Flow deflection angle Calculator

Category	Physics ↺
Physics	Gas Dynamics ↺
Gas-Dynamics	Oblique Shock and Expansion Waves ↺

✖Oblique shock angle is defined as the angle between the shock and the resultant velocity upstream of the shockⓘ Oblique shock angle [β]			+10% -10%
✖Mach Number ahead of shock is the Mach number over the body before a shockwave has occurred ⓘ Mach Number ahead of shock [M₁]			+10% -10%
✖The Specific heat ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.ⓘ Specific heat ratio [κ]			+10% -10%

✖Flow Deflection angle is defined as the angle by which the flow turns towards the oblique shockⓘ Flow deflection angle [θ]

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Vinay Mishra

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

Vinay Mishra has created this Calculator and 300+ more calculators!

Sai Venkata Phanindra Chary Arendra

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

Sai Venkata Phanindra Chary Arendra has verified this Calculator and 100+ more calculators!

< 11 Other formulas that you can solve using the same Inputs

Isentropic temperature 1 given specific volume

Isentropic temperature 1 given specific volume=Temperature of surface 2/(Specific volume at point 1/Specific volume at point 2)^(Specific heat ratio-1) GO

Isentropic temperature 2 given specific volume

Isentropic temperature 2 given specific volume=Temperature of surface 1*(Specific volume at point 1/Specific volume at point 2)^(Specific heat ratio-1) GO

Isentropic temperature 2 given pressure ratio

Isentropic temperature 2 given pressure ratio=Temperature of surface 1*(pressure 2/pressure 1)^((Specific heat ratio-1)/Specific heat ratio) GO

Isentropic temperature 1 given pressure ratio

Isentropic temperature 1 given pressure ratio=Temperature of surface 2/(pressure 2/pressure 1)^((Specific heat ratio-1)/Specific heat ratio) GO

Temperature Ratio when Isentropic Specific Volume is Given

Temperature ratio isentropic specific volume=(Specific volume at point 1/Specific volume at point 2)^(Specific heat ratio-1) GO

Isentropic Pressure at point 2

Isentropic Pressure at point 2 =pressure 1*(Specific volume at point 1/Specific volume at point 2)^Specific heat ratio GO

Isentropic Pressure at point 1

Isentropic Pressure at point 1=pressure 2/(Specific volume at point 1/Specific volume at point 2)^Specific heat ratio GO

Pressure Ratio in Isentropic Process

Pressure ratio isentropic process=(Specific volume at point 1/Specific volume at point 2)^Specific heat ratio GO

Temperature Ratio When Isentropic Pressure is Given

Temperature ratio isentropic pressure=(pressure 2/pressure 1)^((Specific heat ratio-1)/Specific heat ratio) GO

Deflection angle

deflection angle=(2/(Specific Heat Ratio-1))*((1/Mach Number ahead of shock)-(1/Mach Number behind shock)) GO

Relation between Characteristic Mach number and Mach number

Characteristic Mach number=((Specific heat ratio+1)/((Specific heat ratio-1)+(2/(Mach Number^2))))^0.5 GO

< 1 Other formulas that calculate the same Output

Flow deflection angle in terms of Prandtl Meyer function

Flow Deflection angle=Prandtl Meyer Function at downstream Mach no.-Prandtl Meyer Function at upstream Mach no. GO

Flow deflection angle Formula

Flow Deflection angle=atan((2*cot(Oblique shock angle)*(((Mach Number ahead of shock*sin(Oblique shock angle))^2)-1))/(((Mach Number ahead of shock^2)*(Specific heat ratio+cos(2*Oblique shock angle)))+2))
θ=atan((2*cot(β)*(((M<sub>1</sub>*sin(β))^2)-1))/(((M<sub>1</sub>^2)*(κ+cos(2*β)))+2))

More formulas

Component of Upstream Mach normal to oblique shock GO

Component of Downstream Mach normal to oblique shock GO

Density ratio across the oblique shock GO

Pressure ratio across the oblique shock GO

Temperature ratio across the oblique shock GO

Component of downstream Mach no. normal to oblique shock for given normal upstream Mach no. GO

Density behind oblique shock for given upstream density & normal upstream Mach no. GO

Pressure behind oblique shock for given upstream pressure & normal upstream Mach no GO

Temperature behind oblique shock for given upstream temperature & normal upstream Mach no. GO

Pressure ratio across the expansion fan GO

Temperature ratio across the expansion fan GO

Pressure behind expansion fan GO

Temperature behind expansion fan GO

Forward Mach angle of expansion fan GO

Rearward Mach angle of the expansion fan GO

Prandtl Meyer function GO

Flow deflection angle in terms of Prandtl Meyer function GO

Prandtl Meyer function at upstream Mach no. GO

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?

Flow deflection angle calculator uses Flow Deflection angle=atan((2*cot(Oblique shock angle)*(((Mach Number ahead of shock*sin(Oblique shock angle))^2)-1))/(((Mach Number ahead of shock^2)*(Specific heat ratio+cos(2*Oblique shock angle)))+2)) to calculate the Flow Deflection angle, The Flow deflection angle is obtained using θ-β-M relation which is an interrelation between Flow deflection angle, Upstream Mach number, and Oblique Shock angle. Flow Deflection angle and is denoted by θ symbol.

How to calculate Flow deflection angle using this online calculator? To use this online calculator for Flow deflection angle, enter Oblique shock angle (β), Mach Number ahead of shock (M₁) and Specific heat ratio (κ) and hit the calculate button. Here is how the Flow deflection angle calculation can be explained with given input values -> -0.617143 = atan((2*cot(60)*(((1.5*sin(60))^2)-1))/(((1.5^2)*(1.392758+cos(2*60)))+2)).

FAQ

What is Flow deflection angle?

The Flow deflection angle is obtained using θ-β-M relation which is an interrelation between Flow deflection angle, Upstream Mach number, and Oblique Shock angle and is represented as θ=atan((2*cot(β)*(((M₁*sin(β))^2)-1))/(((M₁^2)*(κ+cos(2*β)))+2)) or Flow Deflection angle=atan((2*cot(Oblique shock angle)*(((Mach Number ahead of shock*sin(Oblique shock angle))^2)-1))/(((Mach Number ahead of shock^2)*(Specific heat ratio+cos(2*Oblique shock angle)))+2)). Oblique shock angle is defined as the angle between the shock and the resultant velocity upstream of the shock, Mach Number ahead of shock is the Mach number over the body before a shockwave has occurred and The Specific heat ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.

How to calculate Flow deflection angle?

The Flow deflection angle is obtained using θ-β-M relation which is an interrelation between Flow deflection angle, Upstream Mach number, and Oblique Shock angle is calculated using Flow Deflection angle=atan((2*cot(Oblique shock angle)*(((Mach Number ahead of shock*sin(Oblique shock angle))^2)-1))/(((Mach Number ahead of shock^2)*(Specific heat ratio+cos(2*Oblique shock angle)))+2)). To calculate Flow deflection angle, you need Oblique shock angle (β), Mach Number ahead of shock (M₁) and Specific heat ratio (κ). With our tool, you need to enter the respective value for Oblique shock angle, Mach Number ahead of shock and Specific heat ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Flow Deflection angle?

In this formula, Flow Deflection angle uses Oblique shock angle, Mach Number ahead of shock and Specific heat ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -

Flow Deflection angle=Prandtl Meyer Function at downstream Mach no.-Prandtl Meyer Function at upstream Mach no.

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