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Wave Angle for Small Deflection Angle Formula

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The Wave Angle is the angle between the direction of a hypersonic flow and the wave generated by an oblique shock in fluid mechanics. Check FAQs

β = \frac{Y + 1}{2} \cdot (θ d \cdot \frac{180}{π}) \cdot \frac{π}{180}

β - Wave Angle?Y - Specific Heat Ratio?θ_d - Deflection Angle?π - Archimedes' constant?

Wave Angle for Small Deflection Angle Example

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Here is how the Wave Angle for Small Deflection Angle equation looks like with Values.

Here is how the Wave Angle for Small Deflection Angle equation looks like with Units.

Here is how the Wave Angle for Small Deflection Angle equation looks like.

0.507 = \frac{1.6 + 1}{2} \cdot (0.39 \cdot \frac{180}{3.1416}) \cdot \frac{3.1416}{180}

0.507rad = \frac{1.6 + 1}{2} \cdot (0.39rad \cdot \frac{180}{3.1416}) \cdot \frac{3.1416}{180}

0.507 = \frac{1.6 + 1}{2} \cdot (0.39 \cdot \frac{180}{3.1416}) \cdot \frac{3.1416}{180}

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Wave Angle for Small Deflection Angle Solution

Follow our step by step solution on how to calculate Wave Angle for Small Deflection Angle?

FIRST Step Consider the formula

β = \frac{Y + 1}{2} \cdot (θ d \cdot \frac{180}{π}) \cdot \frac{π}{180}

Next Step Substitute values of Variables

∴

β = \frac{1.6 + 1}{2} \cdot (0.39rad \cdot \frac{180}{π}) \cdot \frac{π}{180}

Next Step Substitute values of Constants

∴

β = \frac{1.6 + 1}{2} \cdot (0.39rad \cdot \frac{180}{3.1416}) \cdot \frac{3.1416}{180}

Next Step Prepare to Evaluate

∴

β = \frac{1.6 + 1}{2} \cdot (0.39 \cdot \frac{180}{3.1416}) \cdot \frac{3.1416}{180}

LAST Step Evaluate

∴

β = 0.507rad

Wave Angle for Small Deflection Angle Formula Elements

Variables

Constants

Wave Angle

The Wave Angle is the angle between the direction of a hypersonic flow and the wave generated by an oblique shock in fluid mechanics.

Symbol: β

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Wave Angle

Specific Heat Ratio

The Specific Heat Ratio is the ratio of the heat capacity at constant pressure to the heat capacity at constant volume, important for understanding fluid behavior in hypersonic flows.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Specific Heat Ratio

Deflection Angle

The Deflection Angle is the angle through which a fluid stream is diverted due to the presence of an obstacle, affecting flow direction in hypersonic conditions.

Symbol: θ_d

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Deflection Angle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Oblique Shock Relation category

Go Coefficient of Pressure Derived from Oblique Shock Theory

C p = 2 \cdot {(\sin (β))}^{2}

Go Parallel Upstream Flow Components after Shock as Mach Tends to Infinite

u2 = V 1 \cdot (1 - \frac{2 \cdot {(\sin (β))}^{2}}{Y - 1})

Go Perpendicular Upstream Flow Components behind Shock Wave

v2 = \frac{V 1 \cdot (\sin (2 \cdot β))}{Y - 1}

Go Exact Pressure Ratio

r p = 1 + 2 \cdot \frac{Y}{Y + 1} \cdot ({(M \cdot \sin (β))}^{2} - 1)

How to Evaluate Wave Angle for Small Deflection Angle?

Wave Angle for Small Deflection Angle evaluator uses Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180 to evaluate the Wave Angle, Wave Angle for Small Deflection Angle formula is defined as a measure of the angle of a shock wave that occurs when a supersonic flow encounters a sudden change in direction, allowing engineers to analyze and predict the behavior of oblique shock waves in various applications. Wave Angle is denoted by β symbol.

How to evaluate Wave Angle for Small Deflection Angle using this online evaluator? To use this online evaluator for Wave Angle for Small Deflection Angle, enter Specific Heat Ratio (Y) & Deflection Angle (θ_d) and hit the calculate button.

FAQs on Wave Angle for Small Deflection Angle

What is the formula to find Wave Angle for Small Deflection Angle?

The formula of Wave Angle for Small Deflection Angle is expressed as Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180. Here is an example- 0.52 = (1.6+1)/2*(0.39*180/pi)*pi/180.

How to calculate Wave Angle for Small Deflection Angle?

With Specific Heat Ratio (Y) & Deflection Angle (θ_d) we can find Wave Angle for Small Deflection Angle using the formula - Wave Angle = (Specific Heat Ratio+1)/2*(Deflection Angle*180/pi)*pi/180. This formula also uses Archimedes' constant .

Can the Wave Angle for Small Deflection Angle be negative?

No, the Wave Angle for Small Deflection Angle, measured in Angle cannot be negative.

Which unit is used to measure Wave Angle for Small Deflection Angle?

Wave Angle for Small Deflection Angle is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Wave Angle for Small Deflection Angle can be measured.

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