Freestream Velocity given Radial 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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✖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 Radial Velocity of an object with respect to a given point is the rate of change of the distance between the object and the point.ⓘ Radial Velocity [V_r]			+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 Radial Velocity [V_∞]

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Formula

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Freestream Velocity given Radial Velocity

Formula

`"V"_{"∞"} = "μ"/(2*pi*"r"^3)-"V"_{"r"}/cos("θ")`

Example

`"67.99874m/s"="9463m³/s"/(2*pi*("2.758m")^3)-"2.9m/s"/cos("0.7rad")`

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Download Three-Dimensional Incompressible Flow Formulas PDF

Freestream Velocity given Radial Velocity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Freestream Velocity = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle)
V_∞ = μ/(2*pi*r^3)-V_r/cos(θ)
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(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.
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.
Radial Velocity - (Measured in Meter per Second) - The Radial Velocity of an object with respect to a given point is the rate of change of the distance between the object and the point.
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

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
Radial Velocity: 2.9 Meter per Second --> 2.9 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_∞ = μ/(2*pi*r^3)-V_r/cos(θ) --> 9463/(2*pi*2.758^3)-2.9/cos(0.7)

Evaluating ... ...

V_∞ = 67.9987372486239

STEP 3: Convert Result to Output's Unit

67.9987372486239 Meter per Second --> No Conversion Required

FINAL ANSWER

67.9987372486239 ≈ 67.99874 Meter per Second <-- Freestream Velocity

(Calculation completed in 00.004 seconds)

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< 5 Radial Velocity Calculators

Radial Coordinate given Radial Velocity

Go Radial Coordinate = (Doublet Strength/(2*pi*(Freestream Velocity+Radial Velocity/cos(Polar Angle))))^(1/3)

Polar Coordinate given Radial Velocity

Go Polar Angle = acos(Radial Velocity/(Doublet Strength/(2*pi*Radial Coordinate^3)-Freestream Velocity))

Radial Velocity for Flow over Sphere

Go Radial Velocity = -(Freestream Velocity-Doublet Strength/(2*pi*Radial Coordinate^3))*cos(Polar Angle)

Freestream Velocity given Radial Velocity

Go Freestream Velocity = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle)

Doublet Strength given Radial Velocity

Go Doublet Strength = 2*pi*Radial Coordinate^3*(Freestream Velocity+Radial Velocity/cos(Polar Angle))

Freestream Velocity given Radial Velocity Formula

Freestream Velocity = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle)
V_∞ = μ/(2*pi*r^3)-V_r/cos(θ)

What is doublet flow?

Doublet flow is a special, degenerate case of a source-sink pair that leads to a singularity. It is frequently used in incompressible flow. When the distance between source-sink pair tends to zero that is when the source-sink falls on top of each other, they do not extinguish each other because the absolute magnitude of their strength becomes infinitely large in the limit.

How to Calculate Freestream Velocity given Radial Velocity?

Freestream Velocity given Radial Velocity calculator uses Freestream Velocity = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle) to calculate the Freestream Velocity, The Freestream Velocity given Radial 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 Radial Velocity using this online calculator? To use this online calculator for Freestream Velocity given Radial Velocity, enter Doublet Strength (μ), Radial Coordinate (r), Radial Velocity (V_r) & Polar Angle (θ) and hit the calculate button. Here is how the Freestream Velocity given Radial Velocity calculation can be explained with given input values -> 67.99874 = 9463/(2*pi*2.758^3)-2.9/cos(0.7).

FAQ

What is Freestream Velocity given Radial Velocity?

The Freestream Velocity given Radial 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_∞ = μ/(2*pi*r^3)-V_r/cos(θ) or Freestream Velocity = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle). 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, The Radial Velocity of an object with respect to a given point is the rate of change of the distance between the object and the point & Polar Angle is the angular position of a point from a reference direction.

How to calculate Freestream Velocity given Radial Velocity?

The Freestream Velocity given Radial 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 = Doublet Strength/(2*pi*Radial Coordinate^3)-Radial Velocity/cos(Polar Angle). To calculate Freestream Velocity given Radial Velocity, you need Doublet Strength (μ), Radial Coordinate (r), Radial Velocity (V_r) & Polar Angle (θ). With our tool, you need to enter the respective value for Doublet Strength, Radial Coordinate, Radial 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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