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Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Formula

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Surface Pressure Coefficient quantifies the local pressure variation on the cylinder's surface due to lift generation. Check FAQs

C p = 1 - ({(2 \cdot \sin (θ))}^{2} + \frac{2 \cdot Γ \cdot \sin (θ)}{π \cdot R \cdot V ∞} + {(\frac{Γ}{2 \cdot π \cdot R \cdot V ∞})}^{2})

C_p - Surface Pressure Coefficient?θ - Polar Angle?Γ - Vortex Strength?R - Cylinder Radius?V_∞ - Freestream Velocity?π - Archimedes' constant?

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Example

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Here is how the Surface Pressure Coefficient for Lifting Flow over Circular Cylinder equation looks like with Values.

Here is how the Surface Pressure Coefficient for Lifting Flow over Circular Cylinder equation looks like with Units.

Here is how the Surface Pressure Coefficient for Lifting Flow over Circular Cylinder equation looks like.

-2.1275 = 1 - ({(2 \cdot \sin (0.9))}^{2} + \frac{2 \cdot 0.7 \cdot \sin (0.9)}{3.1416 \cdot 0.08 \cdot 6.9} + {(\frac{0.7}{2 \cdot 3.1416 \cdot 0.08 \cdot 6.9})}^{2})

-2.1275 = 1 - ({(2 \cdot \sin (0.9rad))}^{2} + \frac{2 \cdot 0.7m²/s \cdot \sin (0.9rad)}{3.1416 \cdot 0.08m \cdot 6.9m/s} + {(\frac{0.7m²/s}{2 \cdot 3.1416 \cdot 0.08m \cdot 6.9m/s})}^{2})

-2.1275 = 1 - ({(2 \cdot \sin (0.9))}^{2} + \frac{2 \cdot 0.7 \cdot \sin (0.9)}{3.1416 \cdot 0.08 \cdot 6.9} + {(\frac{0.7}{2 \cdot 3.1416 \cdot 0.08 \cdot 6.9})}^{2})

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Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Solution

Follow our step by step solution on how to calculate Surface Pressure Coefficient for Lifting Flow over Circular Cylinder?

FIRST Step Consider the formula

C p = 1 - ({(2 \cdot \sin (θ))}^{2} + \frac{2 \cdot Γ \cdot \sin (θ)}{π \cdot R \cdot V ∞} + {(\frac{Γ}{2 \cdot π \cdot R \cdot V ∞})}^{2})

Next Step Substitute values of Variables

∴

C p = 1 - ({(2 \cdot \sin (0.9rad))}^{2} + \frac{2 \cdot 0.7m²/s \cdot \sin (0.9rad)}{π \cdot 0.08m \cdot 6.9m/s} + {(\frac{0.7m²/s}{2 \cdot π \cdot 0.08m \cdot 6.9m/s})}^{2})

Next Step Substitute values of Constants

∴

C p = 1 - ({(2 \cdot \sin (0.9rad))}^{2} + \frac{2 \cdot 0.7m²/s \cdot \sin (0.9rad)}{3.1416 \cdot 0.08m \cdot 6.9m/s} + {(\frac{0.7m²/s}{2 \cdot 3.1416 \cdot 0.08m \cdot 6.9m/s})}^{2})

Next Step Prepare to Evaluate

∴

C p = 1 - ({(2 \cdot \sin (0.9))}^{2} + \frac{2 \cdot 0.7 \cdot \sin (0.9)}{3.1416 \cdot 0.08 \cdot 6.9} + {(\frac{0.7}{2 \cdot 3.1416 \cdot 0.08 \cdot 6.9})}^{2})

Next Step Evaluate

∴

C p = -2.12752412719393

LAST Step Rounding Answer

∴

C p = -2.1275

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Formula Elements

Variables

Constants

Functions

Surface Pressure Coefficient

Surface Pressure Coefficient quantifies the local pressure variation on the cylinder's surface due to lift generation.

Symbol: C_p

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Surface Pressure Coefficient

Polar Angle

Polar Angle is the angular position of a point from a reference direction.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Polar Angle

Vortex Strength

Vortex Strength quantifies the intensity or magnitude of a vortex in fluid dynamics.

Symbol: Γ

Measurement: Velocity PotentialUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Vortex Strength

Cylinder Radius

The Cylinder Radius is the radius of its circular cross section.

Symbol: R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Cylinder Radius

Freestream Velocity

The Freestream Velocity signifies the speed or velocity of a fluid flow far from any disturbances or obstacles.

Symbol: V_∞

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Freestream Velocity

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

Other formulas in Lifting Flow over Cylinder category

Go Stream Function for Lifting Flow over Circular Cylinder

ψ = V ∞ \cdot r \cdot \sin (θ) \cdot (1 - {(\frac{R}{r})}^{2}) + \frac{Γ}{2 \cdot π} \cdot \ln (\frac{r}{R})

Go Radial Velocity for Lifting Flow over Circular Cylinder

V r = (1 - {(\frac{R}{r})}^{2}) \cdot V ∞ \cdot \cos (θ)

Go Tangential Velocity for Lifting Flow over Circular Cylinder

V θ = - (1 + {(\frac{R}{r})}^{2}) \cdot V ∞ \cdot \sin (θ) - \frac{Γ}{2 \cdot π \cdot r}

Go Location of Stagnation Point Outside Cylinder for Lifting Flow

r 0 = \frac{Γ 0}{4 \cdot π \cdot V ∞} + \sqrt{{(\frac{Γ 0}{4 \cdot π \cdot V ∞})}^{2} - R^{2}}

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

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder evaluator 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 evaluate 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 C_p symbol.

How to evaluate Surface Pressure Coefficient for Lifting Flow over Circular Cylinder using this online evaluator? To use this online evaluator 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.

FAQs on Surface Pressure Coefficient for Lifting Flow over Circular Cylinder

What is the formula to find Surface Pressure Coefficient for Lifting Flow over Circular Cylinder?

The formula of Surface Pressure Coefficient for Lifting Flow over Circular Cylinder is expressed as 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). Here is an example- -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).

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

With Polar Angle (θ), Vortex Strength (Γ), Cylinder Radius (R) & Freestream Velocity (V_∞) we can find Surface Pressure Coefficient for Lifting Flow over Circular Cylinder using the 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). This formula also uses Archimedes' constant and Sine function(s).

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Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Formula

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Example

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Solution

Surface Pressure Coefficient for Lifting Flow over Circular Cylinder Formula Elements

Other formulas in Lifting Flow over Cylinder category

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

FAQs on Surface Pressure Coefficient for Lifting Flow over Circular Cylinder

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