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.

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.

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.

This function ϕ is called velocity potential, and such a flow is called potential or irrotational flow. In other words, the velocity potential is a function whose gradient is equal to the velocity vector.

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.

for computing the mass flow across a surface, we only require the normal velocity component. This is typically computed via the dot product V~·nˆ. In terms of the velocity potential, we have V~·nˆ = ∇φ·nˆ = ∂φ ∂n where the final partial derivative ∂φ/∂nis called the directional derivative of the potential along the normal ...

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.

When the LB films are prepared employing more than one substrate, the velocity potential governing the flow orientation effect is obtainable as the superposition of the potential functions, each analogous to Eq.

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.

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...