Radial Coordinate given Radial Velocity Calculator

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

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Radial Coordinate given Radial Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
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.
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.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.

STEP 1: Convert Input(s) to Base Unit

Doublet Strength: 9463 Cubic Meter per Second --> 9463 Cubic Meter per Second No Conversion Required
Freestream Velocity: 68 Meter per Second --> 68 Meter per Second No Conversion Required
Radial Velocity: 2.9 Meter per Second --> 2.9 Meter per Second No Conversion Required
Polar Angle: 0.7 Radian --> 0.7 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = (μ/(2*pi*(V_∞+V_r/cos(θ))))^(1/3) --> (9463/(2*pi*(68+2.9/cos(0.7))))^(1/3)

Evaluating ... ...

r = 2.75798382964409

STEP 3: Convert Result to Output's Unit

2.75798382964409 Meter --> No Conversion Required

FINAL ANSWER

2.75798382964409 ≈ 2.757984 Meter <-- Radial Coordinate

(Calculation completed in 00.020 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)

Radial Coordinate given Radial Velocity Formula

LaTeX Go

Radial Coordinate = (Doublet Strength/(2*pi*(Freestream Velocity+Radial Velocity/cos(Polar Angle))))^(1/3)
r = (μ/(2*pi*(V_∞+V_r/cos(θ))))^(1/3)

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 Radial Coordinate given Radial Velocity?

Radial Coordinate given Radial Velocity calculator uses Radial Coordinate = (Doublet Strength/(2*pi*(Freestream Velocity+Radial Velocity/cos(Polar Angle))))^(1/3) to calculate the Radial Coordinate, The Radial Coordinate given Radial Velocity formula calculates the radial position in the three-dimensional doublet flow over a sphere when there is radial velocity given. Radial Coordinate is denoted by r symbol.

How to calculate Radial Coordinate given Radial Velocity using this online calculator? To use this online calculator for Radial Coordinate given Radial Velocity, enter Doublet Strength (μ), Freestream Velocity (V_∞), Radial Velocity (V_r) & Polar Angle (θ) and hit the calculate button. Here is how the Radial Coordinate given Radial Velocity calculation can be explained with given input values -> 2.757984 = (9463/(2*pi*(68+2.9/cos(0.7))))^(1/3).

FAQ

What is Radial Coordinate given Radial Velocity?

The Radial Coordinate given Radial Velocity formula calculates the radial position in the three-dimensional doublet flow over a sphere when there is radial velocity given and is represented as r = (μ/(2*pi*(V_∞+V_r/cos(θ))))^(1/3) or Radial Coordinate = (Doublet Strength/(2*pi*(Freestream Velocity+Radial Velocity/cos(Polar Angle))))^(1/3). Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength, 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, 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 & Polar Angle is the angular position of a point from a reference direction.

How to calculate Radial Coordinate given Radial Velocity?

The Radial Coordinate given Radial Velocity formula calculates the radial position in the three-dimensional doublet flow over a sphere when there is radial velocity given is calculated using Radial Coordinate = (Doublet Strength/(2*pi*(Freestream Velocity+Radial Velocity/cos(Polar Angle))))^(1/3). To calculate Radial Coordinate given Radial Velocity, you need Doublet Strength (μ), Freestream Velocity (V_∞), Radial Velocity (V_r) & Polar Angle (θ). With our tool, you need to enter the respective value for Doublet Strength, Freestream Velocity, Radial Velocity & Polar Angle 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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