Velocity Potential for Uniform Incompressible Flow in Polar Coordinates Calculator

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Two-Dimensional Incompressible Flow

Compressible Flow

Fundamentals of Inviscid and Incompressible Flow

Three-Dimensional Incompressible Flow

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Elementary Flows

Flow and Lift Distribution

Flow over Airfoils and Wings

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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%
✖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%

✖Velocity Potential is a scalar function whose gradient gives velocity.ⓘ Velocity Potential for Uniform Incompressible Flow in Polar Coordinates [ϕ]

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Formula

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Velocity Potential for Uniform Incompressible Flow in Polar Coordinates

Formula

`"ϕ" = "V"_{"∞"}*"r"*cos("θ")`

Example

`"44.05491m²/s"="6.4m/s"*"9m"*cos("0.7rad")`

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Velocity Potential for Uniform Incompressible Flow in Polar Coordinates Solution

STEP 0: Pre-Calculation Summary

Formula Used

Velocity Potential = Freestream Velocity*Radial Coordinate*cos(Polar Angle)
ϕ = V_∞*r*cos(θ)
This formula uses 1 Functions, 4 Variables

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

Velocity Potential - (Measured in Square Meter per Second) - Velocity Potential is a scalar function whose gradient gives velocity.
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.
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: 6.4 Meter per Second --> 6.4 Meter per Second No Conversion Required
Radial Coordinate: 9 Meter --> 9 Meter No Conversion Required
Polar Angle: 0.7 Radian --> 0.7 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ϕ = V_∞*r*cos(θ) --> 6.4*9*cos(0.7)

Evaluating ... ...

ϕ = 44.0549099875865

STEP 3: Convert Result to Output's Unit

44.0549099875865 Square Meter per Second --> No Conversion Required

FINAL ANSWER

44.0549099875865 ≈ 44.05491 Square Meter per Second <-- Velocity Potential

(Calculation completed in 00.004 seconds)

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Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

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Amrita School of Engineering (ASE), Vallikavu

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< 4 Uniform Flow Calculators

Velocity Potential for Uniform Incompressible Flow in Polar Coordinates

Go Velocity Potential = Freestream Velocity*Radial Coordinate*cos(Polar Angle)

Stream Function for Uniform Incompressible Flow in Polar Coordinates

Go Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)

Velocity Potential for Uniform Incompressible Flow

Go Velocity Potential = Freestream Velocity*Distance on X-Axis

Stream Function for Uniform Incompressible Flow

Go Stream Function = Freestream Velocity*Distance on Y-Axis

Velocity Potential for Uniform Incompressible Flow in Polar Coordinates Formula

Velocity Potential = Freestream Velocity*Radial Coordinate*cos(Polar Angle)
ϕ = V_∞*r*cos(θ)

What is uniform flow?

Uniform flow is a flow of a fluid in which each particle moves along its line of flow with constant speed and in which the cross-section of each stream tube remains unchanged.

What is velocity potential?

For an irrotational flow, there exists a scalar function, such that the velocity is given by the gradient of velocity potential.

How to Calculate Velocity Potential for Uniform Incompressible Flow in Polar Coordinates?

Velocity Potential for Uniform Incompressible Flow in Polar Coordinates calculator uses Velocity Potential = Freestream Velocity*Radial Coordinate*cos(Polar Angle) to calculate the Velocity Potential, The Velocity Potential for Uniform Incompressible Flow in Polar Coordinates states that the function is directly proportional to the radial distance from the origin (r) and the cosine of the angular coordinate (θ), scaled by the velocity of the flow (U). This implies that the value of the velocity potential function increases linearly with radial distance from the origin and varies with the angle's cosine, reflecting the flow's uniform nature and its dependency on the angular direction. Velocity Potential is denoted by ϕ symbol.

How to calculate Velocity Potential for Uniform Incompressible Flow in Polar Coordinates using this online calculator? To use this online calculator for Velocity Potential for Uniform Incompressible Flow in Polar Coordinates, enter Freestream Velocity (V_∞), Radial Coordinate (r) & Polar Angle (θ) and hit the calculate button. Here is how the Velocity Potential for Uniform Incompressible Flow in Polar Coordinates calculation can be explained with given input values -> 468.0834 = 6.4*9*cos(0.7).

FAQ

What is Velocity Potential for Uniform Incompressible Flow in Polar Coordinates?

The Velocity Potential for Uniform Incompressible Flow in Polar Coordinates states that the function is directly proportional to the radial distance from the origin (r) and the cosine of the angular coordinate (θ), scaled by the velocity of the flow (U). This implies that the value of the velocity potential function increases linearly with radial distance from the origin and varies with the angle's cosine, reflecting the flow's uniform nature and its dependency on the angular direction and is represented as ϕ = V_∞*r*cos(θ) or Velocity Potential = Freestream Velocity*Radial Coordinate*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, 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 Velocity Potential for Uniform Incompressible Flow in Polar Coordinates?

The Velocity Potential for Uniform Incompressible Flow in Polar Coordinates states that the function is directly proportional to the radial distance from the origin (r) and the cosine of the angular coordinate (θ), scaled by the velocity of the flow (U). This implies that the value of the velocity potential function increases linearly with radial distance from the origin and varies with the angle's cosine, reflecting the flow's uniform nature and its dependency on the angular direction is calculated using Velocity Potential = Freestream Velocity*Radial Coordinate*cos(Polar Angle). To calculate Velocity Potential for Uniform Incompressible Flow in Polar Coordinates, you need Freestream Velocity (V_∞), Radial Coordinate (r) & Polar Angle (θ). With our tool, you need to enter the respective value for Freestream Velocity, 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.

How many ways are there to calculate Velocity Potential?

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

Velocity Potential = Freestream Velocity*Distance on X-Axis

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