Stream Function for Semi-Infinite Body 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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✖The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.ⓘ Freestream Velocity [V_∞]			+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%
✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Angle [θ]			+10% -10%
✖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%

✖The Stream Function is defined as the quantity of fluid moving across some convenient imaginary line.ⓘ Stream Function for Semi-Infinite Body [ψ]

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Formula

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Stream Function for Semi-Infinite Body

Formula

`"ψ" = "V"_{"∞"}*"r"*sin("θ")+"Λ"/(2*pi)*"θ"`

Example

`"52.03567m²/s"="6.4m/s"*"9m"*sin("0.7rad")+"134m²/s"/(2*pi)*"0.7rad"`

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Stream Function for Semi-Infinite Body Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+Source Strength/(2*pi)*Polar Angle
ψ = V_∞*r*sin(θ)+Λ/(2*pi)*θ
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.
Freestream Velocity - (Measured in Meter per Second) - The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.
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.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
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.

STEP 1: Convert Input(s) to Base Unit

Freestream Velocity: 6.4 Meter per Second --> 6.4 Meter per Second No Conversion Required
Radial Coordinate: 9 Meter --> 9 Meter No Conversion Required
Polar Angle: 0.7 Radian --> 0.7 Radian No Conversion Required
Source Strength: 134 Square Meter per Second --> 134 Square Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = V_∞*r*sin(θ)+Λ/(2*pi)*θ --> 6.4*9*sin(0.7)+134/(2*pi)*0.7

Evaluating ... ...

ψ = 52.0356724469108

STEP 3: Convert Result to Output's Unit

52.0356724469108 Square Meter per Second --> No Conversion Required

FINAL ANSWER

52.0356724469108 ≈ 52.03567 Square Meter per Second <-- Stream Function

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Two-Dimensional Incompressible Flow » Elementary Flows » Source Flow » Stream Function for Semi-Infinite Body

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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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< 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

Stream Function for Semi-Infinite Body Formula

Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+Source Strength/(2*pi)*Polar Angle
ψ = V_∞*r*sin(θ)+Λ/(2*pi)*θ

How to obtain flow over semi-infinite body?

The flow over a semi-infinite body is obtained as the superposition of uniform flow and source flow. This is a half-body that stretches to infinity in the downstream direction; i.e., the body is not closed.

How to Calculate Stream Function for Semi-Infinite Body?

Stream Function for Semi-Infinite Body calculator uses Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+Source Strength/(2*pi)*Polar Angle to calculate the Stream Function, The Stream Function for Semi-Infinite Body is a scalar function that describes the flow field in potential flow theory, it provides a mathematical representation of the flow pattern particularly around solid bodies or obstacles. it captures the influence of the body's geometry and the incoming flow direction. Stream Function is denoted by ψ symbol.

How to calculate Stream Function for Semi-Infinite Body using this online calculator? To use this online calculator for Stream Function for Semi-Infinite Body, enter Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ) & Source Strength (Λ) and hit the calculate button. Here is how the Stream Function for Semi-Infinite Body calculation can be explained with given input values -> 409.19 = 6.4*9*sin(0.7)+134/(2*pi)*0.7.

FAQ

What is Stream Function for Semi-Infinite Body?

The Stream Function for Semi-Infinite Body is a scalar function that describes the flow field in potential flow theory, it provides a mathematical representation of the flow pattern particularly around solid bodies or obstacles. it captures the influence of the body's geometry and the incoming flow direction and is represented as ψ = V_∞*r*sin(θ)+Λ/(2*pi)*θ or Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+Source Strength/(2*pi)*Polar Angle. The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air, Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin, Polar Angle is the angular position of a point from a reference direction & Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point.

How to calculate Stream Function for Semi-Infinite Body?

The Stream Function for Semi-Infinite Body is a scalar function that describes the flow field in potential flow theory, it provides a mathematical representation of the flow pattern particularly around solid bodies or obstacles. it captures the influence of the body's geometry and the incoming flow direction is calculated using Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+Source Strength/(2*pi)*Polar Angle. To calculate Stream Function for Semi-Infinite Body, you need Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ) & Source Strength (Λ). With our tool, you need to enter the respective value for Freestream Velocity, Radial Coordinate, Polar Angle & Source Strength 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 Freestream Velocity, Radial Coordinate, Polar Angle & Source Strength. We can use 1 other way(s) to calculate the same, which is/are as follows -

Stream Function = 0.5*Source Strength

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