Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ
Tải xuống
Heat Transfer Handbook part 4. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | 20 BASIC CONCEPTS _ dV _ d mV dt dt where mV is the momentum. Equation 1.64 is the statement of the conservation of momentum principle. Note that the conservation of momentum principle is stated in terms of the properties of particles and not in terms of the properties of a field. To derive the momentum theorem a region in a fluid confined by the control surface S1 shown in Fig. 1.7 is employed. The surface S1 contains a definite and fixed number of particles at time t1. At time t2 these particles will have moved to a region bounded by the control surface S2 which is shown as a dashed curve to distinguish it from S1. The control surfaces S1 and S2 enclose three separate and distinct regions designated by a b and c. Let the momentum in the three regions be Pa Pb and Pc respectively. At time t1 the particles within surface S1 will possess momentum Pa Pb1. At time t2 these particles will have momentum Pb2 Pc because they have moved into the region enclosed by surface S2. Hence the momentum change during the time interval t2 - t1 may be described by Pb2 Pc - Pb1 Pa _ Pb2 - Pb1 Pc - Pa and the time rate of change of momentum will be lim iPb2 - Pb1 Pc 1.65 iz n t2 - t1 t2 - t1 y As t2 approaches t1 as a limit the control surface S2 will coincide with S1. The first term in eq. 1.65 is therefore the time rate of change of momentum of the fluid contained within region 1 R1 contained within S1. This may be written as the integral over R1. Because the mass of fluid contained in R1 is fff p dR1 R1 the time rate of change of momentum of the fluid contained within region 1 will be III dR1 The second term in eq. 1.65 is the momentum efflux through the control surface S1. If the flux in the outward direction is taken as positive this efflux can be expressed by the integral II pVVn dS1 S1 where Vn is the component of velocity normal to S1. MOMENTUM AND THE MOMENTUM THEOREM 21 Figure 1.7 Regions bounded by control surfaces used for the development of the momentum theorem. The .
