Velocity Potential for 2-D Vortex Flow Calculator

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Two-Dimensional Incompressible Flow

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Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

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Elementary Flows

Flow and Lift Distribution

Flow over Airfoils and Wings

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✖Vortex Strength measure of the intensity or magnitude of a vortex, such as in fluid dynamics. A vortex is a region within a fluid where the flow revolves around an axis line.ⓘ Vortex Strength [γ]			+10% -10%
✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Angle [θ]			+10% -10%

✖Velocity Potential is a scalar function whose gradient gives velocity.ⓘ Velocity Potential for 2-D Vortex Flow [ϕ]

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Formula

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Velocity Potential for 2-D Vortex Flow

Formula

`"ϕ" = -("γ"/(2*pi))*"θ"`

Example

`"46.79155m²/s"=-("-420m²/s"/(2*pi))*"0.7rad"`

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Velocity Potential for 2-D Vortex Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity Potential = -(Vortex Strength/(2*pi))*Polar Angle
ϕ = -(γ/(2*pi))*θ
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Velocity Potential - (Measured in Square Meter per Second) - Velocity Potential is a scalar function whose gradient gives velocity.
Vortex Strength - (Measured in Square Meter per Second) - Vortex Strength measure of the intensity or magnitude of a vortex, such as in fluid dynamics. A vortex is a region within a fluid where the flow revolves around an axis line.
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

Vortex Strength: -420 Square Meter per Second --> -420 Square 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

ϕ = -(γ/(2*pi))*θ --> -((-420)/(2*pi))*0.7

Evaluating ... ...

ϕ = 46.7915532690172

STEP 3: Convert Result to Output's Unit

46.7915532690172 Square Meter per Second --> No Conversion Required

FINAL ANSWER

46.7915532690172 ≈ 46.79155 Square Meter per Second <-- Velocity Potential

(Calculation completed in 00.004 seconds)

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Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has verified this Calculator and 100+ more calculators!

< 3 Vortex Flow Calculators

Stream Function for 2-D Vortex Flow

Go Vortex Stream Function = Vortex Strength/(2*pi)*ln(Radial Coordinate)

Tangential Velocity for 2-D Vortex Flow

Go Tangential Velocity = -(Vortex Strength)/(2*pi*Radial Coordinate)

Velocity Potential for 2-D Vortex Flow

Go Velocity Potential = -(Vortex Strength/(2*pi))*Polar Angle

Velocity Potential for 2-D Vortex Flow Formula

Velocity Potential = -(Vortex Strength/(2*pi))*Polar Angle
ϕ = -(γ/(2*pi))*θ

What is a vortex flow?.

A flow where all the streamlines are concentric circles about a given point, the velocity along any given circular streamline be constant, but it varies from one streamline to another inversely with distance from the common center. Such a flow is called a vortex flow.
Vortex flow is a physically possible incompressible flow at every point, and it is irrotational, at every point except at the origin.

How to Calculate Velocity Potential for 2-D Vortex Flow?

Velocity Potential for 2-D Vortex Flow calculator uses Velocity Potential = -(Vortex Strength/(2*pi))*Polar Angle to calculate the Velocity Potential, The Velocity Potential for 2-D Vortex Flow formula is defined as the function of polar angle and strength of the vortex flow, it describes the flow induced by a vortex, where the velocity potential decreases linearly with the angular coordinate . Velocity Potential is denoted by ϕ symbol.

How to calculate Velocity Potential for 2-D Vortex Flow using this online calculator? To use this online calculator for Velocity Potential for 2-D Vortex Flow, enter Vortex Strength (γ) & Polar Angle (θ) and hit the calculate button. Here is how the Velocity Potential for 2-D Vortex Flow calculation can be explained with given input values -> 11.92071 = -((-420)/(2*pi))*0.7.

FAQ

What is Velocity Potential for 2-D Vortex Flow?

The Velocity Potential for 2-D Vortex Flow formula is defined as the function of polar angle and strength of the vortex flow, it describes the flow induced by a vortex, where the velocity potential decreases linearly with the angular coordinate and is represented as ϕ = -(γ/(2*pi))*θ or Velocity Potential = -(Vortex Strength/(2*pi))*Polar Angle. Vortex Strength measure of the intensity or magnitude of a vortex, such as in fluid dynamics. A vortex is a region within a fluid where the flow revolves around an axis line & Polar Angle is the angular position of a point from a reference direction.

How to calculate Velocity Potential for 2-D Vortex Flow?

The Velocity Potential for 2-D Vortex Flow formula is defined as the function of polar angle and strength of the vortex flow, it describes the flow induced by a vortex, where the velocity potential decreases linearly with the angular coordinate is calculated using Velocity Potential = -(Vortex Strength/(2*pi))*Polar Angle. To calculate Velocity Potential for 2-D Vortex Flow, you need Vortex Strength (γ) & Polar Angle (θ). With our tool, you need to enter the respective value for Vortex Strength & 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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