Stream Function for Uniform Incompressible Flow in Polar Coordinates Calculator

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Two-Dimensional Incompressible Flow

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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%

✖The Stream Function is defined as the quantity of fluid moving across some convenient imaginary line.ⓘ Stream Function for Uniform Incompressible Flow in Polar Coordinates [ψ]

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Formula

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Stream Function for Uniform Incompressible Flow in Polar Coordinates

Formula

`"ψ" = "V"_{"∞"}*"r"*sin("θ")`

Example

`"37.10694m²/s"="6.4m/s"*"9m"*sin("0.7rad")`

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Stream Function for Uniform Incompressible Flow in Polar Coordinates Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)
ψ = V_∞*r*sin(θ)
This formula uses 1 Functions, 4 Variables

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.

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = V_∞*r*sin(θ) --> 6.4*9*sin(0.7)

Evaluating ... ...

ψ = 37.106938784891

STEP 3: Convert Result to Output's Unit

37.106938784891 Square Meter per Second --> No Conversion Required

FINAL ANSWER

37.106938784891 ≈ 37.10694 Square Meter per Second <-- Stream Function

(Calculation completed in 00.004 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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Amrita School of Engineering (ASE), Vallikavu

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< 4 Uniform Flow Calculators

Velocity Potential for Uniform Incompressible Flow in Polar Coordinates

Go Velocity Potential = Freestream Velocity*Radial Coordinate*cos(Polar Angle)

Stream Function for Uniform Incompressible Flow in Polar Coordinates

Go Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)

Velocity Potential for Uniform Incompressible Flow

Go Velocity Potential = Freestream Velocity*Distance on X-Axis

Stream Function for Uniform Incompressible Flow

Go Stream Function = Freestream Velocity*Distance on Y-Axis

Stream Function for Uniform Incompressible Flow in Polar Coordinates Formula

Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)
ψ = V_∞*r*sin(θ)

What is uniform flow?

Uniform flow is a flow of a fluid in which each particle moves along its line of flow with constant speed and in which the cross-section of each stream tube remains unchanged.

What is stream function?

The stream function is defined such that ψ= constant is the equation of a streamline, and the difference in the stream function between two streamlines is equal to the mass flow between the streamlines.

How to Calculate Stream Function for Uniform Incompressible Flow in Polar Coordinates?

Stream Function for Uniform Incompressible Flow in Polar Coordinates calculator uses Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle) to calculate the Stream Function, The Stream Function for Uniform Incompressible Flow in Polar Coordinates represents a linear increase in the streamlines with radial distance from the origin, it characterizes the flow field where fluid particles move uniformly in one direction without rotation or swirl. Stream Function is denoted by ψ symbol.

How to calculate Stream Function for Uniform Incompressible Flow in Polar Coordinates using this online calculator? To use this online calculator for Stream Function for Uniform Incompressible Flow in Polar Coordinates, enter Freestream Velocity (V_∞), Radial Coordinate (r) & Polar Angle (θ) and hit the calculate button. Here is how the Stream Function for Uniform Incompressible Flow in Polar Coordinates calculation can be explained with given input values -> 394.2612 = 6.4*9*sin(0.7).

FAQ

What is Stream Function for Uniform Incompressible Flow in Polar Coordinates?

The Stream Function for Uniform Incompressible Flow in Polar Coordinates represents a linear increase in the streamlines with radial distance from the origin, it characterizes the flow field where fluid particles move uniformly in one direction without rotation or swirl and is represented as ψ = V_∞*r*sin(θ) or Stream Function = Freestream Velocity*Radial Coordinate*sin(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.

How to calculate Stream Function for Uniform Incompressible Flow in Polar Coordinates?

The Stream Function for Uniform Incompressible Flow in Polar Coordinates represents a linear increase in the streamlines with radial distance from the origin, it characterizes the flow field where fluid particles move uniformly in one direction without rotation or swirl is calculated using Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle). To calculate Stream Function for Uniform Incompressible Flow in Polar Coordinates, you need Freestream Velocity (V_∞), Radial Coordinate (r) & Polar Angle (θ). With our tool, you need to enter the respective value for Freestream Velocity, Radial Coordinate & Polar Angle 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. We can use 1 other way(s) to calculate the same, which is/are as follows -

Stream Function = Freestream Velocity*Distance on Y-Axis

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