Copyright by Dr.Zheyan Jin Chapter 3 Fundamentals of Inviscid,Incompressible Flow 3.3 Laplace's Equation 1.Any irrotational,incompressible flow has a velocity potential and stream function that both satisfy Laplace's equation. 2.Conversely,any solution of Laplace's equation represents the velocity potential or stream function(two-dimensional)for an irrotational,incompressible flow. Note that Laplace's equation is a second-order linear partial differential equation.The fact that it is linear is particularly important,because the sum of any particular solutions of a linear differential equation is also a solution of the equation: 0=4+42+…+9。Copyright by Dr. Zheyan Jin Chapter 3 Fundamentals of Chapter 3 Fundamentals of Inviscid Inviscid, Incompressible Flow , Incompressible Flow 3.3 Laplace’s Equation   1  2    n 1. Any irrotational, incompressible flow has a velocity potential and stream function that both satisfy Laplace’s equation. Note that Laplace’s equation is a second-order linear partial differential equation. The fact that it is linear is particularly important, because the sum of any particular solutions of a linear differential equation is also a solution of the equation: 2. Conversely, any solution of Laplace’s equation represents the velocity potential or stream function ( two-dimensional) for an irrotational, incompressible flow