Analytic Determination of the Roller Length of a Hydraulic Jump in an Open Channel Flow Using a Bouncing Ball

Abstract

A hydraulic jump is a natural occurrence that occurs in spillways, rivers, and other open channel flows when water or other liquid flowing with a high velocity discharges into a region of lower velocity with an attendant abrupt rise in the liquid surface. Such a phenomenon, known as hydraulic jump, is normally accompanied by substantial dissipation of energy. Many researchers, in the past, focus attention in the numerical study of the hydraulic jump, under varied working situations. Few attempts are made to study the occurrence analytically. In this paper, the author studied the incident analytically using a bouncing ball to develop a model to examine the lengths of hydraulic jumps in a horizontal open channel flow. The model development is based on the laws of motion, the principles of impulse and momentum, and the classical hydraulic jump formula. The model was later verified with the roller length obtained from the series of experiments conducted in a large-size facility. The roller length that the new model estimated compared well with the experimental results conducted within the Froude number ranges of 2.00 and 16.00. The model is ease to use and its accuracy as determined by the Pearson correlation coefficient is between 0.93 and 1.00.