Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Calculator

✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Angle [θ]			+10% -10%
✖Vortex Strength quantifies the intensity or magnitude of a vortex in fluid dynamics.ⓘ Vortex Strength [Γ]			+10% -10%
✖The Cylinder Radius is the radius of its circular cross section.ⓘ Cylinder Radius [R]			+10% -10%
✖The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.ⓘ Freestream Velocity [V_∞]			+10% -10%

✖Surface Pressure Coefficient quantifies the local pressure variation on the cylinder's surface due to lift generation.ⓘ Surface Pressure Coefficient for Lifting Flow over Circular Cylinder [C_p]

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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)
C_p = 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

C_p = 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 ... ...

C_p = -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)

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Home » Physics » Aerodynamics » Two Dimensional Incompressible Flow » Flow and Lift Distribution » Flow over Cylinder » Aerospace » Lifting Flow over Cylinder » Surface Pressure Coefficient for Lifting Flow over Circular Cylinder

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!

< Lifting Flow over Cylinder Calculators

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder

LaTeX 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

LaTeX 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)

Tangential Velocity for Lifting Flow over Circular Cylinder

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

Radial Velocity for Lifting Flow over Circular Cylinder

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

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Formula

LaTeX Go

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 defined as a measure of the pressure distribution around a circular cylinder in a lifting flow, reflecting the effects of circulation and angle of attack on aerodynamic performance. Surface Pressure Coefficient is denoted by C_p 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 defined as a measure of the pressure distribution around a circular cylinder in a lifting flow, reflecting the effects of circulation and angle of attack on aerodynamic performance and is represented as C_p = 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 defined as a measure of the pressure distribution around a circular cylinder in a lifting flow, reflecting the effects of circulation and angle of attack on aerodynamic performance 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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