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Stream Function for 2-D Vortex Flow Formula

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Vortex Stream Function represents the flow patterns associated with the rotational motion. Check FAQs

ψ vortex = \frac{γ}{2 \cdot π} \cdot \ln (r)

ψ_vortex - Vortex Stream Function?γ - Vortex Strength?r - Radial Coordinate?π - Archimedes' constant?

Stream Function for 2-D Vortex Flow Example

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Here is how the Stream Function for 2-D Vortex Flow equation looks like with Values.

Here is how the Stream Function for 2-D Vortex Flow equation looks like with Units.

Here is how the Stream Function for 2-D Vortex Flow equation looks like.

-146.8736 = \frac{-420}{2 \cdot 3.1416} \cdot \ln (9)

-146.8736m²/s = \frac{-420m²/s}{2 \cdot 3.1416} \cdot \ln (9m)

-146.8736 = \frac{-420}{2 \cdot 3.1416} \cdot \ln (9)

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Stream Function for 2-D Vortex Flow Solution

Follow our step by step solution on how to calculate Stream Function for 2-D Vortex Flow?

FIRST Step Consider the formula

ψ vortex = \frac{γ}{2 \cdot π} \cdot \ln (r)

Next Step Substitute values of Variables

∴

ψ vortex = \frac{-420m²/s}{2 \cdot π} \cdot \ln (9m)

Next Step Substitute values of Constants

∴

ψ vortex = \frac{-420m²/s}{2 \cdot 3.1416} \cdot \ln (9m)

Next Step Prepare to Evaluate

∴

ψ vortex = \frac{-420}{2 \cdot 3.1416} \cdot \ln (9)

Next Step Evaluate

∴

ψ vortex = -146.873644077745m²/s

LAST Step Rounding Answer

∴

ψ vortex = -146.8736m²/s

Stream Function for 2-D Vortex Flow Formula Elements

Variables

Constants

Functions

Vortex Stream Function

Vortex Stream Function represents the flow patterns associated with the rotational motion.

Symbol: ψ_vortex

Measurement: Velocity PotentialUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Vortex Stream Function

Vortex Strength

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.

Symbol: γ

Measurement: Velocity PotentialUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Vortex Strength

Radial Coordinate

Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radial Coordinate

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Vortex Flow category

Go Tangential Velocity for 2-D Vortex Flow

V θ = - \frac{γ}{2 \cdot π \cdot r}

Go Velocity Potential for 2-D Vortex Flow

ϕ = - (\frac{γ}{2 \cdot π}) \cdot θ

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

Stream Function for 2-D Vortex Flow evaluator uses Vortex Stream Function = Vortex Strength/(2*pi)*ln(Radial Coordinate) to evaluate 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 evaluate Stream Function for 2-D Vortex Flow using this online evaluator? To use this online evaluator for Stream Function for 2-D Vortex Flow, enter Vortex Strength (γ) & Radial Coordinate (r) and hit the calculate button.

FAQs on Stream Function for 2-D Vortex Flow

What is the formula to find Stream Function for 2-D Vortex Flow?

The formula of Stream Function for 2-D Vortex Flow is expressed as Vortex Stream Function = Vortex Strength/(2*pi)*ln(Radial Coordinate). Here is an example- -146.873644 = (-420)/(2*pi)*ln(9).

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

With Vortex Strength (γ) & Radial Coordinate (r) we can find Stream Function for 2-D Vortex Flow using the formula - Vortex Stream Function = Vortex Strength/(2*pi)*ln(Radial Coordinate). This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

Can the Stream Function for 2-D Vortex Flow be negative?

Yes, the Stream Function for 2-D Vortex Flow, measured in Velocity Potential can be negative.

Which unit is used to measure Stream Function for 2-D Vortex Flow?

Stream Function for 2-D Vortex Flow is usually measured using the Square Meter per Second[m²/s] for Velocity Potential. are the few other units in which Stream Function for 2-D Vortex Flow can be measured.

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