Velocity Potential for 2-D Source Flow Calculator

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Two-Dimensional Incompressible Flow

Compressible Flow

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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✖Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point.ⓘ Source Strength [Λ]			+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%

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

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Formula

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Velocity Potential for 2-D Source Flow

Formula

`"ϕ" = "Λ"/(2*pi)*ln("r")`

Example

`"46.85969m²/s"="134m²/s"/(2*pi)*ln("9m")`

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Velocity Potential for 2-D Source Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity Potential = Source Strength/(2*pi)*ln(Radial Coordinate)
ϕ = Λ/(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

Velocity Potential - (Measured in Square Meter per Second) - Velocity Potential is a scalar function whose gradient gives velocity.
Source Strength - (Measured in Square Meter per Second) - Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point.
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

Source Strength: 134 Square Meter per Second --> 134 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

ϕ = Λ/(2*pi)*ln(r) --> 134/(2*pi)*ln(9)

Evaluating ... ...

ϕ = 46.859686443852

STEP 3: Convert Result to Output's Unit

46.859686443852 Square Meter per Second --> No Conversion Required

FINAL ANSWER

46.859686443852 ≈ 46.85969 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 Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has verified this Calculator and 200+ more calculators!

< 7 Source Flow Calculators

Stream Function for Flow over Rankine Oval

Go Rankine Oval Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+(Source Strength/(2*pi))*(Polar Angle from Source-Polar Angle from Sink)

Stream Function for Semi-Infinite Body

Go Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+Source Strength/(2*pi)*Polar Angle

Velocity Potential for 2-D Source Flow

Go Velocity Potential = Source Strength/(2*pi)*ln(Radial Coordinate)

Radial Velocity for 2-D Incompressible Source Flow

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

Stream Function for 2-D Incompressible Source Flow

Go Source Stream Function = Source Strength/(2*pi)*Polar Angle

Source Strength for 2-D Incompressible Source Flow

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

Stagnation Streamline Equation for Flow over Semi-Infinite Body

Go Stream Function = 0.5*Source Strength

Velocity Potential for 2-D Source Flow Formula

Velocity Potential = Source Strength/(2*pi)*ln(Radial Coordinate)
ϕ = Λ/(2*pi)*ln(r)

What does the equation of velocity potential for source flow represent?

The equation of velocity potential for source flow represents an equipotential line of the constant radius with its centre at the origin of the source.

What is source strength?

Source strength is physically the rate of volume flow from the source, per unit depth perpendicular to the page.

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

Velocity Potential for 2-D Source Flow calculator uses Velocity Potential = Source Strength/(2*pi)*ln(Radial Coordinate) to calculate the Velocity Potential, The Velocity Potential for 2-D Source Flow formula states that the function is directly proportional to the natural logarithm of the radial distance from the source point and the strength of the source, this logarithmic relationship reflects the property of potential flow where the velocity decreases logarithmically with increasing distance from the source. Velocity Potential is denoted by ϕ symbol.

How to calculate Velocity Potential for 2-D Source Flow using this online calculator? To use this online calculator for Velocity Potential for 2-D Source Flow, enter Source Strength (Λ) & Radial Coordinate (r) and hit the calculate button. Here is how the Velocity Potential for 2-D Source Flow calculation can be explained with given input values -> 36.36871 = 134/(2*pi)*ln(9).

FAQ

What is Velocity Potential for 2-D Source Flow?

The Velocity Potential for 2-D Source Flow formula states that the function is directly proportional to the natural logarithm of the radial distance from the source point and the strength of the source, this logarithmic relationship reflects the property of potential flow where the velocity decreases logarithmically with increasing distance from the source and is represented as ϕ = Λ/(2*pi)*ln(r) or Velocity Potential = Source Strength/(2*pi)*ln(Radial Coordinate). Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point & 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 Velocity Potential for 2-D Source Flow?

The Velocity Potential for 2-D Source Flow formula states that the function is directly proportional to the natural logarithm of the radial distance from the source point and the strength of the source, this logarithmic relationship reflects the property of potential flow where the velocity decreases logarithmically with increasing distance from the source is calculated using Velocity Potential = Source Strength/(2*pi)*ln(Radial Coordinate). To calculate Velocity Potential for 2-D Source Flow, you need Source Strength (Λ) & Radial Coordinate (r). With our tool, you need to enter the respective value for Source 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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