Surface Velocity for Incompressible 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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✖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 Angle [θ]			+10% -10%

✖Tangential Velocity is the component of velocity in the tangential direction.ⓘ Surface Velocity for Incompressible Flow over Sphere [V_θ]

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Formula

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Surface Velocity for Incompressible Flow over Sphere

Formula

`"V"_{"θ"} = 3/2*"V"_{"∞"}*sin("θ")`

Example

`"65.7102m/s"=3/2*"68m/s"*sin("0.7rad")`

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Download Three-Dimensional Incompressible Flow Formulas PDF

Surface Velocity for Incompressible Flow over Sphere Solution

STEP 0: Pre-Calculation Summary

Formula Used

Tangential Velocity = 3/2*Freestream Velocity*sin(Polar Angle)
V_θ = 3/2*V_∞*sin(θ)
This formula uses 1 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)

Variables Used

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.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.

STEP 1: Convert Input(s) to Base Unit

Freestream Velocity: 68 Meter per Second --> 68 Meter per Second No Conversion Required
Polar Angle: 0.7 Radian --> 0.7 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_θ = 3/2*V_∞*sin(θ) --> 3/2*68*sin(0.7)

Evaluating ... ...

V_θ = 65.7102040982445

STEP 3: Convert Result to Output's Unit

65.7102040982445 Meter per Second --> No Conversion Required

FINAL ANSWER

65.7102040982445 ≈ 65.7102 Meter per Second <-- Tangential Velocity

(Calculation completed in 00.020 seconds)

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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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

Surface Velocity for Incompressible Flow over Sphere Formula

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

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 Surface Velocity for Incompressible Flow over Sphere?

Surface Velocity for Incompressible Flow over Sphere calculator uses Tangential Velocity = 3/2*Freestream Velocity*sin(Polar Angle) to calculate the Tangential Velocity, The Surface Velocity for Incompressible Flow over Sphere formula calculates the velocity at the surface of the sphere over which the incompressible flow is taking place. Tangential Velocity is denoted by V_θ symbol.

How to calculate Surface Velocity for Incompressible Flow over Sphere using this online calculator? To use this online calculator for Surface Velocity for Incompressible Flow over Sphere, enter Freestream Velocity (V_∞) & Polar Angle (θ) and hit the calculate button. Here is how the Surface Velocity for Incompressible Flow over Sphere calculation can be explained with given input values -> 65.7102 = 3/2*68*sin(0.7).

FAQ

What is Surface Velocity for Incompressible Flow over Sphere?

The Surface Velocity for Incompressible Flow over Sphere formula calculates the velocity at the surface of the sphere over which the incompressible flow is taking place and is represented as V_θ = 3/2*V_∞*sin(θ) or Tangential Velocity = 3/2*Freestream Velocity*sin(Polar Angle). 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 & Polar Angle is the angular position of a point from a reference direction.

How to calculate Surface Velocity for Incompressible Flow over Sphere?

The Surface Velocity for Incompressible Flow over Sphere formula calculates the velocity at the surface of the sphere over which the incompressible flow is taking place is calculated using Tangential Velocity = 3/2*Freestream Velocity*sin(Polar Angle). To calculate Surface Velocity for Incompressible Flow over Sphere, you need Freestream Velocity (V_∞) & Polar Angle (θ). With our tool, you need to enter the respective value for Freestream Velocity & Polar Angle 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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