Polar Coordinate given Radial Velocity Calculator

✖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.ⓘ Radial Velocity [V_r]			+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%
✖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%

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

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Polar Coordinate given Radial Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream Velocity))
θ = acos(V_r/(μ/(2*pi*r^3)-V_∞))
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., acos(Number)

Variables Used

Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Radial Velocity - (Measured in Meter per Second) - 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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Radial Velocity: 2.9 Meter per Second --> 2.9 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
Freestream Velocity: 68 Meter per Second --> 68 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(V_r/(μ/(2*pi*r^3)-V_∞)) --> acos(2.9/(9463/(2*pi*2.758^3)-68))

Evaluating ... ...

θ = 0.69960438062343

STEP 3: Convert Result to Output's Unit

0.69960438062343 Radian --> No Conversion Required

FINAL ANSWER

0.69960438062343 ≈ 0.699604 Radian <-- Polar Angle

(Calculation completed in 00.004 seconds)

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< Radial Velocity Calculators

Radial Coordinate given Radial Velocity

LaTeX Go Radial Coordinate = (Doublet Strength/(2*pi*(Freestream Velocity+Radial Velocity/cos(Polar Angle))))^(1/3)

Polar Coordinate given Radial Velocity

LaTeX Go Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream Velocity))

Radial Velocity for Flow over Sphere

LaTeX Go Radial Velocity = -(Freestream Velocity-Doublet Strength/(2*pi*Radial Coordinate^3))*cos(Polar Angle)

Freestream Velocity given Radial Velocity

LaTeX Go Freestream Velocity = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle)

Polar Coordinate given Radial Velocity Formula

LaTeX Go

Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream Velocity))
θ = acos(V_r/(μ/(2*pi*r^3)-V_∞))

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 Radial Velocity?

Polar Coordinate given Radial Velocity calculator uses Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream Velocity)) to calculate 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 calculate Polar Coordinate given Radial Velocity using this online calculator? To use this online calculator 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. Here is how the Polar Coordinate given Radial Velocity calculation can be explained with given input values -> 0.699604 = acos(2.9/(9463/(2*pi*2.758^3)-68)).

FAQ

What is Polar Coordinate given Radial Velocity?

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 and is represented as θ = acos(V_r/(μ/(2*pi*r^3)-V_∞)) or Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream 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, 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 & 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.

How to calculate Polar Coordinate given Radial Velocity?

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 is calculated using Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream Velocity)). To calculate Polar Coordinate given Radial Velocity, you need Radial Velocity (V_r), Doublet Strength (μ), Radial Coordinate (r) & Freestream Velocity (V_∞). With our tool, you need to enter the respective value for Radial Velocity, Doublet Strength, Radial Coordinate & Freestream Velocity 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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