Radial Coordinate for 3D Doublet Flow given Velocity Potential Calculator

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Fundamentals of Inviscid and Incompressible Flow

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✖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%
✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Angle [θ]			+10% -10%
✖Source Velocity Potential is the potential of a source, which is a scalar function whose gradient gives velocity.ⓘ Source Velocity Potential [ϕ_s]			+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 for 3D Doublet Flow given Velocity Potential [r]

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Formula

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Radial Coordinate for 3D Doublet Flow given Velocity Potential

Formula

`"r" = sqrt(("modulus"("μ")*cos("θ"))/(4*pi*"modulus"("ϕ"_{"s"})))`

Example

`"8.484972m"=sqrt(("modulus"("9463m³/s")*cos("0.7rad"))/(4*pi*"modulus"("-8m²/s")))`

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Radial Coordinate for 3D Doublet Flow given Velocity Potential Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radial Coordinate = sqrt((modulus(Doublet Strength)*cos(Polar Angle))/(4*pi*modulus(Source Velocity Potential)))
r = sqrt((modulus(μ)*cos(θ))/(4*pi*modulus(ϕ_s)))
This formula uses 1 Constants, 3 Functions, 4 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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
modulus - Modulus of a number is the remainder when that number is divided by another number., modulus

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.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Source Velocity Potential - (Measured in Square Meter per Second) - Source Velocity Potential is the potential of a source, which is a scalar function whose gradient gives velocity.

STEP 1: Convert Input(s) to Base Unit

Doublet Strength: 9463 Cubic Meter per Second --> 9463 Cubic Meter per Second No Conversion Required
Polar Angle: 0.7 Radian --> 0.7 Radian No Conversion Required
Source Velocity Potential: -8 Square Meter per Second --> -8 Square Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = sqrt((modulus(μ)*cos(θ))/(4*pi*modulus(ϕ_s))) --> sqrt((modulus(9463)*cos(0.7))/(4*pi*modulus((-8))))

Evaluating ... ...

r = 8.48497196950429

STEP 3: Convert Result to Output's Unit

8.48497196950429 Meter --> No Conversion Required

FINAL ANSWER

8.48497196950429 ≈ 8.484972 Meter <-- Radial Coordinate

(Calculation completed in 00.004 seconds)

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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< 9 3D Elementry Flows Calculators

Radial Coordinate for 3D Doublet Flow given Velocity Potential

Go Radial Coordinate = sqrt((modulus(Doublet Strength)*cos(Polar Angle))/(4*pi*modulus(Source Velocity Potential)))

Velocity Potential for 3D Incompressible Doublet Flow

Go Velocity Potential = -(Doublet Strength*cos(Polar Angle))/(4*pi*Radial Coordinate^2)

Doublet Strength for 3D Incompressible Flow

Go Doublet Strength = -(4*pi*Velocity Potential*Radial Coordinate^2)/cos(Polar Angle)

Radial Coordinate for 3D Source Flow given Radial Velocity

Go Radial Coordinate = sqrt(Source Strength/(4*pi*Radial Velocity))

Radial Coordinate for 3D Source Flow given Velocity Potential

Go Radial Coordinate = -Source Strength/(4*pi*Source Velocity Potential)

Velocity Potential for 3D Incompressible Source Flow

Go Source Velocity Potential = -Source Strength/(4*pi*Radial Coordinate)

Source Strength for 3D Incompressible Source Flow given Velocity Potential

Go Source Strength = -4*pi*Source Velocity Potential*Radial Coordinate

Radial Velocity for 3D Incompressible Source Flow

Go Radial Velocity = Source Strength/(4*pi*Radial Coordinate^2)

Source Strength for 3D Incompressible Source Flow given Radial Velocity

Go Source Strength = 4*pi*Radial Velocity*Radial Coordinate^2

Radial Coordinate for 3D Doublet Flow given Velocity Potential Formula

Radial Coordinate = sqrt((modulus(Doublet Strength)*cos(Polar Angle))/(4*pi*modulus(Source Velocity Potential)))
r = sqrt((modulus(μ)*cos(θ))/(4*pi*modulus(ϕ_s)))

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 for 3D Doublet Flow given Velocity Potential?

Radial Coordinate for 3D Doublet Flow given Velocity Potential calculator uses Radial Coordinate = sqrt((modulus(Doublet Strength)*cos(Polar Angle))/(4*pi*modulus(Source Velocity Potential))) to calculate the Radial Coordinate, The Radial Coordinate for 3D Doublet Flow given Velocity Potential formula calculates the radial coordinate to the position of where the velocity potential of the three-dimensional incompressible doublet flow has been provided. Radial Coordinate is denoted by r symbol.

How to calculate Radial Coordinate for 3D Doublet Flow given Velocity Potential using this online calculator? To use this online calculator for Radial Coordinate for 3D Doublet Flow given Velocity Potential, enter Doublet Strength (μ), Polar Angle (θ) & Source Velocity Potential (ϕ_s) and hit the calculate button. Here is how the Radial Coordinate for 3D Doublet Flow given Velocity Potential calculation can be explained with given input values -> 8.484972 = sqrt((modulus(9463)*cos(0.7))/(4*pi*modulus((-8)))).

FAQ

What is Radial Coordinate for 3D Doublet Flow given Velocity Potential?

The Radial Coordinate for 3D Doublet Flow given Velocity Potential formula calculates the radial coordinate to the position of where the velocity potential of the three-dimensional incompressible doublet flow has been provided and is represented as r = sqrt((modulus(μ)*cos(θ))/(4*pi*modulus(ϕ_s))) or Radial Coordinate = sqrt((modulus(Doublet Strength)*cos(Polar Angle))/(4*pi*modulus(Source Velocity Potential))). Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength, Polar Angle is the angular position of a point from a reference direction & Source Velocity Potential is the potential of a source, which is a scalar function whose gradient gives velocity.

How to calculate Radial Coordinate for 3D Doublet Flow given Velocity Potential?

The Radial Coordinate for 3D Doublet Flow given Velocity Potential formula calculates the radial coordinate to the position of where the velocity potential of the three-dimensional incompressible doublet flow has been provided is calculated using Radial Coordinate = sqrt((modulus(Doublet Strength)*cos(Polar Angle))/(4*pi*modulus(Source Velocity Potential))). To calculate Radial Coordinate for 3D Doublet Flow given Velocity Potential, you need Doublet Strength (μ), Polar Angle (θ) & Source Velocity Potential (ϕ_s). With our tool, you need to enter the respective value for Doublet Strength, Polar Angle & Source Velocity Potential and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Radial Coordinate?

In this formula, Radial Coordinate uses Doublet Strength, Polar Angle & Source Velocity Potential. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radial Coordinate = sqrt(Source Strength/(4*pi*Radial Velocity))
Radial Coordinate = -Source Strength/(4*pi*Source Velocity Potential)

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