流体力学与传热（伍钦）08-9chapter1-6.pptVIP

Solution For parallel pipes, the continuity equation can be written as And the governing equation of parallel pipes is 1 2 Based on known parameters, Eqs. 2 can be expressed as 3 Combining Eqs.1 and 3 gives Branching system The flow in a relatively simple looking multiple pipe system may be more complex than it appears initially. The branching system termed the three-reservoir problem shown in figure is such a system. Three reservoir at known elevations are connected together with three pipes of known properties (lengths, diameters, and roughnesses). The problem is to determine the flowrates into or out of the reservoirs. If valve(1) were closed, the fluid would flow from reservoir B to C, and flowrate could be easily calculated. Similar calculations could be carried out if valve (2) or (3) were closed with the other open With all valves open, however, it is not necessarily obvious which direction the fluid flows For the conditions indicated in figure, it is clear that fluid flows from reservoirs A because the other two reservoirs are lower. Whether the fluid flows into or out of the reservoirs B depend on the elevation of reservoirs B and C and properties (length, diameter, roughness) of the three pipes. In general, the flow direction is not obvious, and solution process must include the determination of this direction. example Three reservoirs are connected by three pipes as are shown in figure. For simplicity we assume that the diameter of each pipe is 0.305m, the friction coefficient for each is 0.02, and because of the length-to-diameter ratio, form losses are negligible. Determine the flowrate into or out of each reservoir. Solution It is not obvious which direction the fluid flows in pipe(2). However, we assume that it flows out of the reservoir B, write the governing equations for this case, and check the assumption. The continuity equation requires that Q1+Q2=Q3, which, since the diameters are the same for each pipe, becomes simply