Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder Calculator

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Two-Dimensional Incompressible Flow

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

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Flow and Lift Distribution

Elementary Flows

Flow over Airfoils and Wings

Lift Distribution

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Flow over Cylinder

Kutta-Joukowski Lift Theorem

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Nonlifting Flow over Cylinder

Lifting Flow over Cylinder

✖Surface Pressure Coefficient quantifies the local pressure variation on the cylinder's surface due to lift generation.ⓘ Surface Pressure Coefficient [C_p]

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✖Polar Angle is the angular position of a point from a reference direction.ⓘ Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder [θ]

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Formula

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Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder

Formula

`"θ" = arsin(sqrt(1-("C"_{"p"}))/2)`

Example

`"1.083497rad"=arsin(sqrt(1-("-2.123"))/2)`

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Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Angle = arsin(sqrt(1-(Surface Pressure Coefficient))/2)
θ = arsin(sqrt(1-(C_p))/2)
This formula uses 3 Functions, 2 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)
arsin - Arcsine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., arsin(Number)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Surface Pressure Coefficient - Surface Pressure Coefficient quantifies the local pressure variation on the cylinder's surface due to lift generation.

STEP 1: Convert Input(s) to Base Unit

Surface Pressure Coefficient: -2.123 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = arsin(sqrt(1-(C_p))/2) --> arsin(sqrt(1-((-2.123)))/2)

Evaluating ... ...

θ = 1.08349687702023

STEP 3: Convert Result to Output's Unit

1.08349687702023 Radian --> No Conversion Required

FINAL ANSWER

1.08349687702023 ≈ 1.083497 Radian <-- Polar Angle

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Two-Dimensional Incompressible Flow » Flow and Lift Distribution » Flow over Cylinder » Nonlifting Flow over Cylinder » Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder

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Created by Harsh Raj

Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

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National Institute Of Technology (NIT), Hamirpur

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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

Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder Formula

Polar Angle = arsin(sqrt(1-(Surface Pressure Coefficient))/2)
θ = arsin(sqrt(1-(C_p))/2)

What is the range of values of surface pressure coefficient for non-lifting flow?

The pressure coefficient varies from 1 at the stagnation point to -3 at the point of maximum velocity for non-lifting incompressible flow over a circular cylinder.

How to Calculate Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder?

Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder calculator uses Polar Angle = arsin(sqrt(1-(Surface Pressure Coefficient))/2) to calculate the Polar Angle, The Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder formula is defined as the pressure distribution around a cylinder, influenced by various factors like Reynolds number, flow velocity, and cylinder geometry. Polar Angle is denoted by θ symbol.

How to calculate Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder using this online calculator? To use this online calculator for Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder, enter Surface Pressure Coefficient (C_p) and hit the calculate button. Here is how the Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder calculation can be explained with given input values -> 1.083497 = arsin(sqrt(1-((-2.123)))/2).

FAQ

What is Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder?

The Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder formula is defined as the pressure distribution around a cylinder, influenced by various factors like Reynolds number, flow velocity, and cylinder geometry and is represented as θ = arsin(sqrt(1-(C_p))/2) or Polar Angle = arsin(sqrt(1-(Surface Pressure Coefficient))/2). Surface Pressure Coefficient quantifies the local pressure variation on the cylinder's surface due to lift generation.

How to calculate Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder?

The Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder formula is defined as the pressure distribution around a cylinder, influenced by various factors like Reynolds number, flow velocity, and cylinder geometry is calculated using Polar Angle = arsin(sqrt(1-(Surface Pressure Coefficient))/2). To calculate Angular Position given Pressure Coefficient for Non-Lifting Flow over Circular Cylinder, you need Surface Pressure Coefficient (C_p). With our tool, you need to enter the respective value for Surface Pressure Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Polar Angle?

In this formula, Polar Angle uses Surface Pressure Coefficient. We can use 2 other way(s) to calculate the same, which is/are as follows -

Polar Angle = arccos(Radial Velocity/((1-(Cylinder Radius/Radial Coordinate)^2)*Freestream Velocity))
Polar Angle = -arsin(Tangential Velocity/((1+Cylinder Radius^2/Radial Coordinate^2)*Freestream Velocity))

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