Radial Velocity for Non-Lifting Flow over Circular Cylinder Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radial Velocity = (1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity*cos(Polar Angle)
Vr = (1-(R/r)^2)*V*cos(θ)
This formula uses 1 Functions, 5 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Radial Velocity - (Measured in Meter per Second) - Radial Velocity represents the speed of an object's motion along the radial direction.
Cylinder Radius - (Measured in Meter) - The Cylinder Radius is the radius of its circular cross section.
Radial Coordinate - (Measured in Meter) - Radial Coordinate represents the distance measured from a central point or axis.
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.
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
Cylinder Radius: 0.08 Meter --> 0.08 Meter No Conversion Required
Radial Coordinate: 0.27 Meter --> 0.27 Meter No Conversion Required
Freestream Velocity: 6.9 Meter per Second --> 6.9 Meter per Second No Conversion Required
Polar Angle: 0.9 Radian --> 0.9 Radian No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vr = (1-(R/r)^2)*V*cos(θ) --> (1-(0.08/0.27)^2)*6.9*cos(0.9)
Evaluating ... ...
Vr = 3.91256150810692
STEP 3: Convert Result to Output's Unit
3.91256150810692 Meter per Second --> No Conversion Required
FINAL ANSWER
3.91256150810692 3.912562 Meter per Second <-- Radial Velocity
(Calculation completed in 00.020 seconds)

Credits

Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
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Verified by Sanjay Krishna
Amrita School of Engineering (ASE), Vallikavu
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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

Radial Velocity for Non-Lifting Flow over Circular Cylinder Formula

Radial Velocity = (1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity*cos(Polar Angle)
Vr = (1-(R/r)^2)*V*cos(θ)

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 Radial Velocity for Non-Lifting Flow over Circular Cylinder?

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

How to calculate Radial Velocity for Non-Lifting Flow over Circular Cylinder using this online calculator? To use this online calculator for Radial Velocity for Non-Lifting Flow over Circular Cylinder, enter Cylinder Radius (R), Radial Coordinate (r), Freestream Velocity (V) & Polar Angle (θ) and hit the calculate button. Here is how the Radial Velocity for Non-Lifting Flow over Circular Cylinder calculation can be explained with given input values -> 5.582958 = (1-(0.08/0.27)^2)*6.9*cos(0.9).

FAQ

What is Radial Velocity for Non-Lifting Flow over Circular Cylinder?
The Radial velocity for non-lifting flow over circular cylinder formula is defined as the function of radial velocity, the radial distance from the origin, polar angle and freestream velocity and is represented as Vr = (1-(R/r)^2)*V*cos(θ) or Radial Velocity = (1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity*cos(Polar Angle). The Cylinder Radius is the radius of its circular cross section, Radial Coordinate represents the distance measured from a central point or axis, The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles & Polar Angle is the angular position of a point from a reference direction.
How to calculate Radial Velocity for Non-Lifting Flow over Circular Cylinder?
The Radial velocity for non-lifting flow over circular cylinder formula is defined as the function of radial velocity, the radial distance from the origin, polar angle and freestream velocity is calculated using Radial Velocity = (1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity*cos(Polar Angle). To calculate Radial Velocity for Non-Lifting Flow over Circular Cylinder, you need Cylinder Radius (R), Radial Coordinate (r), Freestream Velocity (V) & Polar Angle (θ). With our tool, you need to enter the respective value for Cylinder Radius, Radial Coordinate, Freestream Velocity & Polar Angle 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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