Question

An ideal flow can be described by a velocity potential . What does express? Illustrate (choose your own flow example) how you with help of the velocity potential and equipotential lines can find the flow direction and if the flow velocity increase, is constant or decrease

Answer 1

velocity potential is a scalar field function represented as used to define velocity components in irrotational flow. The definition of velocity potential is applicable to ideal fluid flow only. The gradient of velocity potential gives the velocity of flow.

(1) If velocity potential exists, the flow should be irrotational. This means the velocity potential is applicable only for ideal fluid flow. It exists for 2D or 3D flows.

(2) If velocity potential satisfies the Laplace equation, it is a case of possible steady incompressible irrotational flow.

(3) If the Laplace equation is not satisfied by, velocity potential, the flow is either rotational or non-existing. All real fluid flows are rotational while ideal fluid flows are irrotational.

Lines of constant potential are called potential lines of the flow. Potential lines are perpendicular to the streamlines.

On equipotential lines velocity is constant.

When the flow is outward direction from a point its potential goes on decreasing, for that case velocity goes on increasing.

IN opposite to that direction velocity will decreases.

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