Stream Function for 2-D Vortex Flow Calculator

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Two-Dimensional Incompressible Flow

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Fundamentals of Inviscid and Incompressible Flow

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Elementary Flows

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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%
✖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%

✖Vortex Stream Function represents the flow patterns associated with the rotational motion.ⓘ Stream Function for 2-D Vortex Flow [ψ_vortex]

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Formula

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Stream Function for 2-D Vortex Flow

Formula

`"ψ"_{"vortex"} = "γ"/(2*pi)*ln("r") `

Example

`"-146.873644m²/s"="-420m²/s"/(2*pi)*ln("9m") `

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Stream Function for 2-D Vortex Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vortex Stream Function = Vortex Strength/(2*pi)*ln(Radial Coordinate)
ψ_vortex = γ/(2*pi)*ln(r)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Vortex Stream Function - (Measured in Square Meter per Second) - Vortex Stream Function represents the flow patterns associated with the rotational motion.
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.
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

Vortex Strength: -420 Square Meter per Second --> -420 Square Meter per Second No Conversion Required
Radial Coordinate: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ_vortex = γ/(2*pi)*ln(r) --> (-420)/(2*pi)*ln(9)

Evaluating ... ...

ψ_vortex = -146.873644077745

STEP 3: Convert Result to Output's Unit

-146.873644077745 Square Meter per Second --> No Conversion Required

FINAL ANSWER

-146.873644077745 ≈ -146.873644 Square Meter per Second <-- Vortex Stream Function

(Calculation completed in 00.004 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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

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PSG College of Technology (PSGCT), Coimbatore

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< 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

Stream Function for 2-D Vortex Flow Formula

Vortex Stream Function = Vortex Strength/(2*pi)*ln(Radial Coordinate)
ψ_vortex = γ/(2*pi)*ln(r)

What is vortex flow?

A flow where all the streamlines are concentric circles about agiven 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.

What is stream function?

The stream function is defined such that ψ= constant is the equation of a streamline, and the difference in the stream function between two streamlines is equal to the mass flow between the streamlines.

How to Calculate Stream Function for 2-D Vortex Flow?

Stream Function for 2-D Vortex Flow calculator uses Vortex Stream Function = Vortex Strength/(2*pi)*ln(Radial Coordinate) to calculate the Vortex Stream Function, The Stream Function for 2-D Vortex Flow formula is defined as the function of vortex strength and radial distance, it describes the flow pattern induced by a vortex, where fluid particles circulate the vortex center, they are concentric circles around the vortex center, and the velocity increases logarithmically with distance from the vortex center. Vortex Stream Function is denoted by ψ_vortex symbol.

How to calculate Stream Function for 2-D Vortex Flow using this online calculator? To use this online calculator for Stream Function for 2-D Vortex Flow, enter Vortex Strength (γ) & Radial Coordinate (r) and hit the calculate button. Here is how the Stream Function for 2-D Vortex Flow calculation can be explained with given input values -> -146.873644 = (-420)/(2*pi)*ln(9) .

FAQ

What is Stream Function for 2-D Vortex Flow?

The Stream Function for 2-D Vortex Flow formula is defined as the function of vortex strength and radial distance, it describes the flow pattern induced by a vortex, where fluid particles circulate the vortex center, they are concentric circles around the vortex center, and the velocity increases logarithmically with distance from the vortex center and is represented as ψ_vortex = γ/(2*pi)*ln(r) or Vortex Stream Function = Vortex Strength/(2*pi)*ln(Radial Coordinate). 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 & 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 Stream Function for 2-D Vortex Flow?

The Stream Function for 2-D Vortex Flow formula is defined as the function of vortex strength and radial distance, it describes the flow pattern induced by a vortex, where fluid particles circulate the vortex center, they are concentric circles around the vortex center, and the velocity increases logarithmically with distance from the vortex center is calculated using Vortex Stream Function = Vortex Strength/(2*pi)*ln(Radial Coordinate). To calculate Stream Function for 2-D Vortex Flow, you need Vortex Strength (γ) & Radial Coordinate (r). With our tool, you need to enter the respective value for Vortex 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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