流体力学 陈海霞-6.pptVIP

阿尔茨海默症防治相关知识埃及的金字塔有建造方法动画艾司洛尔在神经外科重症中的应用二级二班防溺水等安全教育 CHAPTER 6 Planar Irrotational Flow of Ideal Incompressible Fluid The velocity potential function ? , defined as : is used to transform the differential form of continuity equation into a differential equation, a Laplace equation, which can easily be solved. Another complex variable function W(z) is more valuable in ideal fluid flow, which combing both of velocity potential ? and stream function ?. § 6.1 Basic Equations and Characters of Irrotational Flow of Ideal Incompressible Fluid 1) basic equation For ideal fluid, ; incompressible fluid, ; Irrotation means the vorticity , defined as , is zero. Meanwhile if a flow is irrotational that this flow must have an nonzero velocity potential function . The velocity potential for every possible irrotational motion of incompressible fluid flow must satisfy the Laplace equation. So, simply the continuity equation and the linear momentum equations like these: with the initial condition: , and boundary condition: on the wall surface, , at the infinite distance, . § 6.1 Basic Equations and Characters of Irrotational Flow of Ideal Incompressible Fluid In scalar form: Consider and , result in This is called Laplace’s equation,and its Cartesian form is in cylindrical coordinates: § 6.1 Basic Equations and Characters of Irrotational Flow of Ideal Incompressible Fluid Example 6.1 Given the velocity field, show that the flow is irrotational ; find the potential function. Solution: the flow is 3-D ,steady and incompressible, calculate the vorticity : Since the vorticity is equal to zero , the flow is irrotational . § 6.1 Basic Equations and Characters of Irrotational Flow of Ideal Incompressible Fluid Because so compari