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

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Formula

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Freestream Velocity given Surface Velocity for Flow over Sphere

Formula

`"V"_{"∞"} = 2/3*"V"_{"θ"}/sin("θ")`

Example

`"68.29989m/s"=2/3*"66m/s"/sin("0.7rad")`

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Freestream Velocity given Surface Velocity for Flow over Sphere Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Tangential Velocity - (Measured in Meter per Second) - Tangential Velocity is the component of velocity in the tangential direction.
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

Tangential Velocity: 66 Meter per Second --> 66 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_∞ = 2/3*V_θ/sin(θ) --> 2/3*66/sin(0.7)

Evaluating ... ...

V_∞ = 68.2998943861126

STEP 3: Convert Result to Output's Unit

68.2998943861126 Meter per Second --> No Conversion Required

FINAL ANSWER

68.2998943861126 ≈ 68.29989 Meter per Second <-- Freestream Velocity

(Calculation completed in 00.020 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

Freestream Velocity given Surface Velocity for Flow over Sphere Formula

Freestream Velocity = 2/3*Tangential Velocity/sin(Polar Angle)
V_∞ = 2/3*V_θ/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 Freestream Velocity given Surface Velocity for Flow over Sphere?

Freestream Velocity given Surface Velocity for Flow over Sphere calculator uses Freestream Velocity = 2/3*Tangential Velocity/sin(Polar Angle) to calculate the Freestream Velocity, The Freestream Velocity given Surface Velocity for Flow over Sphere formula calculates the uniform velocity of the fluid flowing over a sphere called freestream velocity when the velocity over the surface of the sphere is given. Freestream Velocity is denoted by V_∞ symbol.

How to calculate Freestream Velocity given Surface Velocity for Flow over Sphere using this online calculator? To use this online calculator for Freestream Velocity given Surface Velocity for Flow over Sphere, enter Tangential Velocity (V_θ) & Polar Angle (θ) and hit the calculate button. Here is how the Freestream Velocity given Surface Velocity for Flow over Sphere calculation can be explained with given input values -> 60.02112 = 2/3*66/sin(0.7).

FAQ

What is Freestream Velocity given Surface Velocity for Flow over Sphere?

The Freestream Velocity given Surface Velocity for Flow over Sphere formula calculates the uniform velocity of the fluid flowing over a sphere called freestream velocity when the velocity over the surface of the sphere is given and is represented as V_∞ = 2/3*V_θ/sin(θ) or Freestream Velocity = 2/3*Tangential Velocity/sin(Polar Angle). Tangential Velocity is the component of velocity in the tangential direction & Polar Angle is the angular position of a point from a reference direction.

How to calculate Freestream Velocity given Surface Velocity for Flow over Sphere?

The Freestream Velocity given Surface Velocity for Flow over Sphere formula calculates the uniform velocity of the fluid flowing over a sphere called freestream velocity when the velocity over the surface of the sphere is given is calculated using Freestream Velocity = 2/3*Tangential Velocity/sin(Polar Angle). To calculate Freestream Velocity given Surface Velocity for Flow over Sphere, you need Tangential Velocity (V_θ) & Polar Angle (θ). With our tool, you need to enter the respective value for Tangential Velocity & Polar Angle 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 Freestream Velocity?

In this formula, Freestream Velocity uses Tangential Velocity & Polar Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -

Freestream Velocity = 2/3*Maximum Surface Velocity

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