Fluid mechanics potential flow question Thank you for your h

Fluid mechanics.

potential flow question.

Thank you for your help.

How is potential flow useful for studying flow over immersed bodies, even though it ignores viscous effects?

A fluid flow that is isentropic and that, if incompressible, can be mathematically described by Laplace\'s equation.

For anideal 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 sinceany actual fluid has some viscosity, and the effects of this viscosity will be important

near a solid wall, in the region knownas the boundary layer. Nevertheless, the study of potential flow is important in

hydrodynamics, where the fluid is consideredincompressible, and even in aerodynamics, where the fluid is

considered compressible, as long as shock waves are notpresent. 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 thenfollows 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 beentraditionally referred to as the velocity potential, and the flow as a potential

flow.