## Stream Function at Point in Combined Flow Solution

STEP 0: Pre-Calculation Summary
Formula Used
Stream Function = (Uniform Flow Velocity*Distance From End A*sin(Angle A))+(Strength of Source/(2*pi)*Angle A)
ψ = (U*a'*sin(∠A))+(q/(2*pi)*∠A)
This formula uses 1 Constants, 1 Functions, 5 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.
Uniform Flow Velocity - (Measured in Meter per Second) - The Uniform flow velocity is considered in flow past a half body.
Distance From End A - (Measured in Meter) - Distance from end A is the distance of the concentrated load from end A.
Angle A - (Measured in Radian) - The Angle A the space between two intersecting lines or surfaces at or close to the point where they meet.
Strength of Source - (Measured in Square Meter per Second) - The Strength of source, q is defined as the volume flow rate per unit depth of the fluid.
STEP 1: Convert Input(s) to Base Unit
Uniform Flow Velocity: 9 Meter per Second --> 9 Meter per Second No Conversion Required
Distance From End A: 0.5 Meter --> 0.5 Meter No Conversion Required
Angle A: 179 Degree --> 3.12413936106926 Radian (Check conversion ​here)
Strength of Source: 1.5 Square Meter per Second --> 1.5 Square Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ψ = (U*a'*sin(∠A))+(q/(2*pi)*∠A) --> (9*0.5*sin(3.12413936106926))+(1.5/(2*pi)*3.12413936106926)
Evaluating ... ...
ψ = 0.824369162303623
STEP 3: Convert Result to Output's Unit
0.824369162303623 Square Meter per Second --> No Conversion Required
0.824369162303623 0.824369 Square Meter per Second <-- Stream Function
(Calculation completed in 00.008 seconds)
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## Credits

Created by Maiarutselvan V
PSG College of Technology (PSGCT), Coimbatore
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Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune
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## <Incompressible Flow Characteristics Calculators

Stream function at point
​ Go Stream Function = -(Strength of Doublet/(2*pi))*(Length Y/((Length X^2)+(Length Y^2)))
Radius at any point considering radial velocity
​ Go Radius 1 = Strength of Source/(2*pi*Radial Velocity)
​ Go Radial Velocity = Strength of Source/(2*pi*Radius 1)
Strength of source for radial velocity and at any radius
​ Go Strength of Source = Radial Velocity*2*pi*Radius 1

## Stream Function at Point in Combined Flow Formula

Stream Function = (Uniform Flow Velocity*Distance From End A*sin(Angle A))+(Strength of Source/(2*pi)*Angle A)
ψ = (U*a'*sin(∠A))+(q/(2*pi)*∠A)

## What is stream function?

A family of curves ψ = constant represents "streamlines," hence, the stream function remains constant along a streamline. The stream function represents a particular case of a vector potential of velocity, related to velocity by the equality.

## What is flow past half body?

In the field of fluid dynamics, a Rankine half body is a feature of fluid flow discovered by Scottish physicist and engineer William Rankine that is formed when a fluid source is added to a fluid undergoing potential flow. Superposition of uniform flow and source flow yields the Rankine half body flow.

## How to Calculate Stream Function at Point in Combined Flow?

Stream Function at Point in Combined Flow calculator uses Stream Function = (Uniform Flow Velocity*Distance From End A*sin(Angle A))+(Strength of Source/(2*pi)*Angle A) to calculate the Stream Function, The Stream Function at Point in Combined Flow formula is known from the relation of stream function due to uniform flow and stream function due to source considering angle 'θ' and distance from an end at P(x,y) as 'r' in the polar coordinates. Stream Function is denoted by ψ symbol.

How to calculate Stream Function at Point in Combined Flow using this online calculator? To use this online calculator for Stream Function at Point in Combined Flow, enter Uniform Flow Velocity (U), Distance From End A (a'), Angle A (∠A) & Strength of Source (q) and hit the calculate button. Here is how the Stream Function at Point in Combined Flow calculation can be explained with given input values -> 0.824369 = (9*0.5*sin(3.12413936106926))+(1.5/(2*pi)*3.12413936106926).

### FAQ

What is Stream Function at Point in Combined Flow?
The Stream Function at Point in Combined Flow formula is known from the relation of stream function due to uniform flow and stream function due to source considering angle 'θ' and distance from an end at P(x,y) as 'r' in the polar coordinates and is represented as ψ = (U*a'*sin(∠A))+(q/(2*pi)*∠A) or Stream Function = (Uniform Flow Velocity*Distance From End A*sin(Angle A))+(Strength of Source/(2*pi)*Angle A). The Uniform flow velocity is considered in flow past a half body, Distance from end A is the distance of the concentrated load from end A, The Angle A the space between two intersecting lines or surfaces at or close to the point where they meet & The Strength of source, q is defined as the volume flow rate per unit depth of the fluid.
How to calculate Stream Function at Point in Combined Flow?
The Stream Function at Point in Combined Flow formula is known from the relation of stream function due to uniform flow and stream function due to source considering angle 'θ' and distance from an end at P(x,y) as 'r' in the polar coordinates is calculated using Stream Function = (Uniform Flow Velocity*Distance From End A*sin(Angle A))+(Strength of Source/(2*pi)*Angle A). To calculate Stream Function at Point in Combined Flow, you need Uniform Flow Velocity (U), Distance From End A (a'), Angle A (∠A) & Strength of Source (q). With our tool, you need to enter the respective value for Uniform Flow Velocity, Distance From End A, Angle A & Strength of Source and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Stream Function?
In this formula, Stream Function uses Uniform Flow Velocity, Distance From End A, Angle A & Strength of Source. We can use 2 other way(s) to calculate the same, which is/are as follows -
• Stream Function = -(Strength of Doublet/(2*pi))*(Length Y/((Length X^2)+(Length Y^2)))
• Stream Function = Strength of Source/(2*pi)*Angle A
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