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Polar Coordinate given Tangential Velocity Formula

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Polar Angle is the angular position of a point from a reference direction. Check FAQs

θ = a \sin (\frac{V θ}{V ∞ + \frac{μ}{4 \cdot π \cdot r^{3}}})

θ - Polar Angle?V_θ - Tangential Velocity?V_∞ - Freestream Velocity?μ - Doublet Strength?r - Radial Coordinate?π - Archimedes' constant?

Polar Coordinate given Tangential Velocity Example

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Here is how the Polar Coordinate given Tangential Velocity equation looks like with Values.

Here is how the Polar Coordinate given Tangential Velocity equation looks like with Units.

Here is how the Polar Coordinate given Tangential Velocity equation looks like.

0.6883 = a \sin (\frac{66}{68 + \frac{9463}{4 \cdot 3.1416 \cdot {2.758}^{3}}})

0.6883rad = a \sin (\frac{66m/s}{68m/s + \frac{9463m³/s}{4 \cdot 3.1416 \cdot {2.758m}^{3}}})

0.6883 = a \sin (\frac{66}{68 + \frac{9463}{4 \cdot 3.1416 \cdot {2.758}^{3}}})

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Polar Coordinate given Tangential Velocity Solution

Follow our step by step solution on how to calculate Polar Coordinate given Tangential Velocity?

FIRST Step Consider the formula

θ = a \sin (\frac{V θ}{V ∞ + \frac{μ}{4 \cdot π \cdot r^{3}}})

Next Step Substitute values of Variables

∴

θ = a \sin (\frac{66m/s}{68m/s + \frac{9463m³/s}{4 \cdot π \cdot {2.758m}^{3}}})

Next Step Substitute values of Constants

∴

θ = a \sin (\frac{66m/s}{68m/s + \frac{9463m³/s}{4 \cdot 3.1416 \cdot {2.758m}^{3}}})

Next Step Prepare to Evaluate

∴

θ = a \sin (\frac{66}{68 + \frac{9463}{4 \cdot 3.1416 \cdot {2.758}^{3}}})

Next Step Evaluate

∴

θ = 0.688339461066105rad

LAST Step Rounding Answer

∴

θ = 0.6883rad

Polar Coordinate given Tangential Velocity Formula Elements

Variables

Constants

Functions

Polar Angle

Polar Angle is the angular position of a point from a reference direction.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Polar Angle

Tangential Velocity

Tangential Velocity is the component of velocity in the tangential direction.

Symbol: V_θ

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Tangential Velocity

Freestream Velocity

The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.

Symbol: V_∞

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Freestream Velocity

Doublet Strength

Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength.

Symbol: μ

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Doublet Strength

Radial Coordinate

Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radial Coordinate

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

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)

asin

The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio.

Syntax: asin(Number)

Other formulas in Tangential Velocity category

Go Tangential Velocity for Flow over Sphere

V θ = (V ∞ + \frac{μ}{4 \cdot π \cdot r^{3}}) \cdot \sin (θ)

Go Freestream Velocity given Tangential Velocity

V ∞ = \frac{V θ}{\sin (θ)} - \frac{μ}{4 \cdot π \cdot r^{3}}

Go Radial Coordinate given Tangential Velocity

r = {(\frac{μ}{4 \cdot π \cdot (\frac{V θ}{\sin (θ)} - V ∞)})}^{\frac{1}{3}}

Go Doublet Strength given Tangential Velocity

μ = 4 \cdot π \cdot r^{3} \cdot (\frac{V θ}{\sin (θ)} - V ∞)

How to Evaluate Polar Coordinate given Tangential Velocity?

Polar Coordinate given Tangential Velocity evaluator uses Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))) to evaluate the Polar Angle, The Polar Coordinate given Tangential Velocity formula calculates the polar coordinate of the location in the three-dimensional doublet flow over a sphere, of which the tangential velocity is given. Polar Angle is denoted by θ symbol.

How to evaluate Polar Coordinate given Tangential Velocity using this online evaluator? To use this online evaluator for Polar Coordinate given Tangential Velocity, enter Tangential Velocity (V_θ), Freestream Velocity (V_∞), Doublet Strength (μ) & Radial Coordinate (r) and hit the calculate button.

FAQs on Polar Coordinate given Tangential Velocity

What is the formula to find Polar Coordinate given Tangential Velocity?

The formula of Polar Coordinate given Tangential Velocity is expressed as Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))). Here is an example- 0.592281 = asin(66/(68+9463/(4*pi*2.758^3))).

How to calculate Polar Coordinate given Tangential Velocity?

With Tangential Velocity (V_θ), Freestream Velocity (V_∞), Doublet Strength (μ) & Radial Coordinate (r) we can find Polar Coordinate given Tangential Velocity using the formula - Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))). This formula also uses Archimedes' constant and , Sine (sin), Inverse Sine (asin) function(s).

Can the Polar Coordinate given Tangential Velocity be negative?

Yes, the Polar Coordinate given Tangential Velocity, measured in Angle can be negative.

Which unit is used to measure Polar Coordinate given Tangential Velocity?

Polar Coordinate given Tangential Velocity is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Polar Coordinate given Tangential Velocity can be measured.

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Polar Coordinate given Tangential Velocity Formula

Polar Coordinate given Tangential Velocity Example

Polar Coordinate given Tangential Velocity Solution

Polar Coordinate given Tangential Velocity Formula Elements

Other formulas in Tangential Velocity category

How to Evaluate Polar Coordinate given Tangential Velocity?

FAQs on Polar Coordinate given Tangential Velocity

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