武科大流力学Chapter31111.ppt

* * In fluid mechanics, a system is a set of definite fluid particles selected in the interest of researcher. System boundary is the surroundings that distinguish the set from the other material and named it the surface of system. The surface moves with the fluid and changes with time. There is no exchange of the mass but the energy on boundary. The boundary suffers surface forces from surroundings. The dynamics of a system can be expressed by Newton’s second law of motion as (3.3.1) in which ?F is the resultant of all external forces acting on the system; m is the mass of the definite particles, a fixed value; and u is the velocity at the center of mass of the system. * * * * * When (t1?t) comes near zero, volume τ1 approaches to volume τ. Volume τ is a constant volume as it can learn from the definition of CV. So in which dAo is the product of the outflow area element dAo and the outer normal unit vector n * Let the general property N be the mass of system m. Then the general property per unit mass ? is 1 * In other words, the resultant external force acting on a control volume is equal to the sum of variation of the momentum within the control volume plus the net outflow of momentum from the control volume in unit time. * Taking the general property N of as the total energy of system which contains internal energy Ei and kinetic energy mv2/2, and then general property per unit mass is ?=ei+v2/2, from Eq. (3.3.5), the energy conservation equation can be expressed as * * * A stream tube is shown in a flow field of Fig.3.8, the flow sections are A1 and A2, and the other section is no flow section. In the stream tube, a mini-stream tube, with flow sections dA1, dA2; velocities u1, u2; and densities ?l, ?2, are selected. There are inflow and outflow of the fluid on the surface dA1 and dA2 in the mini-stream tube. The other surface is surrounded by stream lines and no fluid can get across it. * * * ??/?t＝0:compressible fluid and steady flow * * p/?___