Stream Function for 2-D Doublet Flow Calculator

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Two-Dimensional Incompressible Flow

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Elementary Flows

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✖Doublet strength is defined as the product of distance between a source-sink pair and source or sink strength.ⓘ Doublet Strength [κ]			+10% -10%
✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Angle [θ]			+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%

✖The Stream Function is defined as the quantity of fluid moving across some convenient imaginary line.ⓘ Stream Function for 2-D Doublet Flow [ψ]

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Formula

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Stream Function for 2-D Doublet Flow

Formula

`"ψ" = ("κ"*sin("θ"))/(2*pi*"r")`

Example

`"38.73372m²/s"=("3400m³/s"*sin("0.7rad"))/(2*pi*"9m")`

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Stream Function for 2-D Doublet Flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stream Function = (Doublet Strength*sin(Polar Angle))/(2*pi*Radial Coordinate)
ψ = (κ*sin(θ))/(2*pi*r)
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Stream Function - (Measured in Square Meter per Second) - The Stream Function is defined as the quantity of fluid moving across some convenient imaginary line.
Doublet Strength - (Measured in Cubic Meter per Second) - Doublet strength is defined as the product of 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.
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

Doublet Strength: 3400 Cubic Meter per Second --> 3400 Cubic Meter per Second No Conversion Required
Polar Angle: 0.7 Radian --> 0.7 Radian No Conversion Required
Radial Coordinate: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = (κ*sin(θ))/(2*pi*r) --> (3400*sin(0.7))/(2*pi*9)

Evaluating ... ...

ψ = 38.7337177548627

STEP 3: Convert Result to Output's Unit

38.7337177548627 Square Meter per Second --> No Conversion Required

FINAL ANSWER

38.7337177548627 ≈ 38.73372 Square Meter per Second <-- Stream Function

(Calculation completed in 00.020 seconds)

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Home » Physics » Aerodynamics » Two-Dimensional Incompressible Flow » Elementary Flows » Doublet Flow » Stream Function for 2-D Doublet Flow

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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< 2 Doublet Flow Calculators

Velocity Potential for 2-D Doublet Flow

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

Stream Function for 2-D Doublet Flow

Go Stream Function = (Doublet Strength*sin(Polar Angle))/(2*pi*Radial Coordinate)

Stream Function for 2-D Doublet Flow Formula

Stream Function = (Doublet Strength*sin(Polar Angle))/(2*pi*Radial Coordinate)
ψ = (κ*sin(θ))/(2*pi*r)

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 fall 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 Stream Function for 2-D Doublet Flow?

Stream Function for 2-D Doublet Flow calculator uses Stream Function = (Doublet Strength*sin(Polar Angle))/(2*pi*Radial Coordinate) to calculate the Stream Function, The Stream function for 2-D Doublet flow formula describes the flow field induced by a doublet of strength it produces a flow pattern where fluid is pushed radially outward from the doublet along the x-axis and radially inward towards the doublet along the y-axis. Stream Function is denoted by ψ symbol.

How to calculate Stream Function for 2-D Doublet Flow using this online calculator? To use this online calculator for Stream Function for 2-D Doublet Flow, enter Doublet Strength (κ), Polar Angle (θ) & Radial Coordinate (r) and hit the calculate button. Here is how the Stream Function for 2-D Doublet Flow calculation can be explained with given input values -> 38.73372 = (3400*sin(0.7))/(2*pi*9).

FAQ

What is Stream Function for 2-D Doublet Flow?

The Stream function for 2-D Doublet flow formula describes the flow field induced by a doublet of strength it produces a flow pattern where fluid is pushed radially outward from the doublet along the x-axis and radially inward towards the doublet along the y-axis and is represented as ψ = (κ*sin(θ))/(2*pi*r) or Stream Function = (Doublet Strength*sin(Polar Angle))/(2*pi*Radial Coordinate). Doublet strength is defined as the product of distance between a source-sink pair and source or sink strength, Polar Angle is the angular position of a point from a reference direction & 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 Doublet Flow?

The Stream function for 2-D Doublet flow formula describes the flow field induced by a doublet of strength it produces a flow pattern where fluid is pushed radially outward from the doublet along the x-axis and radially inward towards the doublet along the y-axis is calculated using Stream Function = (Doublet Strength*sin(Polar Angle))/(2*pi*Radial Coordinate). To calculate Stream Function for 2-D Doublet Flow, you need Doublet Strength (κ), Polar Angle (θ) & Radial Coordinate (r). With our tool, you need to enter the respective value for Doublet Strength, Polar Angle & 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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