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Location of stagnation points for a rotating cylinder in a uniform flow field Solution

STEP 0: Pre-Calculation Summary
Formula Used
Angle at stagnation point = -asin(Circulation/(4*pi*Freestream Velocity*Cylinder Radius))
θ = -asin(Γ/(4*pi*V*R))
This formula uses 1 Constants, 2 Functions, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Trigonometric sine function, sin(Angle)
asin - Inverse trigonometric sine function, asin(Number)
Variables Used
Circulation - Circulation is a scalar integral quantity, is a macroscopic measure of rotation for a finite area of the fluid. (Measured in Meter² per Second)
Freestream Velocity - The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air. (Measured in Meter per Second)
Cylinder Radius - The Cylinder Radius is the radius of its base. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Circulation: 10 Meter² per Second --> 10 Meter² per Second No Conversion Required
Freestream Velocity: 100 Meter per Second --> 100 Meter per Second No Conversion Required
Cylinder Radius: 0.025 Meter --> 0.025 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
θ = -asin(Γ/(4*pi*V*R)) --> -asin(10/(4*pi*100*0.025))
Evaluating ... ...
θ = -0.323946106931981
STEP 3: Convert Result to Output's Unit
-0.323946106931981 Radian --> No Conversion Required
FINAL ANSWER
-0.323946106931981 Radian <-- Angle at stagnation point
(Calculation completed in 00.016 seconds)

10+ Forces on sub-merged bodies Calculators

Location of stagnation points for a rotating cylinder in a uniform flow field
Angle at stagnation point = -asin(Circulation/(4*pi*Freestream Velocity*Cylinder Radius)) Go
Skin friction drag from total drag force on a sphere
Skin friction drag force = 2*pi*Viscosity of Fluid*Diameter of Sphere*Flow Velocity Go
Area of the body for lift force in body moving on fluid
Reference Area = Lift force/(Lift Coefficient*0.5*Density of Fluid*(Velocity^2)) Go
Pressure drag from total drag force on a sphere
Pressure drag force = pi*Viscosity of Fluid*Diameter of Sphere*Flow Velocity Go
Length of the cylinder for lift force on a cylinder
Length of Cylinder = Lift force/(Density*Circulation*Freestream Velocity) Go
Drag force for a body moving in a fluid of certain density
Drag Force = Coefficient of drag*Area of Surface*Density*(Velocity^2)/2 Go
Lift force on a cylinder for circulation
Lift force = Density*Length of Cylinder*Circulation*Freestream Velocity Go
Total drag force on a sphere
Drag Force = 3*pi*Viscosity of Fluid*Diameter of Sphere*Flow Velocity Go
Lift force for a body moving in a fluid of certain density
Lift Force = Lift Coefficient*Reference Area*Density*(Velocity^2)/2 Go
Radius of cylinder for lift coefficient in a rotating cylinder with circulation
Cylinder Radius = Circulation/(Lift Coefficient*Freestream Velocity) Go

Location of stagnation points for a rotating cylinder in a uniform flow field Formula

Angle at stagnation point = -asin(Circulation/(4*pi*Freestream Velocity*Cylinder Radius))
θ = -asin(Γ/(4*pi*V*R))

What is a stagnation point

In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object.

What is circulation in fluid mechanics?

In physics, circulation is the line integral of a vector field around a closed curve. In fluid dynamics, the field is the fluid velocity field. In electrodynamics, it can be the electric or the magnetic field.

How to Calculate Location of stagnation points for a rotating cylinder in a uniform flow field?

Location of stagnation points for a rotating cylinder in a uniform flow field calculator uses Angle at stagnation point = -asin(Circulation/(4*pi*Freestream Velocity*Cylinder Radius)) to calculate the Angle at stagnation point, The Location of stagnation points for a rotating cylinder in a uniform flow field formula is known while considering the sin inverse with a ratio of circulation to the freestream velocity and the radius of the cylinder. Angle at stagnation point is denoted by θ symbol.

How to calculate Location of stagnation points for a rotating cylinder in a uniform flow field using this online calculator? To use this online calculator for Location of stagnation points for a rotating cylinder in a uniform flow field, enter Circulation (Γ), Freestream Velocity (V) & Cylinder Radius (R) and hit the calculate button. Here is how the Location of stagnation points for a rotating cylinder in a uniform flow field calculation can be explained with given input values -> -0.323946 = -asin(10/(4*pi*100*0.025)).

FAQ

What is Location of stagnation points for a rotating cylinder in a uniform flow field?
The Location of stagnation points for a rotating cylinder in a uniform flow field formula is known while considering the sin inverse with a ratio of circulation to the freestream velocity and the radius of the cylinder and is represented as θ = -asin(Γ/(4*pi*V*R)) or Angle at stagnation point = -asin(Circulation/(4*pi*Freestream Velocity*Cylinder Radius)). Circulation is a scalar integral quantity, is a macroscopic measure of rotation for a finite area of the fluid, The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air & The Cylinder Radius is the radius of its base.
How to calculate Location of stagnation points for a rotating cylinder in a uniform flow field?
The Location of stagnation points for a rotating cylinder in a uniform flow field formula is known while considering the sin inverse with a ratio of circulation to the freestream velocity and the radius of the cylinder is calculated using Angle at stagnation point = -asin(Circulation/(4*pi*Freestream Velocity*Cylinder Radius)). To calculate Location of stagnation points for a rotating cylinder in a uniform flow field, you need Circulation (Γ), Freestream Velocity (V) & Cylinder Radius (R). With our tool, you need to enter the respective value for Circulation, Freestream Velocity & Cylinder Radius 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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