Wave Angle for Small Deflection Angle Calculator

✖The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.ⓘ Specific Heat Ratio [Y]			+10% -10%
✖A Deflection angle is the angle between the onward extension of the previous leg and the line ahead.ⓘ Deflection Angle [θ_d]			+10% -10%

✖Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.ⓘ Wave Angle for Small Deflection Angle [β]

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Formula

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Wave Angle for Small Deflection Angle

Formula

`"β" = ("Y"+1)/2*("θ"_{"d"}*180/pi)*pi/180`

Example

`"0.249582rad"=("1.6"+1)/2*("0.191986rad"*180/pi)*pi/180`

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Wave Angle for Small Deflection Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180
β = (Y+1)/2*(θ_d*180/pi)*pi/180
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Wave Angle - (Measured in Radian) - Wave Angle is the shock angle created by the oblique shock, this is not similar to the mach angle.
Specific Heat Ratio - The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.
Deflection Angle - (Measured in Radian) - A Deflection angle is the angle between the onward extension of the previous leg and the line ahead.

STEP 1: Convert Input(s) to Base Unit

Specific Heat Ratio: 1.6 --> No Conversion Required
Deflection Angle: 0.191986 Radian --> 0.191986 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

β = (Y+1)/2*(θ_d*180/pi)*pi/180 --> (1.6+1)/2*(0.191986*180/pi)*pi/180

Evaluating ... ...

β = 0.2495818

STEP 3: Convert Result to Output's Unit

0.2495818 Radian --> No Conversion Required

FINAL ANSWER

0.2495818 ≈ 0.249582 Radian <-- Wave Angle

(Calculation completed in 00.020 seconds)

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Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Oblique Shock Relation » Wave Angle for Small Deflection Angle

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< 15 Oblique Shock Relation Calculators

Exact Density Ratio

Go Density Ratio = ((Specific Heat Ratio+1)*(Mach Number*(sin(Wave Angle)))^2)/((Specific Heat Ratio-1)*(Mach Number*(sin(Wave Angle)))^2+2)

Temperature Ratio when Mach Becomes Infinite

Go Temperature Ratio = (2*Specific Heat Ratio*(Specific Heat Ratio-1))/(Specific Heat Ratio+1)^2*(Mach Number*sin(Wave Angle))^2

Exact Pressure Ratio

Go Pressure Ratio = 1+2*Specific Heat Ratio/(Specific Heat Ratio+1)*((Mach Number*sin(Wave Angle))^2-1)

Pressure Ratio when Mach becomes Infinite

Go Pressure Ratio = (2*Specific Heat Ratio)/(Specific Heat Ratio+1)*(Mach Number*sin(Wave Angle))^2

Parallel Upstream Flow Components after Shock as Mach Tends to Infinite

Go Parallel upstream flow components = Velocity of the fluid at 1*(1-(2*(sin(Wave Angle))^2)/(Specific Heat Ratio-1))

Perpendicular Upstream Flow Components behind Shock Wave

Go Perpendicular upstream flow components = (Velocity of the fluid at 1*(sin(2*Wave Angle)))/(Specific Heat Ratio-1)

Pressure Coefficient behind Oblique Shock Wave

Go Pressure Coefficient = 4/(Specific Heat Ratio+1)*((sin(Wave Angle))^2-1/Mach Number^2)

Wave Angle for Small Deflection Angle

Go Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180

Velocity of Sound using Dynamic Pressure and Density

Go Speed of Sound = sqrt((Specific Heat Ratio*Pressure)/Density)

Dynamic Pressure for given Specific Heat Ratio and Mach Number

Go Dynamic Pressure = Specific Heat Ratio Dynamic*Static Pressure*(Mach Number^2)/2

Pressure Coefficient behind Oblique Shock Wave for Infinite Mach Number

Go Pressure Coefficient = 4/(Specific Heat Ratio+1)*(sin(Wave Angle))^2

Non-Dimensional Pressure Coefficient

Go Pressure Coefficient = Change in static pressure/Dynamic Pressure

Density Ratio when Mach Becomes Infinite

Go Density Ratio = (Specific Heat Ratio+1)/(Specific Heat Ratio-1)

Temperature Ratios

Go Temperature Ratio = Pressure Ratio/Density Ratio

Coefficient of Pressure Derived from Oblique Shock Theory

Go Pressure Coefficient = 2*(sin(Wave Angle))^2

Wave Angle for Small Deflection Angle Formula

Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180
β = (Y+1)/2*(θ_d*180/pi)*pi/180

what are the changes due to small deflection angle?

When the deflection angle is small the value of wave angle becomes 1.2 times the deflection angle. It is interesting to observe that, in the hypersonic limit for a slender wedge, the
wave angle is only 20% larger than the wedge angle—

How to Calculate Wave Angle for Small Deflection Angle?

Wave Angle for Small Deflection Angle calculator uses Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180 to calculate the Wave Angle, Wave angle for small deflection angle formula is defined as the product of specific heat ratio and deflection angle. Wave Angle is denoted by β symbol.

How to calculate Wave Angle for Small Deflection Angle using this online calculator? To use this online calculator for Wave Angle for Small Deflection Angle, enter Specific Heat Ratio (Y) & Deflection Angle (θ_d) and hit the calculate button. Here is how the Wave Angle for Small Deflection Angle calculation can be explained with given input values -> 0.249582 = (1.6+1)/2*(0.191986*180/pi)*pi/180.

FAQ

What is Wave Angle for Small Deflection Angle?

Wave angle for small deflection angle formula is defined as the product of specific heat ratio and deflection angle and is represented as β = (Y+1)/2*(θ_d*180/pi)*pi/180 or Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180. The Specific heat ratio of a gas is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume & A Deflection angle is the angle between the onward extension of the previous leg and the line ahead.

How to calculate Wave Angle for Small Deflection Angle?

Wave angle for small deflection angle formula is defined as the product of specific heat ratio and deflection angle is calculated using Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180. To calculate Wave Angle for Small Deflection Angle, you need Specific Heat Ratio (Y) & Deflection Angle (θ_d). With our tool, you need to enter the respective value for Specific Heat Ratio & Deflection Angle 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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