# 19fa-1910-workshop02-pipeflow-sol.pdf - MATH 1910 Workshop...

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MATH 1910 Workshop Solution Pipeflow Introduction: When fluid flows down a pipe not all parts travel at the same velocity. In laminar flow, fluid particles move along straight parallel paths in layers, called laminae. The velocities in adjacent layers are not the same. Those in the center of the pipe are faster than those that are closer to the interior surface of the pipe. We consider the case of stationary, fully developed flow in a circular tube. “Stationary” means that the flow is independent of time, while “fully developed” means that the flow velocity is independent of distance in the direction of the flow (i.e., that entrance effects can be neglected). Practically speaking, that means we’re considering regions of pipe far from bends, junctions, pumps, holes, etc. The pressure in the pipe is taken to be a function of distance in the direction of the flow, only. For the flow to be stationary, the forces on a cylindrical tube of fluid of length L and radius r must balance (see figure).