Civil Engineering nOVEMBER 2021

Civil Engineering November 2021 15 5. A tail water channel where the water level is a function of the flow rate and the hydraulic properties of the downstream channel and structures. DESIGN OF THE LONG-THROATED FLUME In producing these flumes, designers are often discouraged by the complex mathematics of hydraulics. The flow conditions considered are uniquely dependent on the upstream head, i.e. subcritical flow must exist upstream of the flume, after which the flow accelerates through the contraction and passes through its critical depth. The water level downstream of the struc- ture should be low enough to have no influence upon its performance. The calculations needed to compute head-discharge relationships and evaluate design alternatives are iterative, and computer programs greatly facilitate analysis of these structures. Early programs written in FORTRAN used a batch mode of operation to analyse the per- formance of single designs. In the 1990s the International Institute for Land Reclamation and Improvement in The Netherlands and the Agricultural Research Service in the United States developed interactive computer programs for long-throated flume design. With the advent of modern spread sheets, the ISO standard, the flume geometry and a design optimisation routine, the rating tables, staff gauge data, and stage discharge-head curves can be generated. The primary advantage of these long-throated flumes for open-channel flow measurement is the theoretical predictability of their hydraulic performance. Provided that critical flow occurs in the throat, a rating table can be calculated with an error of less than 2% of the measured discharge. The throat, perpendicular to the direction of flow, can be designed in such a way that the complete range of discharges can be measured accurately. The required head loss over the flume is minimal, ensured by modular flow which occurs when a unique relationship exists between the upstream referenced head and the discharge. With their gradual converging transition, these structures have little problem with floating debris. Field observations and laboratory tests have shown that these structures can be designed to pass sediment transported by open channels with subcritical flow. CONDITIONAL CONSTRAINTS TO THE FLUME GEOMETRY In order to obtain critical flow within the throat of the flume, the following conditions are applied: Q Q To obtain the required hydrostatic pressure conditions occur- ring at the control section, the throat of the flume should be long enough for the flow to be parallel with the flume invert Q Q The flume throat must be shaped so that there is no energy loss between where the head is gauged and the point where critical flow occurs Q Q To obtain the ‘modular’ condition the flume throat shall constrict the channel enough to raise the energy level in the throat sufficiently higher than the downstream energy level. Modular flow is not dependent on the tail water levels. The following geometric constraints must be taken into consid- eration with the iterative design process: Channel/flume width �� B > b / 0.7 (145 mm min) Throat width �� b ≥ 100 mm Throat width �� b < 0.7 * B Flume inlet radius �� 2 * (B–b) Flume inlet length �� (1.75 0.5 )*(B–b) Throat length �� h max / L ≤ 0.5 (maximum 0.67 with +2% uncertainty) Discharge length (1:6) �� 3 * (B–b) Total flume length �� K + L + D Maximum head �� h max / b ≤ 3 Discharge truncation (1:33) �� 0.5 * D CONCLUSION The RLT flume also known as a “critical depth” flume is covered by the ISO 4359:2013 standard and relies on the occurrence of critical flow in the flume throat. When this occurs, independent of the conditions downstream, there is a unique relationship between the upstream head and the discharge for a given flume geometry. Under similar hydraulic and other boundary conditions, these are usually the most economical of all structures for accurately Image of a rectangular long-throat flume from the TV programme BBC Horizon – The Secret Science of Sewage (2021) © Tern Television Productions Ltd MMXXI About the author Peter van der Merwe is an independent consultant who, in a private professional capacity, advises on hydraulic matters relating to open channel flow monitoring. He has nine years of extensive experience in the design, manufacture and supply of a wide range of flumes and weirs and has consulted and supplied products to over 170 local and international clients. RLT design annotation

Civil Engineering nOVEMBER 2021 | Vol 29 No 10