Radial Velocity for Flow over Sphere Calculator

✖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%

✖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 for Flow over Sphere [V_r]

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Radial Velocity for Flow over Sphere Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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_r = -(V_∞-μ/(2*pi*r^3))*cos(θ) --> -(68-9463/(2*pi*2.758^3))*cos(0.7)

Evaluating ... ...

V_r = 2.89903419447553

STEP 3: Convert Result to Output's Unit

2.89903419447553 Meter per Second --> No Conversion Required

FINAL ANSWER

2.89903419447553 ≈ 2.899034 Meter per Second <-- Radial 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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< Radial Velocity Calculators

Radial Coordinate given Radial Velocity

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

Polar Coordinate given Radial Velocity

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

Radial Velocity for Flow over Sphere

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

Freestream Velocity given Radial Velocity

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

Radial Velocity for Flow over Sphere Formula

LaTeX Go

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

What is the effect of fluid flow over 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 Radial Velocity for Flow over Sphere?

Radial Velocity for Flow over Sphere calculator uses Radial Velocity = -(Freestream Velocity-Doublet Strength/(2*pi*Radial Coordinate^3))*cos(Polar Angle) to calculate the Radial Velocity, The Radial Velocity for Flow over Sphere formula calculates the radial velocity at the desired location when the three-dimensional doublet flow with a uniform velocity field takes over a sphere. Radial Velocity is denoted by V_r symbol.

How to calculate Radial Velocity for Flow over Sphere using this online calculator? To use this online calculator for Radial 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 Radial Velocity for Flow over Sphere calculation can be explained with given input values -> 2.899034 = -(68-9463/(2*pi*2.758^3))*cos(0.7).

FAQ

What is Radial Velocity for Flow over Sphere?

The Radial Velocity for Flow over Sphere formula calculates the radial 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_r = -(V_∞-μ/(2*pi*r^3))*cos(θ) or Radial Velocity = -(Freestream Velocity-Doublet Strength/(2*pi*Radial Coordinate^3))*cos(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 Radial Velocity for Flow over Sphere?

The Radial Velocity for Flow over Sphere formula calculates the radial velocity at the desired location when the three-dimensional doublet flow with a uniform velocity field takes over a sphere is calculated using Radial Velocity = -(Freestream Velocity-Doublet Strength/(2*pi*Radial Coordinate^3))*cos(Polar Angle). To calculate Radial 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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