流体力学第三章 (2).ppt

清华大学工程力学系 III. CONTROL VOLUME RELATIONS FOR FLUID ANALYSIS 流体力学控制方程 CONTROL VOLUME RELATIONS FOR FLUID ANALYSIS From consideration of hydrostatics, we now move to problems involving fluid flow with the addition of effects due to fluid motion, e.g. inertia and convective mass, momentum, and energy terms. We will present the analysis based on a control volume (not differential element) formulation, e.g. similar to that used in Thermodynamics for the First Law. Basic Conservation Laws Each of the following basic conservation laws is presented in its most fundamental, fixed mass form. We will subsequently develop an equivalent expression for each law that includes the effects of the flow of mass, momentum, and energy (as appropriate) across a control volume boundary. These transformed equations will be the basis for the control volume analyses developed in this chapter. Basic Conservation Laws Conservation of Mass: Defining m as the mass of a fixed mass system, the mass for a control volume V is given by: The basic equation for conservation of mass is then expressed as: Basic Conservation Laws Linear Momentum: Defining m as the linear momentum of a fixed mass, the linear momentum of a fixed mass control volume is given by: where: is the local fluid velocity and dV is a differential volume element in the control volume. The basic linear momentum equation is then written as: Basic Conservation Laws Moment of Momentum: Defining as the moment of momentum for a fixed mass, the moment of momentum for a fixed mass control volume is given by: where is the moment arm from an inertial coordinate system to the differential control volume of interest. The basic equation is then written as: Basic Conservation Laws Energy: Defining Esys as the total energy of an element of fixed mass, the energy of a fixed mass control volume is given by: where e is the total energy per unit mass ( includes kinetic, potential, and internal energy