Examples of Laminar Flows Site Disabled（层流流动的例子网站禁用）.pdfVIP

CBE 6333, R. Levicky 1 Examples of Laminar Flows In laminar flows the fluid moves in layers or laminae, in contrast to the apparently chaotic motion of turbulent flow. Laminar flows in many different geometries have been investigated with the help of transport models; here we consider just a few well known examples. We also take this opportunity to introduce the use of integral equation models and of the method of combination of variables to solve transport problems. In general, when setting up a problem you will need to address several questions: The 1st question to ask is: What are we trying to find out about the flow (i.e. velocities, pressure, etc)? In other words, what are the unknowns that we are after? The 2nd question to ask is: What equations do we use? Recall that we need as many equations as we have unknowns, together with any boundary conditions and possibly also relations between intensive thermodynamic variables (such as equations of state). The 3rd step is to solve the equations for the unknowns (i.e. velocities, pressure) of interest. This can be a long process, and often requires that we make certain approximations along the way, in addition to a fair amount of mathematical manipulations. Internal Flows Internal flows are those that occur within a channel or pipe. The fluid body is of finite dimensions and is confined by the channel or pipe walls. At the entry region to a channel, the fluid develops a boundary layer next to the channel walls, while the central core of the fluid may remain as a uniform flow (Figure 1). Within the boundary layer, viscous stresses are very prominent, slowing down the fluid due to its friction with the channel walls. This slowdown propagates away from the walls: as the fluid enters the channel the fluid particles immediately next to the walls