This article was downloaded by: [University of Southern Queensland] On: 11 October 2014, At: 19:36 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Water International Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/rwin20 Energy Loss at a Drop Structure with a Step at the Base a a Ismail I. Esen , Jasem M. Alhumoud & Khoanddkar A. Hannan a b Kuwait University , Kuwait b Public Authority for Housing Welfare , Kuwait Published online: 22 Jan 2009. To cite this article: Ismail I. Esen , Jasem M. Alhumoud & Khoanddkar A. Hannan (2004) Energy Loss at a Drop Structure with a Step at the Base, Water International, 29:4, 523-529, DOI: 10.1080/02508060408691816 To link to this article: http://dx.doi.org/10.1080/02508060408691816 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions International Water Resources Association Water International, Volume 29, Number 4, Pages 523–529, December 2004 2004 International Water Resources Association Technical Note Energy Loss at a Drop Structure with a Step at the Base Downloaded by [University of Southern Queensland] at 19:36 11 October 2014 Ismail I. Esen and Jasem M. Alhumoud, Kuwait University, Kuwait, and Khoanddkar A. Hannan, Public Authority for Housing Welfare, Kuwait Abstract: The flow over a drop structure placed in a rectangular channel was investigated through an experimental program. It was noted that the downstream depth of flow was crucial to the formulation of the problem. Two procedures were developed for the estimation of the downstream depth. The first procedure was physically based with an empirical component for the estimation of the depth of the pool formed at the base of the drop. The second was a purely empirical procedure, which resulted in an equation for the direct estimation of the downstream depth. The parameters of the equation were determined by least-squares techniques. Both procedures resulted in reasonably accurate estimates of the downstream depth. The energy loss at the drop was then calculated and compared with the results of previous studies. The investigations were repeated with a single step placed at the base of the drop. It was observed that the step significantly increased the energy loss at the drop. Keywords: drop structures, downstream depth, energy dissipation, energy loss, step Introduction Vertical drop structures with a free overfall are usually built in irrigation canals where the slope of the canal is less than the ground slope. Flow over a drop results in an energy loss due to the mixing of the falling jet with the recirculating flow in the pool of water formed at the base of the drop. Previous studies made by Moore (1943), White (1943), Rand (1955), Gill (1979), and Rajaratnam and Chamani (1995) contributed towards the evaluation of this loss. The occurrence of this loss at the base of a drop is usually beneficial in the hydraulic design of open channels in which low flow velocities are required. In fact, in certain cases it may be desirable to increase the energy loss as much as possible. For this reason, we attached a single step to the base of the drop. This step had a square crosssection and extended through the entire width of the channel. It effectively pushed the overfalling jet of water downstream, reduced the depth of water in the pool, increased the downstream depth of flow, and increased the energy loss through the drop. Previous studies made on the subject mostly emphasized the estimation of the energy loss. In this study, we used the procedure proposed by Rajaratnam and Chamani 523 (1995) to predict the downstream depth of flow for drops with and without a step. This procedure required knowledge of the pool depth, and empirical equations were developed for this purpose. Alternately, we developed entirely empirical equations for the direct determination of the downstream flow depth. The head loss was then calculated by the energy equation. Literature Review Literature survey of the flow over a drop is limited to cases without a step. As far as the authors know, flows with a step were not investigated before. A definition sketch of a vertical drop of height h placed in a rectangular channel is shown in Figure 1. Here we follow the notation adopted by Rajaratnam and Chamani (1995) and note that the upstream flow is subcritical, the flow near the drop is critical with depth yc and velocity Vc, and the flow immediately downstream of the drop is supercritical with depth y1 and velocity V1 . The nominal depth of the pool formed at the base of the drop is denoted by yp , and hs is the height of the step. The length of the step is also hs since only steps with a square section were investigated. The free water jet makes an angle of φ when it hits the pool with velocity V. 524 Technical Notes The relative energy loss ∆E/Eo is defined as ∆E E o − E1 = Eo Eo Downloaded by [University of Southern Queensland] at 19:36 11 October 2014 Figure 1. Definition sketch of a drop with a step at the base The first analytical study of the flow over a drop was reported by Bakhmeteff (1932) who showed that the energy equation could be applied to determine the downstream depth y1 from the equation V1 = C 2g (Eo − y1 ) (1) where C is a velocity coefficient, and Eo is the total energy head in the approach channel with respect to the downstream channel bottom. For rectangular channels E o is given by the following equation: 3 Eo = h + y c (2) 2 The value of C was proposed as unity by Bakhmeteff. Moore (1941) noted, however, that in such a condition there would be no energy loss associated with the drop. Moore also cited Bobin (1934) who had proposed a value of 0.95 for C to account for the losses. Nevertheless, Moore (1941) carried out the first experimental work on the hydraulics of drops and reported the results in the form of a dimensionless chart. In calculating the downstream velocity head, Moore relied on the actual velocity measurements rather than using the continuity equation for the determination of the average velocity. Moore also used the momentum equation for the determination of the depth of water in the pool as 2 y y = 1 + 2 c − 3 yc y c y1 yp (3) A well known discussion of Moore’s paper was made by White (1943) in which the flow at the drop was considered to be similar to an inclined jet striking a flat plate. The water jet is divided into two: one part forming the downstream flow, and the other part flowing towards the pool, causing circulation in the pool and finally combining with the initial jet near the pool surface. By applying the energy and momentum equations, the specific energy E1 at the downstream section was determined as 1.06 + h + 3 y 2 E1 2 c = + y1 4 h 3 1. 06 + + yc 2 2 and its value can be obtained by Equations 3 and 4. Inspection of these equations shows that the relative energy loss is a function of only h/yc or yc/h. In reaching Equation 4, White (1943) made several important assumptions. These assumptions are summarized by Rajaratnam and Chamani (1995) as: i) the circulating flow in the pool at the bottom of the drop, Qc is the same as the backward flow in an impinging jet of the same angle Qb ; ii) the velocity of the supercritical stream immediately downstream of the drop is the same as the uniform velocity at the side of the pool; iii) the angle of the falling jet is not affected by the presence of the pool; iv) the energy loss at the drop is due to mixing with the pool; v) the presence of the pool does not affect the velocity, V, of the free water jet; and vi) the horizontal component of the velocity, V, can be determined by applying the momentum equation between the critical flow section upstream of the drop and the water jet. Rand (1955) investigated the flow geometry at straight drop spillways followed by a hydraulic jump. Using his own and Moore’s experimental data, Rand developed a set of empirical equations for the initial and sequent depths and the location of the jump, and the depth of water in the pool in terms of a dimensionless drop number D. The drop number is defined as D= q 2 yc = gh3 h 3 (6) where q is the discharge per unit width in the rectangular channel, and g is the acceleration of gravity. Gill (1979) modified several assumptions of White (1943), but neglected the energy loss in the pool. He also proposed to use Rand’s (1955) empirical equation for the pool depth y = D0.22 = c h h yp 0.66 (7) Gill (1979) then obtained the following equations for the determination of φ and y1 : cosφ (1 + cosφ ) = y1 = yc 3 h y 3 2 − p + y c yc 2 (8) 1 (1 + cos φ )2 2 (4) (5) y p y1 h hp y − y + 1.5 + 2 y − y c c c c (9) Rajaratnam and Chamani (1995) carried out an experimental investigation and checked the assumptions made IWRA, Water International, Volume 29, Number 4, December 2004 Downloaded by [University of Southern Queensland] at 19:36 11 October 2014 Technical Notes by White (1943) and modifications proposed by Gill (1979). They made velocity measurements at the base of a drop including pool flow and also at the base of an impinging jet. With these measurements it was possible to compute the backflow rates Qc and Qb , and it was observed that they were distinctly different from each other for a wide range of flow conditions. Thus, the first assumption of White was found not to be valid. Similarly, they observed that the angle φ also varied with flow conditions and the pool depth, and the pool depth affected the terms in the energy equation. Thus, Rajaratnam and Chamani (1995) showed that White’s third and fifth assumptions were also not valid. Additionally, they showed that the downstream velocity head must be calculated with the introduction of an appropriate kinetic energy correction coefficient. Using Moore’s, Rand’s, and their own data, Rajaratnam and Chamani (1995) developed the following empirical equations for the computation of the relative energy loss and the pool depth: ∆E y = 0.0896 c Eo h y = 1.107 c h h yp −0.766 (10) 0 .719 (11) Rajaratnam and Chamani (1995) also developed a physically-based model to predict the drop characteristics. Referring to Figure 1 and applying the momentum equation to the control volume between the critical flow section and the pool (Control Volume 1), they obtained the following: ρq V cosφ + 1 1 γ y 2p = ρq V1 + γ y12 2 2 (12) where ρ and γ are the density and specific weight of the fluid. The momentum and continuity equations for the control volume between the pool and the downstream section (Control Volume 2) were written as ρq Vc + 1 γ y 2c = ρq V cosφ 2 (13) and h+ 3 V2 yc = yp + 2 2g (14) The continuity equation was written in the form q = yc gyc (15) and Equation 11 was used for the estimation of yp . Equations 11 through 15 were solved for φ, y1 /h, and V1 for different values of yc/h and the results were observed to compare well with the measured values. We shall also use these equations in our study for the prediction of the downstream depth of flow. Other studies on the hydraulic characteristics of drop structures include the investigation of the wave type of 525 flow and the oscillating hydraulic jump downstream of the drop (Turner and Mulvihill, 1987; Kawagoshi and Hager, 1990, Ohtsu and Yasuda, 1994), submerged flow downstream of the drop (Fiuzat, 1987), supercritical flow upstream of the drop (Chamani, 2002), and flow over drops placed in trapezoidal channels (Noutsopoulos, 1984). These topics are not within the scope of the present study. Description of Equipment and Experimental Procedure The tilting Universal Modular Flow Channel manufactured by Plint Partners Ltd., England, was the main laboratory facility. The channel was 20 m long, 0.60 m wide, and 0.78 m deep; it had glass walls, stainless steel bed, a stilling basin at the inlet supporting structure, and an independent water recirculation system. The pump capacity was 125 l/s. For flow measurements, a mercury manometer was connected to the orifice meter located on the water supply pipe. The maximum flow rate used in this study was 100 l/s, and the range of yc/h values was between 0.07 and 0.56. Three different drop structures with heights of 0.25 m, 0.35 m, and 0.45 m were used in the study. A slope was provided at the upstream end of the drop structure to ensure a smooth transition. To serve as a step restricting circulation at the base of the drop, concrete blocks of length 0.595 m having square cross-sections of seven different sizes were used. Each side of the square sections were 0.050 m, 0.075 m, 0.100 m, 0.150 m, 0.200 m, 0.225 m, and 0.275 m. When placed in the channel, the edges of the drop structure and the step were sealed with a sealing compound. The range of hs /h values was between 0.11 and 0.61. The flow velocities were measured by two probes of Type 403 (for lower velocities) and Type 404 (for higher velocities) manufactured by Nixon Instruments, England. Water depths were measured with point gages. At the downstream end of the drop, the flow became supercritical and was relatively unstable. Since the determination of the downstream depth of flow was extremely important, its accurate measurement was essential. For this reason, the channel bottom was connected to a glass cylinder with a flexible tube and the representative water level was measured inside the cylinder. Overall, 123 experimental runs were made. Each run was repeated twice: first without any step, then with a step of a specific size. In each run, flow rate, drop height, step size, and downstream depth of flow with and without a step were recorded. Other measurements such as upstream depth of flow, depth of water in the pool yp , and the downstream velocity V1 will not be reported here. Description of the experimental runs is given in Table 1. Semi-empirical Procedure for the Estimation of y1 Here we shall use Rajaratnam and Chamani’s (1995) physically-based model with two modifications. First, the IWRA, Water International, Volume 29, Number 4, December 2004 526 Technical Notes 0.07 Drop height (mm) Step size (mm) Number of experimental runs 0.06 250 75 x 75 100 x 100 50 x 50 75 x 75 100 x 100 150 x 150 50 x 50 75 x 75 100 x 100 150 x 150 200 x 200 225 x 225 275 x 275 12 12 10 9 9 8 8 9 9 10 9 9 7 Calculated values of y1 (m) Table 1. Description of the experimental runs 0.05 Total 123 Figure 2. Cross plot of calculated and measured values of downstream depth of flow y1 for drops without a step (semi-empirical procedure) Downloaded by [University of Southern Queensland] at 19:36 11 October 2014 450 q y1 0.01 0.01 0.02 y = 1.215 c h h yp (16) ( 2q (V1 − Vc ) − y 2c − y 21 g ) (17) with the measured values of y and q, yc was calculated by Equation 15, V1 was calculated by Equation 16, and yp values were calculated by Equation 17 for both drops without a step and with a step. With the yp values obtained for drops without a step, a non-linear least-squares procedure gave the following result: y = 1.215 c h h yp 0.02 0.03 0.04 0.05 0.06 0.07 Measured values of y1 (m) and the downstream velocity head will be calculated with this value of V1 without using any Kinetic energy correction coefficient. Next, Equation 7, which gives the pool depth, will be revised. The reason for this is that it is very difficult to make a definitive measurement of yp . As Rajaratnam and Chamani (1995) have shown, water surface in the pool oscillates with time, and there is a backwards water surface slope. The difference between the minimum and maximum pool depths was almost 20 percent. The simultaneous solution of Equations 12, 13, and 16 for yp yields yp = 0.03 0 downstream velocity will be directly obtained from the continuity equation as V1 = 0.04 0 0 .8124 (18) This equation is comparable to Equation 11 and predicts yp /h values within a difference of ± 5 percent from those predicted by Equation 11 for yc/h values between 0.2 and 0.6. Whenever there was a step, the pool depth varied with q, h, and hs . For that reason, we assumed a relationship such that the expression for yp /h would reduce to Equation 18 when there was no step, and yp /h would be a function of both yc/h and hs /h when there was a step. The resulting equation thus obtained by least-squares analysis is 0. 8124 1. 4952 0 .1882 hs yc 1 − 0.5662 h h (19) Equation 19 can be considered as the general equation that predicts the pool depth. Now, using Equations 12, 13, 14, 15, and 19, the downstream depth of flow y1 can be determined for given values of q, h, and hs . Using the corresponding values for these parameters in our experimental runs, we calculated y1 for drops without a step and with a step. Figures 2 and 3 show calculated values of y1 plotted against measured values of y1 for drops without a step, and for drops with a single step, respectively. Empirical Procedure for the Estimation of y1 The procedure described in the previous section was in principle physically based with one exception: the pool depth yp had to be experimentally determined. At this stage, one can argue that instead of using a relatively complicated procedure with a component which needs to be es0.09 0.08 0.07 Calculated values of y1 (m) 350 0.06 0.05 0.04 0.03 0.02 0.01 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Measured values of y1 (m) 0.08 0.09 Figure 3. Cross plot of calculated and measured values of downstream depth of flow y 1 for drops with a step (semi-empirical procedure) IWRA, Water International, Volume 29, Number 4, December 2004 527 Technical Notes 0.35 0.30 h s/ h=0.6 measured calculated h s/ h=0.4 h s/ h=0.2 0.3 0.25 h s/ h=0 ( no step) 0.25 0.20 y1/h y1/h 0.2 0.15 0.15 0.10 0.1 0.05 0.05 0 0.00 0 0.1 0.2 0.3 0.4 0.5 0 0.6 0.1 0.2 timated by statistical methods, the end result could directly be obtained by similar techniques. Therefore, it seemed appropriate to attempt to determine y1 directly by leastsquares procedures. Consequently, for the case of drops without a step, the following equation was obtained: 1.1854 (20) The linear correlation coefficient for this equation is R = 0.9986. Figure 4 shows measured and computed values of y1 /h plotted against yc/h for drops without a step. For drops with a step, y1 /h would be a function of both yc/ h and hs /h. Additionally, we would require the empirical equation to reduce to Equation 20 when there would be no step. With these conditions, the resulting regression equation is 1. 1854 y1 y = 0.4824 c h h 1 .4877 hs 1 + 0.5243 h yc h 0. 07571 (21) 0.25 0.2 0.15 0.1 0.05 0 0.1 0.15 0.6 against each other. The solution of Equation 21 is shown in graphical form in Figure 6 in which y1 /h has been plotted against yc/h for different values of hs /h. Equations 20 and 21 will be referred to as the empirical equations developed for the prediction of y1 . Comparison of the Two Methods As a representative selection of the experimental data, we have used the information available for each twentieth run and calculated y1 /h values by both procedures described above. This choice of experimental runs resulted in a wide range of values for ych and hs /h. The measured and calculated values of y1 /h are given in Table 2 for drops with and without a step. The energy loss at the drop is calculated as the difference between the total head in the approach channel Eo and the total head in the downstream section E 1 . The value of Eo can readily be determined by Equation 2, and E 1 can be computed by E1 = y 1 + 0.05 0.5 Figure 6. Values of y 1 /h estimated by Equation 21 0.3 0 0.4 Energy Loss at the Drop with a linear correlation coefficient of R = 0.9958. Figure 5 shows measured and computed values of y1 /h plotted Calculated values of y1 /h Downloaded by [University of Southern Queensland] at 19:36 11 October 2014 Figure 4. Measured and calculated values of y 1 /h plotted against y c/h for drops without a step (empirical procedure) y1 y = 0.4824 c h h 0.3 yc yc/h 0.2 0.25 0.3 Measured values of y1 /h Figure 5. Cross plot of calculated and measured values of y1 /h for drops with a step (empirical procedure) v12 2g (22) where V1 is directly determined by Equation 16. In the computation of the downstream energy head, no corrections for velocity variations within the cross-section were made. The relative energy loss can then be computed by Equation 5. For drops without a step, we calculated y1 using Equation 2, and the relative energy loss by Equation 5. The results are shown in Figure 7. On the same figure, relative energy losses reported by Moore, and Rajaratnam and Chamani (1995) are also shown. Relative energy losses for different hs /h values for drops with a step are shown in Figure 8. IWRA, Water International, Volume 29, Number 4, December 2004 528 Technical Notes 80 1 yc/h 0.064 21 0.360 41 0.291 61 0.309 81 0.207 101 0.380 121 0.468 hs/h Measured 0 0.300 0 0.214 0 0.444 0 0.166 0 0.500 0 0.429 0 0.400 0.024 0.025 0.146 0.154 0.111 0.133 0.120 0.131 0.072 0.089 0.157 0.179 0.200 0.216 0.018 0.019 0.144 0.151 0.112 0.127 0.120 0.125 0.075 0.087 0.153 0.173 0.195 0.218 0.019 0.020 0.144 0.151 0.112 0.127 0.119 0.126 0.075 0.087 0.153 0.174 0.196 0.221 Rajaratnam and Chamani 60 50 40 30 20 10 0 0.3 0.4 yc/h Figure 7. Relative energy loss for drops without a step 0.5 50 40 30 0.1 0.2 0.3 yc 0.4 0.5 0.6 Figure 8. Relative energy loss for drops with a step Moore 0.2 hs /h=0 (no step) 0 present study 0.1 60 0 80 0 h s/h =0.6 h s /h=0.4 hs /h=0.2 10 Inspection of the values listed in Table 2 shows that in general the values of y1 calculated by the semi-empirical and empirical equations are almost identical. However, comparison of Figures 2 and 3 with Figures 4 and 5 indicates that the semi-empirical procedure predicts higher than actual y1 values at higher values of yc (or y1 ). This coupled with the unusually high correlation coefficients associated with them are points in favor for the use of Equations 20 and 21 for the prediction of y1 . It is also relatively easier to apply the empirical procedure. As can be observed from Figure 6, presence of a step results in higher y1 values: as the step size is increased, y1 increases at an increasing rate. Figure 7 shows the relative energy loss computed by the empirical equations for y1 together with the relative energy losses reported by previous researchers for drops without a step. Although the fit is reasonably good for a wide range of values of yc/h, at high values of yc/h, the energy loss reported is higher than that determined by the proposed procedure. This indicates 70 70 20 Discussion E/Eo (%) Downloaded by [University of Southern Queensland] at 19:36 11 October 2014 Run y1/h Calculated by Calculated by semi-empirical empirical procedure procedures ∆E/Eo (%) Table 2. Measured and calculated values of y1/h for selected experimental runs 0.6 that corrections for the velocity head should be made at large flow rates. The effect of the step on the relative energy loss is shown in Figure 8. The presence of a step is observed to significantly increase the head loss. As the flow rate and step size increase, the effect of the step becomes more pronounced. For example, at yc/h = 0.2, having a step with hs /h = 0.6 increases the relative energy loss by about 50 percent. At yc/h = 0.4, a step of the same size increases the relative energy loss by more than 150 percent. In this study, the downstream depth of flow was considered to be supercritical. Consequently, there was a hydraulic jump further downstream. Cases in which the jump moved upstream and affected the flow over the drop structure were not investigated. The maximum hs /h value used in the study was 0.61. For larger step sizes, the flow over the drop structure fell over the step and the flow characteristics changed. This situation resembled cascading flows and was not investigated. Conclusions In irrigation systems where the slope of the canal is less than the ground slope, drop structures are built to reduce the cost of excavation and earth fill. Drops are also used for prevention of erosion and a grade control structure in drainage channels and as a spillway for small earth dams. The simplest drop structure is a vertical fall placed in a rectangular channel. Description of the flow characteristics at drops is important for the design of a stilling basin downstream of the drop. The stilling basin can be a flat concrete apron, or a detailed structure which may include chute blocks, baffle piers, and an end sill. In this study, we proposed placing a concrete step having a square cross-section at the base of the drop running through the entire width of the channel. To the benefit of the engineer, this drop increases the energy loss through the drop, and the downstream depth of flow can be precisely estimated. The downstream depth of flow y1 over a drop with or IWRA, Water International, Volume 29, Number 4, December 2004 529 Technical Notes without a step can be determined by a semi-empirical procedure which requires the solution of a number of equations based on continuity, momentum, and energy principles, and one additional empirical equation for the depth of pool at the base of the drop. Alternatively, the downstream depth of flow can be directly determined by Equation 21, as given above. Equation 21 can be used for drops with and without a step, and it has a correlation coefficient of R = 0.9958 with the values of y1 predicted by Equation 21. The energy loss at the drop was calculated, and it was observed that a step placed at the base of the drop significantly increases the energy loss. Downloaded by [University of Southern Queensland] at 19:36 11 October 2014 Acknowledgement The experimental data used in this study were collected during the M.Sc. Thesis work of K.M.A. Hannan which was supported by the College of Graduate Studies, Kuwait University. The authors wish to thank the distinguished reviewers of the journal. Notations C D Eo E1 g h hs q Qb Qc R V V1 Vc y1 yc yp γ ρ φ velocity coefficient drop number defined by Equation (6) total energy head in the approach channel total energy head at the downstream section acceleration of gravity height of drop height of step discharge per unit width of channel backward flow of an impinging jet circulating flow in the pool linear correlation coefficient velocity of the free water jet velocity of flow at the downstream section critical velocity downstream depth of flow critical depth of flow depth of water in the pool specific weight of water density of water the angle the water jet makes with the pool neering. He can be reached at E-mail: jasem@kuc01. kuniv.edu.kw Khoanddkar A. Hannan. is with the Public Authority for Housing Welfare in Safat, Kuwait. Discussions open until June 1, 2005. References Bakhmeteff, B.A. 1932. Hydraulics of open channels. New York: McGraw-Hill. Bobin, P.M. 1934. The design of stilling basins. Leningrad: Transactions, Scientific Research Institute of Hydrotechnics, Vol. VIII. Chamani, M. R. 2002. “Flow characteristics at drops.” Journal of Hydraulic Engineering 128: 788-791. Fiuzat, A. A. 1987. “Head loss in submerged drop structures.” Journal of Hydraulic Engineering 113: 1559-1562. Gill, M.A. 1979. “Hydraulics of rectangular vertical drops structures.” Journal of Hydraulic Research 17: 289-302. Kawagoshi, N. and W.H. Hager. 1990. “Wave type flow at abrupt drops.” Journal of Hydraulic Research 28: 235-252. Moore, W.L. 1943. “Energy loss at the base of free overfall.” Transactions (ASCE) 108: 1343-1360. Noutsopoulos, G. C. 1984. “Hydraulic characteristics in a straight drop structure of trapezoidal cross section.” Channels and Channels Control Structures, Proceedings of the 1 st International Conference on Hydraulic Design in Water Recourses Engineering. Southampton, England. Ohtsu, T and Y. Yasuda. 1994. “Characteristics of flow over drop structure.” Proceedings of the 1994 International Conference on Hydraulics in Civil Engineering. Brisbane, Australia. Rand, W. 1955. “Flow geometry at straight drop spillways.” Proceedings ASCE 81: 1-13. Rajaratnam, N. and M.R. Chamani. 1995. “Energy loss at drops.” Journal of Hydraulic Research 33: 373-384. Turner, H. O. and M.E. Mulvihill. 1987. “General design for modifications to exiting lower Santa Ana drop structures.” Hydraulic Engineering, Proceedings of the 1987 National Conference, ASCE. Williamsburg, VA, USA: ASCE. White, M.P. 1943. Discussion of Moore (1943). Transactions (ASCE) 108: 1361-1364. About the Authors Dr. Ismail I. Esen, is a member of the Department of Civil Engineering at Kuwait University. Dr. Esen’s research interests include fluid mechanics, hydraulics, environmental engineering, and transport processes. Dr. Jasem M. Alhumoud, is a member of the Department of Civil Engineering at Kuwait University. Dr. Alhumoud’s research interests include the principles of environmental engineering, hydrology and hydrualics, solid waste management, geoenvironmental and geohydrology engineering, and the principles of water resources engiIWRA, Water International, Volume 29, Number 4, December 2004