Tangential 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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✖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%
✖Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength.ⓘ Doublet Strength [μ]			+10% -10%
✖Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.ⓘ Radial Coordinate [r]			+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.ⓘ Tangential Velocity for Flow over Sphere [V_θ]

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Formula

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Tangential Velocity for Flow over Sphere

Formula

`"V"_{"θ"} = ("V"_{"∞"}+"μ"/(4*pi*"r"^3))*sin("θ")`

Example

`"66.93112m/s"=("68m/s"+"9463m³/s"/(4*pi*("2.758m")^3))*sin("0.7rad")`

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Download Three-Dimensional Incompressible Flow Formulas PDF

Tangential Velocity for Flow over Sphere Solution

STEP 0: Pre-Calculation Summary

Formula Used

Tangential Velocity = (Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))*sin(Polar Angle)
V_θ = (V_∞+μ/(4*pi*r^3))*sin(θ)
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Doublet Strength - (Measured in Cubic Meter per Second) - Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength.
Radial Coordinate - (Measured in Meter) - Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.
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
Doublet Strength: 9463 Cubic Meter per Second --> 9463 Cubic Meter per Second No Conversion Required
Radial Coordinate: 2.758 Meter --> 2.758 Meter 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 = (V_∞+μ/(4*pi*r^3))*sin(θ) --> (68+9463/(4*pi*2.758^3))*sin(0.7)

Evaluating ... ...

V_θ = 66.9311155065304

STEP 3: Convert Result to Output's Unit

66.9311155065304 Meter per Second --> No Conversion Required

FINAL ANSWER

66.9311155065304 ≈ 66.93112 Meter per Second <-- Tangential Velocity

(Calculation completed in 00.004 seconds)

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

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< 5 Tangential Velocity Calculators

Radial Coordinate given Tangential Velocity

Go Radial Coordinate = (Doublet Strength/(4*pi*(Tangential Velocity/sin(Polar Angle)-Freestream Velocity)))^(1/3)

Polar Coordinate given Tangential Velocity

Go Polar Angle = asin(Tangential Velocity/(Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3)))

Tangential Velocity for Flow over Sphere

Go Tangential Velocity = (Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))*sin(Polar Angle)

Freestream Velocity given Tangential Velocity

Go Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3)

Doublet Strength given Tangential Velocity

Go Doublet Strength = 4*pi*Radial Coordinate^3*(Tangential Velocity/sin(Polar Angle)-Freestream Velocity)

Tangential Velocity for Flow over Sphere Formula

Tangential Velocity = (Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))*sin(Polar Angle)
V_θ = (V_∞+μ/(4*pi*r^3))*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 Tangential Velocity for Flow over Sphere?

Tangential Velocity for Flow over Sphere calculator uses Tangential Velocity = (Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))*sin(Polar Angle) to calculate the Tangential Velocity, The Tangential Velocity for Flow over Sphere formula calculates the tangential velocity at the desired location when the three-dimensional doublet flow with a uniform velocity field takes over a sphere. Tangential Velocity is denoted by V_θ symbol.

How to calculate Tangential Velocity for Flow over Sphere using this online calculator? To use this online calculator for Tangential Velocity for Flow over Sphere, enter Freestream Velocity (V_∞), Doublet Strength (μ), Radial Coordinate (r) & Polar Angle (θ) and hit the calculate button. Here is how the Tangential Velocity for Flow over Sphere calculation can be explained with given input values -> 66.93112 = (68+9463/(4*pi*2.758^3))*sin(0.7).

FAQ

What is Tangential Velocity for Flow over Sphere?

The Tangential Velocity for Flow over Sphere formula calculates the tangential velocity at the desired location when the three-dimensional doublet flow with a uniform velocity field takes over a sphere and is represented as V_θ = (V_∞+μ/(4*pi*r^3))*sin(θ) or Tangential Velocity = (Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))*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, Doublet Strength is defined as the product of the distance between a source-sink pair and source or sink strength, Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin & Polar Angle is the angular position of a point from a reference direction.

How to calculate Tangential Velocity for Flow over Sphere?

The Tangential Velocity for Flow over Sphere formula calculates the tangential velocity at the desired location when the three-dimensional doublet flow with a uniform velocity field takes over a sphere is calculated using Tangential Velocity = (Freestream Velocity+Doublet Strength/(4*pi*Radial Coordinate^3))*sin(Polar Angle). To calculate Tangential Velocity for Flow over Sphere, you need Freestream Velocity (V_∞), Doublet Strength (μ), Radial Coordinate (r) & Polar Angle (θ). With our tool, you need to enter the respective value for Freestream Velocity, Doublet Strength, Radial Coordinate & 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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