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Polar Coordinate given Radial Velocity Formula

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

θ = a \cos (\frac{V r}{\frac{μ}{2 \cdot π \cdot r^{3}} - V ∞})

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

Polar Coordinate given Radial Velocity Example

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

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

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

0.6996 = a \cos (\frac{2.9}{\frac{9463}{2 \cdot 3.1416 \cdot {2.758}^{3}} - 68})

0.6996rad = a \cos (\frac{2.9m/s}{\frac{9463m³/s}{2 \cdot 3.1416 \cdot {2.758m}^{3}} - 68m/s})

0.6996 = a \cos (\frac{2.9}{\frac{9463}{2 \cdot 3.1416 \cdot {2.758}^{3}} - 68})

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Polar Coordinate given Radial Velocity Solution

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

FIRST Step Consider the formula

θ = a \cos (\frac{V r}{\frac{μ}{2 \cdot π \cdot r^{3}} - V ∞})

Next Step Substitute values of Variables

∴

θ = a \cos (\frac{2.9m/s}{\frac{9463m³/s}{2 \cdot π \cdot {2.758m}^{3}} - 68m/s})

Next Step Substitute values of Constants

∴

θ = a \cos (\frac{2.9m/s}{\frac{9463m³/s}{2 \cdot 3.1416 \cdot {2.758m}^{3}} - 68m/s})

Next Step Prepare to Evaluate

∴

θ = a \cos (\frac{2.9}{\frac{9463}{2 \cdot 3.1416 \cdot {2.758}^{3}} - 68})

Next Step Evaluate

∴

θ = 0.69960438062343rad

LAST Step Rounding Answer

∴

θ = 0.6996rad

Polar Coordinate given Radial 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

Radial Velocity

The Radial Velocity of an object with respect to a given point is the rate of change of the distance between the object and the point.

Symbol: V_r

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Radial 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

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

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

cos

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

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

Other formulas in Radial Velocity category

Go Radial Velocity for Flow over Sphere

V r = - (V ∞ - \frac{μ}{2 \cdot π \cdot r^{3}}) \cdot \cos (θ)

Go Freestream Velocity given Radial Velocity

V ∞ = \frac{μ}{2 \cdot π \cdot r^{3}} - \frac{V r}{\cos (θ)}

Go Radial Coordinate given Radial Velocity

r = {(\frac{μ}{2 \cdot π \cdot (V ∞ + \frac{V r}{\cos (θ)})})}^{\frac{1}{3}}

Go Doublet Strength given Radial Velocity

μ = 2 \cdot π \cdot r^{3} \cdot (V ∞ + \frac{V r}{\cos (θ)})

How to Evaluate Polar Coordinate given Radial Velocity?

Polar Coordinate given Radial Velocity evaluator uses Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream Velocity)) to evaluate the Polar Angle, The Polar Coordinate given Radial Velocity formula calculates the polar coordinate of the location in the three-dimensional doublet flow over a sphere, of which the radial velocity is given. Polar Angle is denoted by θ symbol.

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

FAQs on Polar Coordinate given Radial Velocity

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

The formula of Polar Coordinate given Radial Velocity is expressed as Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream Velocity)). Here is an example- 0.699604 = acos(2.9/(9463/(2*pi*2.758^3)-68)).

How to calculate Polar Coordinate given Radial Velocity?

With Radial Velocity (V_r), Doublet Strength (μ), Radial Coordinate (r) & Freestream Velocity (V_∞) we can find Polar Coordinate given Radial Velocity using the formula - Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream Velocity)). This formula also uses Archimedes' constant and , Cosine (cos), Inverse Cosine (acos) function(s).

Can the Polar Coordinate given Radial Velocity be negative?

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

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

Polar Coordinate given Radial 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 Radial Velocity can be measured.

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Polar Coordinate given Radial Velocity Formula

Polar Coordinate given Radial Velocity Example

Polar Coordinate given Radial Velocity Solution

Polar Coordinate given Radial Velocity Formula Elements

Other formulas in Radial Velocity category

How to Evaluate Polar Coordinate given Radial Velocity?

FAQs on Polar Coordinate given Radial Velocity

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