A velocity potential is a scalar potential used in potential flow theory. It was introduced by Joseph-Louis Lagrange in 1788. [1] It is used in continuum mechanics, when a continuum occupies a simply-connected region and is irrotational. In such a case, =, where u denotes the flow velocity.

2023年7月26日 · In fluid mechanics, the velocity potential function is a mathematical concept used to describe the flow field of an incompressible fluid. It is a scalar field that represents the velocity of the fluid as a function of position. The velocity potential function is defined such that its gradient gives the velocity vector of the fluid.

Velocity potential function and stream function are two scalar functions that help study whether the given fluid flow is rotational or irrotational. Both the functions provide a specific Laplace equation.

Velocity potential is a powerful tool in analysing irrotational flows. First of all it meets with the irrotationality condition readily. In fact, it follows from that condition.

Definition 13.1 The velocity potential of an irrotational flow is a function ϕ such that (13.1) u ― = ∇ ― ϕ. As you know from Vector Calculus, the velocity potential can be obtained from a line integral: (13.2) ϕ (x ―) = ∫ 0 ― x ― u ― (x ― ~) ⋅ d x ― ~.

In potential flow, the fluid moves in streamlines, which are lines that are tangent to the velocity vector at any given point. The fluid’s velocity is determined by the gradient of the flow’s scalar potential, the flow is irrotational, and the fluid’s pressure is yielded from the Bernoulli equation.

2022年5月2日 · For ideal flows we focus on the use of the velocity potential and streamfunction, both of which adhere to the Laplace equation, the former representing the conservation of mass, and the latter indicating irrotational flow.

We can define a potential function, ! ( x , z , t ) , as a continuous function that satisfies the basic laws of fluid mechanics: conservation of mass and momentum, assuming incompressible, inviscid and irrotational flow. Therefore ! where ! =! ( x , y , z , t ) is the velocity potential function.

Consider defining the components of the velocity vector V as the gradient of a scalar velocity potential function, denoted by φ(x, y, z). y ! which has a corkscrew shape as shown in the figure. The implied velocity components are then. which corresponds to a vortex flow around the origin.

The velocity potential is a scalar potential that is used to represent the potential flow. In order to find the velocity potential you will need to use...