Discussion of “Preliminary Study of Surface Hydraulic Jumps” by S. Ahmed, Y. Ye, H. Liu, and N. Rajaratnam

Abstract

The authors carried out three series of flume experiments to investigate surface jump characteristics. Different hydraulic features of the surface jump like the depth variation of the plane jet upstream of the surface jump [Eq. (2) of the original paper], the relative energy loss [Eq. (4) of the original paper], the height of surface jump [Eq. (5) of the original paper], and the length of the roller [Eq. (6) of the original paper] were investigated. The aims of this discussion are to (1) comment on the derivation of the supercritical jet depth, y 1 , (2) determine the submergence zone for which the surface jump is expected, and (3) verify Eq. (4) of the original paper by the measurements carried out in this discussion to determine the head loss through surface jumps. For discussing the objectives, a specific experimental program (Fig. 1) was carried out at the Hydraulic Laboratory of the Imam Khomeini International University (IKIU), Iran. A recirculating experimental flume 12 m long, 0.5 m wide, and 0.6 m high was used. The discharge was measured using a magnetic flowmeter with an accuracy of AE0.5% of the full scale, i.e., Q ¼ 45 L=s, and the water depths were measured by point gauges with a precision of AE0.1 mm. An inclined adjustable weir was installed at the downstream end of the flume to set a desire tailwater depth. Two sharp-crested rectangular weirs with weir heights of p ¼ 309 and p ¼ 391.5 mm were located 2 m downstream of the flume entrance. In each experimental run for a steady-state flow condition, the tailwater depth was increased to create different submergence ratios. Then, the associated discharge, upstream depth, and tail-water depth were recorded. The first part of this discussion deals with the derivation of the depth of the jet, y 1 and the associated velocity, V 1. The authors stated that "the depth of this jet, y 1 , was obtained as q=V 1 , where q is the discharge per unit width." The ratio q=V 1 , shown in Fig. 2, is equal to d, which is different from y 1. Furthermore, the difference between y 1 and d depends on the jet angle and this angle is related to the discharge (Bautista-Capetillo et al. 2013). This choice affects the derivation of the velocity V 1 and the reliability of Eqs. (1)-(3) of the original paper. Developing a criterion to distinguish the surface jump condition is the second step of this discussion. The flow through a weir can be either free or submerged depending on the tailwater level. The submerged flow condition reveals when the tailwater depth y t affects the upstream flow depth. In this discussion, the submergence threshold depth value, y td , is defined as the depth for which the upstream flow head, h, increases less than or equal to 0.5% of the associated free flow depth, h 0 (Bos 1989; Lin et al. 2002). Any downstream water depth, y t , that is greater than the threshold value, y td , determines a weir working under submerged flow conditions. The pairs of ðy t =p; h=pÞ measured in this experimental investigation are plotted in Fig. 3. This figure demonstrates that the sub-mergence threshold corresponds to the ratio y t =p ¼ 1, i.e., all tailwater depths y t being greater than the weir height p make the weir work under submerged flow conditions. The experimental observations of our investigation also showed that when the tailwater depth increases slightly above the weir crest level (y t > p), a surface hydraulic jump occurred. For a specific downstream water depth, named y w , standing waves appeared at the downstream pool (Fig. 1). The experimental observations also demonstrated that the standing waves vanish when the tailwater depth y t is slightly greater than y w. When y t > y w , the flow condition is called the fully submerged flow condition for which no surface jump is observed. The standing wave flow condition is defined by the following functional relationship: Fðy w ; Q; B; p; ρ; g; μÞ ¼ 0 ð1Þ Fig. 1. Standing wave flow formed downstream of a submerged sharp-crested rectangular weir. Fig. 2. Flow over submerged sharp-crested weir. © ASCE 07020001-1 J. Irrig. Drain. Eng.