Polar Coordinate given Tangential Velocity Calculator

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Three-Dimensional Incompressible Flow

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Two-Dimensional Incompressible Flow

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✖Tangential Velocity is the component of velocity in the tangential direction.ⓘ Tangential Velocity [V_θ]			+10% -10%
✖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.ⓘ Freestream Velocity [V_∞]			+10% -10%
✖Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength.ⓘ Doublet Strength [μ]			+10% -10%
✖Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.ⓘ Radial Coordinate [r]			+10% -10%

✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Coordinate given Tangential Velocity [θ]

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Formula

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Polar Coordinate given Tangential Velocity

Formula

`"θ" = asin("V"_{"θ"}/("V"_{"∞"}+"μ"/(4*pi*"r"^3)))`

Example

`"0.688339rad"=asin("66m/s"/("68m/s"+"9463m³/s"/(4*pi*("2.758m")^3)))`

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Download Three-Dimensional Incompressible Flow Formulas PDF

Polar Coordinate given Tangential Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3)))
θ = asin(V_θ/(V_∞+μ/(4*pi*r^3)))
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., 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., asin(Number)

Variables Used

Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Tangential Velocity - (Measured in Meter per Second) - Tangential Velocity is the component of velocity in the tangential direction.
Freestream Velocity - (Measured in Meter per Second) - 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.
Doublet Strength - (Measured in Cubic Meter per Second) - Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength.
Radial Coordinate - (Measured in Meter) - Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.

STEP 1: Convert Input(s) to Base Unit

Tangential Velocity: 66 Meter per Second --> 66 Meter per Second No Conversion Required
Freestream Velocity: 68 Meter per Second --> 68 Meter per Second No Conversion Required
Doublet Strength: 9463 Cubic Meter per Second --> 9463 Cubic Meter per Second No Conversion Required
Radial Coordinate: 2.758 Meter --> 2.758 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = asin(V_θ/(V_∞+μ/(4*pi*r^3))) --> asin(66/(68+9463/(4*pi*2.758^3)))

Evaluating ... ...

θ = 0.688339461066105

STEP 3: Convert Result to Output's Unit

0.688339461066105 Radian --> No Conversion Required

FINAL ANSWER

0.688339461066105 ≈ 0.688339 Radian <-- Polar Angle

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Three-Dimensional Incompressible Flow » Flow over Sphere » Tangential Velocity » Polar Coordinate given Tangential Velocity

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< 5 Tangential Velocity Calculators

Radial Coordinate given Tangential Velocity

Go Radial Coordinate = (Doublet Strength/(4*pi*(Tangential Velocity/sin(Polar Angle)-Freestream Velocity)))^(1/3)

Polar Coordinate given Tangential Velocity

Go Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3)))

Tangential Velocity for Flow over Sphere

Go Tangential Velocity = (Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))*sin(Polar Angle)

Freestream Velocity given Tangential Velocity

Go Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3)

Doublet Strength given Tangential Velocity

Go Doublet Strength = 4*pi*Radial Coordinate^3*(Tangential Velocity/sin(Polar Angle)-Freestream Velocity)

Polar Coordinate given Tangential Velocity Formula

Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3)))
θ = asin(V_θ/(V_∞+μ/(4*pi*r^3)))

What is doublet flow?

Doublet flow is a special, degenerate case of a source-sink pair that leads to a singularity. It is frequently used in incompressible flow. When the distance between source-sink pair tends to zero that is when the source-sink falls on top of each other, they do not extinguish each other because the absolute magnitude of their strength becomes infinitely large in the limit.

How to Calculate Polar Coordinate given Tangential Velocity?

Polar Coordinate given Tangential Velocity calculator uses Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))) to calculate 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 calculate Polar Coordinate given Tangential Velocity using this online calculator? To use this online calculator 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. Here is how the Polar Coordinate given Tangential Velocity calculation can be explained with given input values -> 0.592281 = asin(66/(68+9463/(4*pi*2.758^3))).

FAQ

What is Polar Coordinate given Tangential Velocity?

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 and is represented as θ = asin(V_θ/(V_∞+μ/(4*pi*r^3))) or Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))). Tangential Velocity is the component of velocity in the tangential direction, 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, Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength & Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.

How to calculate Polar Coordinate given Tangential Velocity?

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 is calculated using Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))). To calculate Polar Coordinate given Tangential Velocity, you need Tangential Velocity (V_θ), Freestream Velocity (V_∞), Doublet Strength (μ) & Radial Coordinate (r). With our tool, you need to enter the respective value for Tangential Velocity, Freestream Velocity, Doublet Strength & Radial Coordinate 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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