Modeling laminar sheet flow over rough surfaces

Abstract

A mathematical model for two‐dimensional laminar flow over a rough surface is developed. Explicit formulae are presented for the height and average and maximum velocities in terms of measurable quantities and a friction factor. The correction factor α, the ratio of the average to maximum velocity, is also discussed and shown to vary significantly from the value on a smooth surface. Predictions for the film height and velocities are presented and compared with previous experiments. Good agreement is obtained between the theory and experiments. The saline technique for measuring velocities is shown to significantly underpredict the fluid velocity. The Manning, Chezy, and Darcy‐Weisbach formulae all overpredict the velocity in the laminar flow regime. It is also shown that there is a relation between the correction factor and the height or inundation ratio, but there is no relation to the Reynolds number in laminar flow.