » Flow Deflection Angle due to Oblique Shock

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNRVJIET), Hyderabad

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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)

Flow Deflection Angle due to Oblique Shock Formula

What are the characteristics of oblique Shockwave?

An oblique shock wave is a shock wave that, unlike a normal shock, is inclined with respect to the incident upstream flow direction. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The upstream streamlines are uniformly deflected after the shock wave.

How to Calculate Flow Deflection Angle due to Oblique Shock?

Flow Deflection Angle due to Oblique Shock calculator uses 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)) to calculate the Flow Deflection Angle Oblique Shock, The Flow Deflection Angle due to Oblique Shock formula describes the change in flow direction caused by an oblique shock wave. It calculates the deflection angle experienced by the flow as it encounters the shock, taking into account the shock angle and the upstream Mach number. Flow Deflection Angle Oblique Shock is denoted by θ symbol.

How to calculate Flow Deflection Angle due to Oblique Shock using this online calculator? To use this online calculator for Flow Deflection Angle due to Oblique Shock, enter Oblique Shock Angle (β), Mach Number Ahead of Oblique Shock (M₁) & Specific Heat Ratio Oblique Shock (γ_o) and hit the calculate button. Here is how the Flow Deflection Angle due to Oblique Shock calculation can be explained with given input values -> 1145.272 = atan((2*cot(0.932005820564797)*((2*sin(0.932005820564797))^2-1))/(2^2*(1.4+cos(2*0.932005820564797))+2)).

FAQ

What is Flow Deflection Angle due to Oblique Shock?

The Flow Deflection Angle due to Oblique Shock formula describes the change in flow direction caused by an oblique shock wave. It calculates the deflection angle experienced by the flow as it encounters the shock, taking into account the shock angle and the upstream Mach number and is represented as θ = atan((2*cot(β)*((M₁*sin(β))^2-1))/(M₁^2*(γ_o+cos(2*β))+2)) or 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)). Oblique Shock Angle signifies the angle formed by the direction of an incoming airflow or fluid with respect to the oblique shock wave, Mach Number Ahead of Oblique Shock signifies the velocity of a fluid or airflow relative to the speed of sound before encountering an oblique shock wave & The Specific Heat Ratio Oblique Shock is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.

How to calculate Flow Deflection Angle due to Oblique Shock?

The Flow Deflection Angle due to Oblique Shock formula describes the change in flow direction caused by an oblique shock wave. It calculates the deflection angle experienced by the flow as it encounters the shock, taking into account the shock angle and the upstream Mach number is calculated using 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)). To calculate Flow Deflection Angle due to Oblique Shock, you need Oblique Shock Angle (β), Mach Number Ahead of Oblique Shock (M₁) & Specific Heat Ratio Oblique Shock (γ_o). With our tool, you need to enter the respective value for Oblique Shock Angle, Mach Number Ahead of Oblique Shock & Specific Heat Ratio 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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