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)

Credits

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
Vinay Mishra has verified this Calculator and 100+ more calculators!

10+ Nonlifting Flow over Cylinder Calculators

Stream Function for Non-Lifting Flow over Circular Cylinder
Go Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)*(1-(Cylinder Radius/Radial Coordinate)^2)
Angular Position given Tangential Velocity for Non-Lifting Flow over Circular Cylinder
Go Polar Angle = -arsin(Tangential Velocity/((1+Cylinder Radius^2/Radial Coordinate^2)*Freestream Velocity))
Tangential Velocity for Non-Lifting Flow over Circular Cylinder
Go Tangential Velocity = -(1+((Cylinder Radius)/(Radial Coordinate))^2)*Freestream Velocity*sin(Polar Angle)
Angular Position given Radial Velocity for Non-Lifting Flow over Circular Cylinder
Go Polar Angle = arccos(Radial Velocity/((1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity))
Radial Velocity for Non-Lifting Flow over Circular Cylinder
Go Radial Velocity = (1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity*cos(Polar Angle)
Radius of Cylinder for Non-Lifting Flow
Go Cylinder Radius = sqrt(Doublet Strength/(2*pi*Freestream Velocity))
Freestream Velocity given Doublet Strength for Non-Lifting Flow over Circular Cylinder
Go Freestream Velocity = Doublet Strength/(Cylinder Radius^2*2*pi)
Doublet Strength given Radius of Cylinder for Non-Lifting Flow
Go Doublet Strength = Cylinder Radius^2*2*pi*Freestream Velocity
Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder
Go Polar Angle = arsin(sqrt(1-(Surface Pressure Coefficient))/2)
Surface Pressure Coefficient for Non-Lifting Flow over Circular Cylinder
Go Surface Pressure Coefficient = 1-4*(sin(Polar Angle))^2

Stream Function for Non-Lifting Flow over Circular Cylinder Formula

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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