Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface Pressure Coefficient = 1-((2*sin(Polar Angle))^2+(2*Vortex Strength*sin(Polar Angle))/(pi*Cylinder Radius*Freestream Velocity)+((Vortex Strength)/(2*pi*Cylinder Radius*Freestream Velocity))^2)
Cp = 1-((2*sin(θ))^2+(2*Γ*sin(θ))/(pi*R*V)+((Γ)/(2*pi*R*V))^2)
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
Surface Pressure Coefficient - Surface Pressure Coefficient quantifies the local pressure variation on the cylinder's surface due to lift generation.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Vortex Strength - (Measured in Square Meter per Second) - Vortex Strength quantifies the intensity or magnitude of a vortex in fluid dynamics.
Cylinder Radius - (Measured in Meter) - The Cylinder Radius is the radius of its circular cross section.
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.
STEP 1: Convert Input(s) to Base Unit
Polar Angle: 0.9 Radian --> 0.9 Radian No Conversion Required
Vortex Strength: 0.7 Square Meter per Second --> 0.7 Square Meter per Second No Conversion Required
Cylinder Radius: 0.08 Meter --> 0.08 Meter No Conversion Required
Freestream Velocity: 6.9 Meter per Second --> 6.9 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Cp = 1-((2*sin(θ))^2+(2*Γ*sin(θ))/(pi*R*V)+((Γ)/(2*pi*R*V))^2) --> 1-((2*sin(0.9))^2+(2*0.7*sin(0.9))/(pi*0.08*6.9)+((0.7)/(2*pi*0.08*6.9))^2)
Evaluating ... ...
Cp = -2.12752412719393
STEP 3: Convert Result to Output's Unit
-2.12752412719393 --> No Conversion Required
FINAL ANSWER
-2.12752412719393 -2.127524 <-- Surface Pressure Coefficient
(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+ Lifting Flow over Cylinder Calculators

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

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Formula

Surface Pressure Coefficient = 1-((2*sin(Polar Angle))^2+(2*Vortex Strength*sin(Polar Angle))/(pi*Cylinder Radius*Freestream Velocity)+((Vortex Strength)/(2*pi*Cylinder Radius*Freestream Velocity))^2)
Cp = 1-((2*sin(θ))^2+(2*Γ*sin(θ))/(pi*R*V)+((Γ)/(2*pi*R*V))^2)

What is the pressure coefficient?

The pressure coefficient is the dimensionless pressure used in aerodynamics. It is obtained as the ratio of the difference between surface pressure & free-stream pressure to the free stream dynamic pressure.

How to Calculate Surface Pressure Coefficient for Lifting Flow over Circular Cylinder?

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder calculator uses Surface Pressure Coefficient = 1-((2*sin(Polar Angle))^2+(2*Vortex Strength*sin(Polar Angle))/(pi*Cylinder Radius*Freestream Velocity)+((Vortex Strength)/(2*pi*Cylinder Radius*Freestream Velocity))^2) to calculate the Surface Pressure Coefficient, Surface pressure coefficient for lifting flow over circular cylinder formula is a function of radial distance, freestream velocity, the radius of the cylinder, vortex strength and polar angle. Surface Pressure Coefficient is denoted by Cp symbol.

How to calculate Surface Pressure Coefficient for Lifting Flow over Circular Cylinder using this online calculator? To use this online calculator for Surface Pressure Coefficient for Lifting Flow over Circular Cylinder, enter Polar Angle (θ), Vortex Strength (Γ), Cylinder Radius (R) & Freestream Velocity (V) and hit the calculate button. Here is how the Surface Pressure Coefficient for Lifting Flow over Circular Cylinder calculation can be explained with given input values -> -27.247822 = 1-((2*sin(0.9))^2+(2*0.7*sin(0.9))/(pi*0.08*6.9)+((0.7)/(2*pi*0.08*6.9))^2).

FAQ

What is Surface Pressure Coefficient for Lifting Flow over Circular Cylinder?
Surface pressure coefficient for lifting flow over circular cylinder formula is a function of radial distance, freestream velocity, the radius of the cylinder, vortex strength and polar angle and is represented as Cp = 1-((2*sin(θ))^2+(2*Γ*sin(θ))/(pi*R*V)+((Γ)/(2*pi*R*V))^2) or Surface Pressure Coefficient = 1-((2*sin(Polar Angle))^2+(2*Vortex Strength*sin(Polar Angle))/(pi*Cylinder Radius*Freestream Velocity)+((Vortex Strength)/(2*pi*Cylinder Radius*Freestream Velocity))^2). Polar Angle is the angular position of a point from a reference direction, Vortex Strength quantifies the intensity or magnitude of a vortex in fluid dynamics, The Cylinder Radius is the radius of its circular cross section & The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.
How to calculate Surface Pressure Coefficient for Lifting Flow over Circular Cylinder?
Surface pressure coefficient for lifting flow over circular cylinder formula is a function of radial distance, freestream velocity, the radius of the cylinder, vortex strength and polar angle is calculated using Surface Pressure Coefficient = 1-((2*sin(Polar Angle))^2+(2*Vortex Strength*sin(Polar Angle))/(pi*Cylinder Radius*Freestream Velocity)+((Vortex Strength)/(2*pi*Cylinder Radius*Freestream Velocity))^2). To calculate Surface Pressure Coefficient for Lifting Flow over Circular Cylinder, you need Polar Angle (θ), Vortex Strength (Γ), Cylinder Radius (R) & Freestream Velocity (V). With our tool, you need to enter the respective value for Polar Angle, Vortex Strength, Cylinder Radius & Freestream Velocity 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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