Stream Function for Non-Lifting Flow over Circular Cylinder Calculator

✖The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.ⓘ Freestream Velocity [V_∞]			+10% -10%
✖Radial Coordinate represents the distance measured from a central point or axis.ⓘ Radial Coordinate [r]			+10% -10%
✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Angle [θ]			+10% -10%
✖The Cylinder Radius is the radius of its circular cross section.ⓘ Cylinder Radius [R]			+10% -10%

✖Stream Function is a mathematical function used in fluid dynamics to describe the flow patterns within a fluid.ⓘ Stream Function for Non-Lifting Flow over Circular Cylinder [ψ]

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Stream Function for Non-Lifting Flow over Circular Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)
ψ = V_∞*r*sin(θ)*(1-(R/r)^2)
This formula uses 1 Functions, 5 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) - Stream Function is a mathematical function used in fluid dynamics to describe the flow patterns within a fluid.
Freestream Velocity - (Measured in Meter per Second) - The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.
Radial Coordinate - (Measured in Meter) - Radial Coordinate represents the distance measured from a central point or axis.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Cylinder Radius - (Measured in Meter) - The Cylinder Radius is the radius of its circular cross section.

STEP 1: Convert Input(s) to Base Unit

Freestream Velocity: 6.9 Meter per Second --> 6.9 Meter per Second No Conversion Required
Radial Coordinate: 0.27 Meter --> 0.27 Meter No Conversion Required
Polar Angle: 0.9 Radian --> 0.9 Radian No Conversion Required
Cylinder Radius: 0.08 Meter --> 0.08 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ = V_∞*r*sin(θ)*(1-(R/r)^2) --> 6.9*0.27*sin(0.9)*(1-(0.08/0.27)^2)

Evaluating ... ...

ψ = 1.33122056475026

STEP 3: Convert Result to Output's Unit

1.33122056475026 Square Meter per Second --> No Conversion Required

FINAL ANSWER

1.33122056475026 ≈ 1.331221 Square Meter per Second <-- Stream Function

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Two Dimensional Incompressible Flow » Flow and Lift Distribution » Flow over Cylinder » Aerospace » Nonlifting Flow over Cylinder » Stream Function for Non-Lifting Flow over Circular Cylinder

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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< Nonlifting Flow over Cylinder Calculators

Stream Function for Non-Lifting Flow over Circular Cylinder

LaTeX Go Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)

Tangential Velocity for Non-Lifting Flow over Circular Cylinder

LaTeX Go Tangential Velocity = -(1+((Cylinder Radius)/(Radial Coordinate))^2)*Freestream Velocity*sin(Polar Angle)

Radial Velocity for Non-Lifting Flow over Circular Cylinder

LaTeX Go Radial Velocity = (1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity*cos(Polar Angle)

Radius of Cylinder for Non-Lifting Flow

LaTeX Go Cylinder Radius = sqrt(Doublet Strength/(2*pi*Freestream Velocity))

Stream Function for Non-Lifting Flow over Circular Cylinder Formula

LaTeX Go

Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)
ψ = V_∞*r*sin(θ)*(1-(R/r)^2)

How to obtain non-lifting flow over circular cylinder?

The non-lifting flow over a circular cylinder is obtained by the superimposition of uniform flow and doublet flow. The pressure distribution is symmetrical about the horizontal and vertical axis for non-lifting flow.

How to Calculate Stream Function for Non-Lifting Flow over Circular Cylinder?

Stream Function for Non-Lifting Flow over Circular Cylinder calculator uses Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2) to calculate the Stream Function, The Stream function for non-lifting flow over circular cylinder formula is obtained as the function of radial velocity, the radial distance from the origin, polar angle and freestream velocity. Stream Function is denoted by ψ symbol.

How to calculate Stream Function for Non-Lifting Flow over Circular Cylinder using this online calculator? To use this online calculator for Stream Function for Non-Lifting Flow over Circular Cylinder, enter Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ) & Cylinder Radius (R) and hit the calculate button. Here is how the Stream Function for Non-Lifting Flow over Circular Cylinder calculation can be explained with given input values -> 1.331221 = 6.9*0.27*sin(0.9)*(1-(0.08/0.27)^2).

FAQ

What is Stream Function for Non-Lifting Flow over Circular Cylinder?

The Stream function for non-lifting flow over circular cylinder formula is obtained as the function of radial velocity, the radial distance from the origin, polar angle and freestream velocity and is represented as ψ = V_∞*r*sin(θ)*(1-(R/r)^2) or Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2). The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles, Radial Coordinate represents the distance measured from a central point or axis, Polar Angle is the angular position of a point from a reference direction & The Cylinder Radius is the radius of its circular cross section.

How to calculate Stream Function for Non-Lifting Flow over Circular Cylinder?

The Stream function for non-lifting flow over circular cylinder formula is obtained as the function of radial velocity, the radial distance from the origin, polar angle and freestream velocity is calculated using Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2). To calculate Stream Function for Non-Lifting Flow over Circular Cylinder, you need Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ) & Cylinder Radius (R). With our tool, you need to enter the respective value for Freestream Velocity, Radial Coordinate, Polar Angle & Cylinder Radius 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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