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Flow Deflection Angle due to Oblique Shock Formula

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Flow Deflection Angle Oblique Shock is defined as the angle by which the flow turns towards the oblique shock. Check FAQs

θ = a \tan (\frac{2 \cdot \cot (β) \cdot ({(M 1 \cdot \sin (β))}^{2} - 1)}{{M 1}^{2} \cdot (γ o + \cos (2 \cdot β)) + 2})

θ - Flow Deflection Angle Oblique Shock?β - Oblique Shock Angle?M₁ - Mach Number Ahead of Oblique Shock?γ_o - Specific Heat Ratio Oblique Shock?

Flow Deflection Angle due to Oblique Shock Example

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Here is how the Flow Deflection Angle due to Oblique Shock equation looks like with Values.

Here is how the Flow Deflection Angle due to Oblique Shock equation looks like with Units.

Here is how the Flow Deflection Angle due to Oblique Shock equation looks like.

19.9888 = a \tan (\frac{2 \cdot \cot (53.4) \cdot ({(2 \cdot \sin (53.4))}^{2} - 1)}{2^{2} \cdot (1.4 + \cos (2 \cdot 53.4)) + 2})

19.9888° = a \tan (\frac{2 \cdot \cot (53.4°) \cdot ({(2 \cdot \sin (53.4°))}^{2} - 1)}{2^{2} \cdot (1.4 + \cos (2 \cdot 53.4°)) + 2})

19.9888 = a \tan (\frac{2 \cdot \cot (53.4) \cdot ({(2 \cdot \sin (53.4))}^{2} - 1)}{2^{2} \cdot (1.4 + \cos (2 \cdot 53.4)) + 2})

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Flow Deflection Angle due to Oblique Shock Solution

Follow our step by step solution on how to calculate Flow Deflection Angle due to Oblique Shock?

FIRST Step Consider the formula

θ = a \tan (\frac{2 \cdot \cot (β) \cdot ({(M 1 \cdot \sin (β))}^{2} - 1)}{{M 1}^{2} \cdot (γ o + \cos (2 \cdot β)) + 2})

Next Step Substitute values of Variables

∴

θ = a \tan (\frac{2 \cdot \cot (53.4°) \cdot ({(2 \cdot \sin (53.4°))}^{2} - 1)}{2^{2} \cdot (1.4 + \cos (2 \cdot 53.4°)) + 2})

Next Step Convert Units

∴

θ = a \tan (\frac{2 \cdot \cot (0.932rad) \cdot ({(2 \cdot \sin (0.932rad))}^{2} - 1)}{2^{2} \cdot (1.4 + \cos (2 \cdot 0.932rad)) + 2})

Next Step Prepare to Evaluate

∴

θ = a \tan (\frac{2 \cdot \cot (0.932) \cdot ({(2 \cdot \sin (0.932))}^{2} - 1)}{2^{2} \cdot (1.4 + \cos (2 \cdot 0.932)) + 2})

Next Step Evaluate

∴

θ = 0.348869743776527rad

Next Step Convert to Output's Unit

∴

θ = 19.9887639182092°

LAST Step Rounding Answer

∴

θ = 19.9888°

Flow Deflection Angle due to Oblique Shock Formula Elements

Variables

Functions

Flow Deflection Angle Oblique Shock

Flow Deflection Angle Oblique Shock is defined as the angle by which the flow turns towards the oblique shock.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Flow Deflection Angle Oblique Shock

Oblique Shock Angle

Oblique Shock Angle signifies the angle formed by the direction of an incoming airflow or fluid with respect to the oblique shock wave.

Symbol: β

Measurement: AngleUnit: °

Note: Value should be less than 91.

Formulas to find Oblique Shock Angle

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.

Symbol: M₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number Ahead of 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.

Symbol: γ_o

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Specific Heat Ratio Oblique Shock

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: 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.

Syntax: 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.

Syntax: atan(Number)

Other formulas in Oblique Shock category

Go Component of Upstream Mach Normal to Oblique Shock

M n1 = M 1 \cdot \sin (β)

Go Component of Downstream Mach Normal to Oblique Shock

M n2 = M 2 \cdot \sin (β - θ)

Go Density Ratio across Oblique Shock

ρ r = (γ o + 1) \cdot \frac{{M n1}^{2}}{2 + (γ o - 1) \cdot {M n1}^{2}}

Go Pressure Ratio across Oblique Shock

P r = 1 + (\frac{2 \cdot γ o}{γ o + 1}) \cdot ({M n1}^{2} - 1)

How to Evaluate Flow Deflection Angle due to Oblique Shock?

Flow Deflection Angle due to Oblique Shock evaluator 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 evaluate 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 evaluate Flow Deflection Angle due to Oblique Shock using this online evaluator? To use this online evaluator 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.

FAQs on Flow Deflection Angle due to Oblique Shock

What is the formula to find Flow Deflection Angle due to Oblique Shock?

The formula of Flow Deflection Angle due to Oblique Shock is expressed as 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)). Here is an example- 1145.272 = atan((2*cot(0.932005820564797)*((2*sin(0.932005820564797))^2-1))/(2^2*(1.4+cos(2*0.932005820564797))+2)).

How to calculate Flow Deflection Angle due to Oblique Shock?

With Oblique Shock Angle (β), Mach Number Ahead of Oblique Shock (M₁) & Specific Heat Ratio Oblique Shock (γ_o) we can find Flow Deflection Angle due to Oblique Shock using the formula - 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)). This formula also uses Sine (sin)Cosine (cos)Tangent (tan)Cotangent (cot), Inverse Tan (atan) function(s).

Can the Flow Deflection Angle due to Oblique Shock be negative?

Yes, the Flow Deflection Angle due to Oblique Shock, measured in Angle can be negative.

Which unit is used to measure Flow Deflection Angle due to Oblique Shock?

Flow Deflection Angle due to Oblique Shock is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Flow Deflection Angle due to Oblique Shock can be measured.

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