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Next: Elements of Potential Flow

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Elements of Potential Flow

General
Conservation of Mass

Continuity Equation in Cylindrical Polar Coordinates
Continuity Equation for steady flow
Continuity Equation for an Incompressible flow

Stream function

Properties of Stream Function

(a) Line $\psi = constant$ is a streamline
(b) $d\psi$ between two streamlines is proportional to the Volumetric Flow

Stream Function in Polar Coordinates

Kinematics of Fluid Motion

Translation
Linear Deformation
Rotation

Meaning of Irrotationality

Angular Deformation

Circulation
Velocity Potential

Relationship between $\phi$ and $\psi$
Occurrence of Irrotational Flows

Simple Examples of Plane Potential Flows

Equations in Cartesian Coordinates
Equations in Polar Coordinates
Uniform Flow
Source and Sink
Vortex

Circulation around a Vortex

A Source-Sink Pair
Doublet

Superposition of Elementary Flows

Uniform Flow and a Source
Rankine Oval
Flow Around a Circular Cylinder
Flow about a Lifting Cylinder
Stagnation Points for a lifting circular cylinder
Surface Pressure Distribution and Lift
Kutta-Joukowsky Theorem
Magnus Effect

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(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney