Polar Coordinate given Surface Velocity for Flow over Sphere Calculator

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Three-Dimensional Incompressible Flow

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Two-Dimensional Incompressible Flow

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✖Tangential Velocity is the component of velocity in the tangential direction.ⓘ Tangential Velocity [V_θ]			+10% -10%
✖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.ⓘ Freestream Velocity [V_∞]			+10% -10%

✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Coordinate given Surface Velocity for Flow over Sphere [θ]

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Formula

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Polar Coordinate given Surface Velocity for Flow over Sphere

Formula

`"θ" = asin(2/3*"V"_{"θ"}/"V"_{"∞"})`

Example

`"0.703721rad"=asin(2/3*"66m/s"/"68m/s")`

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Polar Coordinate given Surface Velocity for Flow over Sphere Solution

STEP 0: Pre-Calculation Summary

Formula Used

Polar Angle = asin(2/3*Tangential Velocity/Freestream Velocity)
θ = asin(2/3*V_θ/V_∞)
This formula uses 2 Functions, 3 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)
asin - The inverse sine 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., asin(Number)

Variables Used

Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Tangential Velocity - (Measured in Meter per Second) - Tangential Velocity is the component of velocity in the tangential direction.
Freestream Velocity - (Measured in Meter per Second) - 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.

STEP 1: Convert Input(s) to Base Unit

Tangential Velocity: 66 Meter per Second --> 66 Meter per Second No Conversion Required
Freestream Velocity: 68 Meter per Second --> 68 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = asin(2/3*V_θ/V_∞) --> asin(2/3*66/68)

Evaluating ... ...

θ = 0.703720508083224

STEP 3: Convert Result to Output's Unit

0.703720508083224 Radian --> No Conversion Required

FINAL ANSWER

0.703720508083224 ≈ 0.703721 Radian <-- Polar Angle

(Calculation completed in 00.004 seconds)

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< 5 Surface Velocity Calculators

Polar Coordinate given Surface Velocity for Flow over Sphere

Go Polar Angle = asin(2/3*Tangential Velocity/Freestream Velocity)

Freestream Velocity given Surface Velocity for Flow over Sphere

Go Freestream Velocity = 2/3*Tangential Velocity/sin(Polar Angle)

Surface Velocity for Incompressible Flow over Sphere

Go Tangential Velocity = 3/2*Freestream Velocity*sin(Polar Angle)

Freestream Velocity given Maximum Surface Velocity

Go Freestream Velocity = 2/3*Maximum Surface Velocity

Maximum Surface Velocity for Flow over Sphere

Go Maximum Surface Velocity = 3/2*Freestream Velocity

Polar Coordinate given Surface Velocity for Flow over Sphere Formula

Polar Angle = asin(2/3*Tangential Velocity/Freestream Velocity)
θ = asin(2/3*V_θ/V_∞)

What are the characteristics of the flow field near and far from the sphere?

The flow lines are straight and uniform in the free stream far in front of the sphere, but they are deflected as they pass around the sphere. For a large distance away from the sphere the flow lines become somewhat more widely spaced, indicating that the fluid velocity is less than the free-stream velocity.

How to Calculate Polar Coordinate given Surface Velocity for Flow over Sphere?

Polar Coordinate given Surface Velocity for Flow over Sphere calculator uses Polar Angle = asin(2/3*Tangential Velocity/Freestream Velocity) to calculate the Polar Angle, The Polar Coordinate given Surface Velocity for Flow over Sphere formula calculates the polar coordinate or the angle at which the surface velocity of the flow over the sphere is given. Polar Angle is denoted by θ symbol.

How to calculate Polar Coordinate given Surface Velocity for Flow over Sphere using this online calculator? To use this online calculator for Polar Coordinate given Surface Velocity for Flow over Sphere, enter Tangential Velocity (V_θ) & Freestream Velocity (V_∞) and hit the calculate button. Here is how the Polar Coordinate given Surface Velocity for Flow over Sphere calculation can be explained with given input values -> 0.604836 = asin(2/3*66/68).

FAQ

What is Polar Coordinate given Surface Velocity for Flow over Sphere?

The Polar Coordinate given Surface Velocity for Flow over Sphere formula calculates the polar coordinate or the angle at which the surface velocity of the flow over the sphere is given and is represented as θ = asin(2/3*V_θ/V_∞) or Polar Angle = asin(2/3*Tangential Velocity/Freestream Velocity). Tangential Velocity is the component of velocity in the tangential direction & 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.

How to calculate Polar Coordinate given Surface Velocity for Flow over Sphere?

The Polar Coordinate given Surface Velocity for Flow over Sphere formula calculates the polar coordinate or the angle at which the surface velocity of the flow over the sphere is given is calculated using Polar Angle = asin(2/3*Tangential Velocity/Freestream Velocity). To calculate Polar Coordinate given Surface Velocity for Flow over Sphere, you need Tangential Velocity (V_θ) & Freestream Velocity (V_∞). With our tool, you need to enter the respective value for Tangential Velocity & 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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