An analytical series solution to the steady laminar flow of a Newtonian fluid in a partially filled pipe, including the velocity distribution and the dip phenomenon

摘要

In the current work, we advance the integral equation solution of Guo & Meroney (2013, Theoretical solution for laminar flow in partially-filled pipes. J. Hydraul. Res., 51, 408-416) for the velocity distribution of a Newtonian fluid flowing under the effect of gravity in a partially filled pipe. Unlike in previous work, our new solution is analytical and is in series form. The solution is able to evaluate the velocity profile in a partially filled pipe for any fill depth. Additionally, the well-known velocity dip phenomenon is observed, and, using our new solution, it is predicted that the dip will begin once the pipe is filled above 86% of the channel depth. Excellent agreement is found between the analytical and a computed numerical solution to the flow problem.