Freestream Velocity given Tangential Velocity 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%
✖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%

✖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 Tangential Velocity [V_∞]

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Formula

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Freestream Velocity given Tangential Velocity

Formula

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

Example

`"66.55466m/s"="66m/s"/sin("0.7rad")-"9463m³/s"/(4*pi*("2.758m")^3)`

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Download Three-Dimensional Incompressible Flow Formulas PDF

Freestream Velocity given Tangential Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3)
V_∞ = V_θ/sin(θ)-μ/(4*pi*r^3)
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

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.
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.

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
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_∞ = V_θ/sin(θ)-μ/(4*pi*r^3) --> 66/sin(0.7)-9463/(4*pi*2.758^3)

Evaluating ... ...

V_∞ = 66.5546570282432

STEP 3: Convert Result to Output's Unit

66.5546570282432 Meter per Second --> No Conversion Required

FINAL ANSWER

66.5546570282432 ≈ 66.55466 Meter per Second <-- Freestream Velocity

(Calculation completed in 00.004 seconds)

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Created by Ravi Khiyani

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)

Freestream Velocity given Tangential Velocity Formula

Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3)
V_∞ = V_θ/sin(θ)-μ/(4*pi*r^3)

What is doublet flow?

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 Tangential Velocity?

Freestream Velocity given Tangential Velocity calculator uses Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3) to calculate the Freestream Velocity, The Freestream Velocity given Tangential Velocity formula calculates the freestream velocity of the uniform velocity field around the flow that has been induced by the three-dimensional doublet. Freestream Velocity is denoted by V_∞ symbol.

How to calculate Freestream Velocity given Tangential Velocity using this online calculator? To use this online calculator for Freestream Velocity given Tangential Velocity, enter Tangential Velocity (V_θ), Polar Angle (θ), Doublet Strength (μ) & Radial Coordinate (r) and hit the calculate button. Here is how the Freestream Velocity given Tangential Velocity calculation can be explained with given input values -> 54.13649 = 66/sin(0.7)-9463/(4*pi*2.758^3).

FAQ

What is Freestream Velocity given Tangential Velocity?

The Freestream Velocity given Tangential Velocity formula calculates the freestream velocity of the uniform velocity field around the flow that has been induced by the three-dimensional doublet and is represented as V_∞ = V_θ/sin(θ)-μ/(4*pi*r^3) or Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3). Tangential Velocity is the component of velocity in the tangential direction, Polar Angle is the angular position of a point from a reference direction, 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.

How to calculate Freestream Velocity given Tangential Velocity?

The Freestream Velocity given Tangential Velocity formula calculates the freestream velocity of the uniform velocity field around the flow that has been induced by the three-dimensional doublet is calculated using Freestream Velocity = Tangential Velocity/sin(Polar Angle)-Doublet Strength/(4*pi*Radial Coordinate^3). To calculate Freestream Velocity given Tangential Velocity, you need Tangential Velocity (V_θ), Polar Angle (θ), Doublet Strength (μ) & Radial Coordinate (r). With our tool, you need to enter the respective value for Tangential Velocity, Polar Angle, Doublet Strength & Radial Coordinate 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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