# Potential Flow

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## Potential flow

A fluid flow that is isentropic and that, if incompressible, can be mathematically described by Laplace's equation. For an ideal fluid, or a flow in which viscous effects are ignored, vorticity (defined as the curl of the velocity) cannot be produced, and any initial vorticity existing in the flow simply moves unchanged with the fluid. Ideal fluids, of course, do not exist since any actual fluid has some viscosity, and the effects of this viscosity will be important near a solid wall, in the region known as the boundary layer. Nevertheless, the study of potential flow is important in hydrodynamics, where the fluid is considered incompressible, and even in aerodynamics, where the fluid is considered compressible, as long as shock waves are not present. *See* Boundary-layer flow, Compressible flow, Isentropic flow

In the absence of viscous effects, a flow starting from rest will be irrotational for all subsequent time. For an irrotational flow, the curl of the velocity is zero (∇ × *V* = 0). The curl of the gradient of any scalar function is zero (∇ × ∇&phgr; = 0). It then follows mathematically that the condition of irrotationality can be satisfied identically by choosing the scalar function, &phgr;, such that the velocity is the gradient of &phgr; (*V* = ∇&phgr;). For this reason, this scalar function &phgr; has been traditionally referred to as the velocity potential, and the flow as a potential flow. *See* Potentials

By applying the continuity equation to the definition of the potential function, it becomes possible to represent the flow by the well-known Laplace equation (∇^{2}&phgr; = 0), instead of the coupled system of the continuity and nonlinear Euler equations. The linearity of the Laplace equation, which also governs other important physical phenomena such as electricity and magnetism, makes it possible to use the principle of superposition to combine elementary solutions in solving more complex problems. *See* Fluid flow

## Potential Flow

the irrotational flow of a fluid in which each small volume is deformed and displaced progressively without any rotation being present (or vortices developing). A potential flow occurs under certain conditions only for an ideal, frictionless fluid. These conditions occur, for example, when the motion begins from a state of rest and a body immersed in an incompressible fluid begins to move, or when a body strikes the surface of the fluid. In nonideal liquids and gases, a potential flow occurs in those regions where the forces of viscosity are negligible in comparison with those of pressure and no vortices are present. The study of potential flow is greatly simplified in that it involves the determination of only one function of the coordinates and time, called the potential function.