Evaluation of Energy Dissipation Using Different Drop Broken-Back Culverts Under Pressure Flow Conditions

Transcription

1 E154 Evaluation of Energy Dissipation Using Different Drop Broken-Back Culverts Under Pressure Flow Conditions AVDHESH K. TYAGI, 1 ABDELFATAH ALI, 2 AND MATTHEW HAMILTON 2 1 Oklahoma Infrastructure Consortium, School of Civil and Environmental Engineering, Oklahoma State University, Stillwater, Okla. 2 School of Civil and Environmental Engineering, Oklahoma State University, Stillwater, Okla. Hydraulic jumps formed in broken-back culverts were investigated experimentally by using energy dissipation devices. Additional examination measured the reduction in scour downstream of different-height broken-back culverts by forming a hydraulic jump inside the culverts. A broken-back culvert model in the laboratory represents 150 in the field. The results were analyzed in terms of the inlet Froude number and different drop heights of broken-back culverts. The calculated efficiency of energy dissipation in the culverts ranged between 55 and 90%. The dimensionless charts were created on the basis of data collection showing the relationship between the different relative drops and optimal sill height, optimal sill location, total head losses, optimal end sill, Froude number, and efficiency of hydraulic jump. The objective of this research was to obtain the maximum energy dissipation in different drop heights using analysis of dimensionless relationship charts. Keywords: broken-back culvert, culvert drop, efficiency of jump, energy dissipation, friction blocks, hydraulic jump, pressure flow conditions, sill A broken-back culvert (BBC) is capable of dissipating energy, thus lowering the effects of water scour and leading to an overall reduction in damage from water scour. This evaluation looked at different parameters thought to be related to the damaging effects of scour on BBCs. These parameters include characteristics of hydraulic jumps such as the Froude number, energy loss, and efficiency. The Froude number related to the ratio of inertial and gravity forces is presented by the average flow velocity before the jump (V 1 ) and the acceleration of gravity wave in shallow water ( g y 1 ). In Oklahoma, nearly 121 scour-critical culverts on the Interstate System, the National Highway System, and the State Transportation Program have been inventoried by the Oklahoma Transportation Center at Oklahoma State University (Tyagi 2002). A survey of culverts in Oklahoma and surrounding areas indicated that the drop in flowline between upstream and downstream ends ranges between 6 and 30. The hydraulic jump is a natural phenomenon of a water level s sudden rise resulting from a change from supercritical flow to subcritical flow that is, when there is a sudden decrease in flow velocity. This sudden change in the velocity causes considerable turbulence and loss of energy. Consequently, the hydraulic jump has been recognized as an effective method for energy dissipation for many years. Results of this research could maximize the energy loss within a culvert, thus minimizing the scour around a culvert and decreasing the degradation downstream in a channel. This could reduce the construction and rehabilitation costs of culverts in Oklahoma. This research also investigates the ability to shorten a culvert by inducing a hydraulic jump closer to the front of the culvert than the original rearward placement, which might be needed in certain scenarios. PREVIOUS STUDIES Many studies have examined the characteristics of the hydraulic jump. Ohtsu et al. (1996) evaluated incipient hydraulic jump conditions on flows over vertical sills. They identified two methods of obtaining an incipient jump: (1) increasing the sill height or (2) increasing the tail water depth until a surface roller forms upstream of the sill. For wide channels, predicted and experimental data were in agreement, but in the case of narrow channels, incipient jump was affected by channel width. Hotchkiss et al. (2003) described the available predictive tools for hydraulic jumps, the performance of the Broken-back Culvert Analysis Program (BCAP) in analyzing a BBC s hydraulics, and the current applications and distribution of the BCAP. They conducted tests on a BBC made of Plexiglas to assess the BCAP s performance in predicting headwater rating curves and the locations and lengths of hydraulic jumps. They concluded that predictions of flow hydraulics within the culvert barrel may be improved Dimensions of broken-back culvert under the pressure flow condition.

2 E155 A B C (A) Front view of the laboratory model. (B) Side view of the laboratory model. (C) Downstream plywood channel aer the wing wall. by accounting for losses within a jump from friction in corrugated metal pipes and more accurate predictions of the locations of hydraulic jumps. Larson (2004) suggested the possibility of forcing hydraulic jumps to reduce the outlet energy. She considered two design examples to create a hydraulic jump within a culvert barrel: (1) a rectangular weir placed on a flat apron and (2) a vertical drop along with a rectangular weir. These two designs were used to study the reduction in the energy of the flow at the outlet. From these experiments, she found that both designs were effective in reducing outlet velocity, momentum, and energy. These reductions would decrease the need for downstream scour mitigation. Lowe et al. (2011) indicated that the subcritical sequent depth is a function of conduit shape, upstream depth, and Froude number. They studied the theoretical determination of subcritical sequent depths for pressure and free-surface jump and the momentum equation, which consists of terms for the top width, area, and centroid of flow. They also presented the general solution to the sequent depth problem for four prismatic conduits: rectangular, circular, elliptical, and pipe arch. Lowe et al. provided a numerical solution for these shapes but neglected the effects of friction and air entrainment. The authors concentrated on the cost of downstream energy dissipation by forcing a jump to occur within the culvert barrel. Tyagi et al. (2009) investigated hydraulic jumps under pressure and open-channel flow conditions in a BBC with a 24- drop. It was found that for pressure flow, a two-sill solution induced the most desirable jump; for open channel, a single sill close to the middle of the culvert was most desirable. Chamani et al. (2008) conducted an experimental study on the energy loss produced by a vertical drop upstream with a model of a 0.20-m drop. They developed models by using shear layer theories and a fully developed surface to estimate energy loss. They found similarity between a turbulent surface jet and flow over the drop. The results were compared with previous experimental data; the predictions of their models agreed well with the experimental data. Moreover, the authors used the predicted values of the energy loss to calculate the downstream depth of flow. Mignot and Cienfuegos (2010) focused on an experimental investigation of energy dissipation and turbulence production in weak hydraulic jumps. Froude numbers ranged from 1.34 to The researchers observed two peak turbulence production regions for the partially developed inflow jump one in the upper shear layer and the other in the near-wall region. The energy dissipation distribution in the jumps was measured and revealed a similar longitudinal decay of energy dissipation integrated over the flow sections and maximum turbulence production values from the intermediate jump region toward its downstream section. The energy dissipation and the turbulence production were strongly affected by the inflow development. Turbulence production showed a common behavior for all measured jumps. It appeared that the elevation of maximum turbulent kinetic energy and turbulence production in the shear layer were similar. Alikhani et al. (2010) conducted many experiments to evaluate the effects of a continuous vertical end sill in a stilling basin. They measured the effects of sill position on the depth and length of a hydraulic jump without considering the tail water depth. They used five sill heights placed at three separate longitudinal distances in their 1:30 scaled model. The characteristics of the hydraulic jump were measured and compared with the classical hydraulic jump under varied discharges. They proposed a new relationship between sill height and position and sequent depth-to-basin length ratio. The study concluded that a 30% reduction in basin length could be accomplished by efficiently controlling the hydraulic jump length through sill height. PRESENT STUDY There are no prior studies investigating the energy dissipation inside BBCs other than the research completed to compile this report. This research is designed to serve as a reference for future research in this area. This research aims to investigate the best option to maximize energy dissipation under pressure channel flow conditions to evaluate the energy dissipation between upstream and downstream ends of a BBC without and with friction blocks. This research also aims to observe in physical experiments the efficiency of a hydraulic jump with and without friction blocks between upstream and downstream ends of the culvert and the location of hydraulic jump from the toe of the drop in the culvert (Tyagi et al. 2009). A scale model was built as a prototype of a BBC 150 long with two barrels of and vertical drops of 6, 12, 18, 24, and 30. Simulations were performed of different flow conditions for 0.8, 1.0, and 1.2 times the hydraulic head in the constructed scale model (see photographs A through C on this page).

3 E156 THEORETICAL EXPRESSION The nature of the hydraulic jump cannot be accounted for by use of the energy equation because there is a substantial dissipation of energy from the turbulence associated with the jump. However, because momentum flux is conserved across hydraulic jumps under assumptions to be discussed later, momentum theory may be applied to determine the jump size and location (Hotchkiss et al. 2003). Momentum theory states that the sum of the external forces acting upon a system equals the change in momentum flux across that system (US Department of Transportation 2006). This principle can be successfully applied to complete or incomplete hydraulic jumps. According to Lowe et al. (2011), using an axis parallel to the channel, a one-dimensional form of the momentum equation may be written as follows: F S = (M S ) out (M S ) in (1) where F S is the external forces (lb, N) acting on water within the control volume and M S is the momentum flux (lb, N) through the control volume. To solve the momentum equation for pressure flow conditions in the culvert hydraulic jump and then to simplify the solution graphically, numerous studies have been undertaken for open channel flow conditions derived from the Belanger equation. This equation expresses the ratio between sequent depths as functions of the upstream Froude number (Lowe et al. 2011, Chow 1959). Chow stated the hydraulic jump will form in the channel if the Froude number in supercritical flow (F r1 ), water depth before hydraulic jump in supercritical flow (Y 1 ; in.), and water depth aer hydraulic jump in subcritical flow (Y 2 ; in.) satisfy the following equation: Y 2 Y F 2 r1 1 (2) Eq 3 was used to calculate the F r1 of the hydraulic jump in the upstream part of the culvert: F r1 V 1 g Y 1 (3) where g is the acceleration resulting from gravity and Y 1 indicates flow depth before the hydraulic jump. A complete derivation of momentum theory of incomplete hydraulic jumps can be reviewed in Lowe et al. (2011). The following equations are provided for sequent depth of incomplete jumps for a rectangular cross-section: Y 1 Y 1 D (4) Y F2 r1 1 2 Y 2 1 F2 r1 Y 3 1 (5) Eq 6 provides the dimensionless form of the sequent depth: Y 2 Y 2 D (6) where Y 1 and Y 2, from Eqs 4 and 6, are the dimensionless sequent depths before and aer the jump, respectively, and D is the height of the culvert (). According to Lowe et al. (2011), equations to calculate the Froude number in the incomplete hydraulic jump are as follows. Calculate the Y 2 from Y 2, dimensionless flow depth. Y 2 = Y 2 D (7) From Eq 2, the actual Froude number at upstream supercritical flow can be calculated. The adjusted Froude number (F9 r1 ) is F r1(adjusted) 2Y 2 Y (8) 8 The efficiency of the jump was calculated by taking the ratio of the specific energy before and aer the jump (Chow 1959): E 2 (8F r1 2 1) 3/2 4F 2 r1 1 E1 8Fr 2 1 (2 F 2 r1 ) The efficiency of the jump in the incomplete jump can be calculated by using F9 r1(adjusted) : E 2 E1 (8F 2 r1(adjusted) 1) 3/2 4F 2 r1(adjusted) 1 8F 2 r1(adjusted) (2 F 2 r1(adjusted) (9) (10) where E 1 is the energy head before the jump (in.), E 2 is the energy head aer the jump (in.), and F9 r1(adjusted) is the Froude number before the jump. The total head loss (THL; in.) between upstream and downstream of the structure was calculated by applying the Bernoulli equation: THL H V2 u/s 2g Z Y d/s V2 d/s 2g (11) where H is water depth upstream of the culvert (in.), and Z is the drop between upstream and downstream, which, in the model, was 3.60, 7.2, 10.8, 14.4, and 18 in., representing a 6-, 12-, 18-, 24-, and 30- drop in the prototype, respectively. The downstream location is dictated as the point at the end of the culvert before the flow is spread by the wing walls. The loss of energy or energy dissipation in the jump was calculated by taking the difference between the specific energy before the jump and aer the jump. E E 1 E 2 (Y 2 Y 1 )3 4Y1 Y 2 (12) Y 2 was calculated from Eq 7 or when the Y 2 was equal to D. EXPERIMENTAL SETUP AND INSTRUMENTATION A scale model represented a 150--long BBC with two barrels of each and vertical drops of 6, 12, 18, 24, and 30

4 E157 A B C (A) Typical sill dimensions. (B) Example of a flat-faced friction block. (C) Example of flat-faced friction blocks arranged on model bottom. in the field condition. The 1:20 scale was adopted because of space limitations. The scale model contains two barrels with dimensions of 6 in. wide 6 in. high. Table 1 shows the dimensions in terms of the prototype culvert for five drops. Table 2 shows the dimensions in terms of the laboratory models in five drops (Figures 1 3). At the upstream end, a reservoir collected the flow discharge at three flow rates, depending on the experiment being conducted. The flow rates were dictated by three flow conditions measured by the depth of the barrel multiplied by 0.8, 1.0, and 1.2. These depth-of-flow scenarios simulated a culvert when water was less than, equal to, and greater than the height of the culvert barrel. Supercritical flow was enforced by a steep, sloped flume section. At the downstream end of the flume, an expansion of the flow section by a wing wall further reduced the downstream velocity. The location of the hydraulic jump was simply controlled by the discharge rate upstream and TABLE 1 Model TABLE 2 Prototype dimensions Drop Length of Slant Part Mild Part With 1% Slope Model Laboratory model dimensions (1:20 scale) Drop in. Length of Slant Part in. Mild Part With 1% Slope in the sill and/or friction block location. The slope of the culvert did not contribute in controlling the hydraulic jump location. The objective of the test was to determine the effect of sill and friction blocks on the hydraulic jump within the prototype; therefore, the model was constructed so that different arrangements of friction blocks could be placed and observed within the model (see photographs A through C on this page). Flat-faced friction blocks were mounted inside the barrel in different arrangements on a sheet of Plexiglas that was the same width as the barrels and were placed in the barrel. Sills were located only on the mild section of the model, and the sills contained two small orifices at the bottom to allow the culvert to completely drain. Access holes were cut into the top of these sections to allow for placement of a velocity meter. EXPERIMENTAL PROCEDURE AND DATA COLLECTION Many experiments were conducted to create energy dissipation within the BBC. In different drops, experiments were performed for this model with variations in the lengths, heights, widths, and energy dissipaters used. Each experiment tested three scenarios and were run with upstream heads of 0.8 culvert depth (d; inches), 1.0 d, and 1.2 d, with each depth denoted by A, B, or C, respectively. For example, 20A represents the 20th experiment run at 0.8 d, 20B represents the 20th experiment run at 1.0 d, and 20C represents the 20th experiment run at 1.2 d. A two-dimensional side-looking micro-acoustic Doppler velocimeter (ADV) 1 was used to measure the velocity at the intake of the structure and at the downstream end of the culvert. It was difficult to measure the velocity at the toe before the hydraulic jump because it was necessary to maintain a closed structure to satisfy pressure conditions (Chanson 2008, SonTek/YSI 2001). This difficulty precluded us from using the ADV to measure the velocity before the hydraulic jump. Therefore, a Pitot tube was used to measure velocity at the toe before the hydraulic jump. In these experiments, the length of the hydraulic jump (L), Y 1, Y 2, the distance from the beginning of the hydraulic jump to the beginning of the sills (X), the depth of the water in the inclined channel (Y s ), and the depth of the water downstream of the culvert (Y d/s ) were measured. All dimensions were measured by using a ruler and point gauge. As mentioned previously, the velocity before the jump, V 1, the velocity aer the jump (V 2 ), and the

5 Tyagi et al. E158 FIGURE 1 Pressure flow laboratory model schematic in three dimensions with a 1:20 scale All measurements are in inches. 60º 60º FIGURE 2 (A) Profile and plan view of reservoir inlet (upstream) and (B) plan view of culvert outlet (downstream) A B Reservoir Reservoir 60º º All measurements are in inches, with a 1:20 scale.

6 E159 velocity downstream of the culvert (V d/s ; /s) were measured by a Pitot tube. The experimental procedure was as follows: (1) install energy dissipation devices (such as sills or friction blocks) in the model; (2) set the point gauge to the correct height in the reserve; (3) turn on the pump in the station; (4) adjust the valve and coordinate the opening to obtain the amount of head for the experiment; (5) take the reading for flow rate; (6) run the model for 10 min before taking measurements; (7) measure Y s, Y 1, Y 2, L, X, and Y d/s (inches); and (8) measure velocities along the channel velocity upstream of the culvert (feet per second), V t, V 1, V 2, and V d/s, as shown in Figure 4. DATA ANALYSIS Nine experiments were selected on the basis of optimal energy dissipation from the 19 performed in the hydraulic laboratory. These experiments show model runs without friction blocks, the effects of a sill at the end of the model, and with friction blocks and a sill. The flat-faced friction blocks were used with sills. Aer the effectiveness was evaluated, the number of blocks was varied by 15, 30, and 45. In each of these experiments, the optimum sill height is the height required to create a consistent hydraulic jump overall and in flow conditions. The optimum sill was determined first, the optimum sill location was found next, and the effectiveness of friction blocks in combination with the optimum sill parameters was determined last. The friction blocks were arranged in many configurations; the highest energy dissipation was found by trial and error. Aer many experiments were performed, consistent results showed that the best location for energy dissipation using friction blocks was located in front of the sill, beginning where the hydraulic jump started. Additional friction blocks were added moving toward the front of the model until the hydraulic jump was located at the toe of the drop. For each drop, experiments were also performed without friction blocks or sills to investigate FIGURE 3 (A) Profile view of the laboratory model schematic in pressure flow and (B) plan view of the laboratory model schematic A Reservoir 1:2 Slope 1% Slope Friction blocks Sill 2 B Reservoir Friction blocks Sill Sill All measurements are in inches, with a 1:20 scale.

7 E160 the possibility of a hydraulic jump occurring. It was found that there were no hydraulic jumps without energy dissipation. Different sill heights were used in the experiments to produce the hydraulic jump. The sill heights were increased to produce a hydraulic jump and to try to locate it at the toe of the sloped channel as a means of maintaining subcritical flow throughout the mild section of the BBC. First, different sills were placed the end of culvert to get the optimal end sills. Second, to get the optimal location of the hydraulic jump with the lowest possible sill height, the sill was moved from the end of the culvert toward the center of the culvert. Aer these experiments were chosen as possible solutions for the end and middle sills, further investigation of energy dissipation was undertaken by placing the friction blocks at the front of the sill. Different configurations and numbers of friction blocks were used in the same sill arrangement. Table 3 illustrates dimensionless parameters for the optimal end- and middle-sill experiments. An optimal sill in this research was a sill that gave the maximum dissipation of energy over the spectrum of flow conditions but required the lowest height possible. This would usually manifest in the culvert as a sill that would give the longest hydraulic jump under pressure flow for all simulated conditions. Figure 5 shows the relationship between relative drops and F r1 and illustrates that the relative middle sill increases as the drop height of the BBC decreases. Figure 6 shows the relationship between relative drops and efficiency of hydraulic jumps (E 2 /E 1 ; percent) and that the increase in BBC drop height will decrease because of E 2 /E 1. Figure 7 shows the relationship between the dimensionless relative drops and energy loss for the middle sill (case B). The relative energy loss was calculated by dividing the energy loss by the depth (10 ). As drop height increases, the energy loss increases. Figure 8 shows the relationship between dimensionless relative drops and relative THL. The relative energy loss was calculated by dividing the THL by the culvert depth. As drop heights increase, the THL increases. Figure 9 shows the relationship between relative drop height and relative middle sill height and illustrates the increase in drop height also increases the relative sill height. The relative sill height was calculated by dividing the sill height by the culvert depth. Figure 10 shows the relationship between drop height and relative middle sill location from the end of the culvert. The relative middle sill is calculated by dividing the middle sill location by the culvert length (150 ). The relationship between the relative drop height and the relative sill location varied. To review, a series of dimensionless figures was created by taking both the drop height and the sill height and dividing both by the culvert depth, which was 10. This allowed sills for intermediate FIGURE 4 Hydraulic jump variables in a broken-back culvert V u/s H y s V 2 y t V 1 V d/s L X H height of the inclined channel, L length of the hydraulic jump, V 1 flow velocity before the jump, V 2 the velocity aer the jump, V d/s velocity downstream of the culvert, V u/s velocity at upstream of culvert (/s), X distance from the beginning of the hydraulic jump to the beginning of the sills, Y 1 water depth before hydraulic jump in supercritical flow (in.), y 2 water depth aer hydraulic jump in subcritical flow (in.), y d/s water depth at downstream of culvert (in.), y s depth of the water in the inclined channel, y t water depth at toe TABLE 3 Dimensional to dimensionless calculation for middle and end sills Drop Relative Drop by 10 E 2 /E 1 % F r1 Middle Sill Height Prototype Relative Middle Sill by 10 Relative Location End Sill Height Prototype Relative E in. Relative THL in E loss of energy, E 2 /E 1 efficiency of hydraulic jump, F r1 Froude number in supercritical flow, THL total head loss for entire culvert

8 E161 FIGURE 5 versus F r1 experiment for the middle sill FIGURE 6 versus efficiency of hydraulic jump for the middle sill F r Relative drop versus Froude number Relative Drops F r1 Froude number in supercritical flow Efficiency of Jump Relative drop versus efficiency of jump 0.00 Relative Drops Divided by d d culvert depth (10 ) FIGURE 7 versus E for the middle sill FIGURE 8 versus total head loss for the middle sill Relative E Divided by d Dimensionless relative drops versus relative energy loss Relative Drops Divided by d d culvert depth (10 ), E loss of energy (in.) Relative THL divided by d Dimensionless relative drop versus relative THL Relative Drops Divided by d d culvert depth (10 ), THL total head loss (in.) FIGURE 9 versus relative middle sill heights FIGURE 10 versus relative middle sill location from the end of the culvert Relative drop versus relative sill Relative Drops Divided by d d culvert depth (10 ) Relative Middle Sill Heights Relative Sill Location Divided by d Dimensionless relative drop versus sill location Relative Drops Divided by d d culvert depth (10 )

9 E162 drop heights to be calculated by interpolating between two drop heights. The idealized prototype had a 150- length; the drop was a 1 (vertical) to 2 (horizontal) slope. This slope was chosen for ease of construction. The horizontal length of the culvert s mild part continued down to complete the 150- culvert length. The mild section was built with a slope of 1% and the models were made to a 1:20 scale. The dimensions in the following section are from the prototype culvert. The current practice of not using any energy dissipaters allowed all the energy to flow through the culvert instead of reducing or dissipating it. RESULTS Sills of different heights can be effective in controlling hydraulic jumps. The function of the sill is to ensure the formation of a jump and control its position under open channel (Chow 1959). The occurrence of a hydraulic jump consumes energy, resulting in energy loss or dissipation; hence, analyzing energy dissipation of hydraulic jumps can shed light on the optimal sill and its position. The higher the F r1, the more energy is dissipated by the jump; this occurs because more energy must be dissipated at a higher F r1 to achieve subcritical (F r1 < 1) flow depth. The height of the flow and the inflow F r1 allow the prediction of which hydraulic jump inducement system would be necessary. Table 1 shows the prototype culvert dimensions for 6-, 12-, 18-, 24-, and 30- culvert drops. Information for this table as well as Tables 2 and 3 used data from Tyagi et al. (2014, 2013, 2012, 2010, 2009). The results of this study provide some insight about factors limiting hydraulic jumps through BBCs, with the focus on velocity limitations, high total hydraulic head losses, and hydraulic jump efficiency for different drops in BBCs. Relationships between hydraulic jump characteristics were developed. From these dimensionless relationships, considering the relative drop height and efficiency of hydraulic jump and relative sill height and relative sill location, any drops that are not included in the research can be interpolated for a best first guess. Also, middle sill height, end sill height, sill location, and efficiency for any drops between 6 and 30 may be predicted. The following discussion presents the relationships between characteristics of the jumps. Under pressure flow, determining the correct sill height and location was accomplished by many trials. Under the three stated flow conditions (0.8 d, 1.0 d, and 1.2 d), it was difficult to find the correct sill height that would induce a jump for all three. Sometimes in the model, a difference of 0.5 in. would cause the entire barrel to flood in the 1.2 d condition and cause a sky jump in the 0.8 d condition. A sky jump was formed when the tail water was lower than the permissible lower limit; the incoming velocity jet sweeps out and the rollers do not form but instead move to the surface, causing little dissipation of energy. That is why it was important to exhaust all options in finding the correct placement. All values listed in this section are dimensionless. As shown in Figure 5, the F r1 increased from 1.8 to 4.6 over the relative drop height difference of 0.6 to 3. Other than the 18- drop data point, the rest of the data show a consistent increase in F r1 to relative drop height. The data point could be an inconsistency in the reading; these experiments were completed over several years and not tested at the same time. In Figure 6 it is seen that the efficiency drops from 0.95 to 0.63 over the relative drop heights. The trend is consistently down, although there is enough variation in efficiency points that it cannot be determined by a linear expression. If the point at the 18- drop location were removed or retested, it may resemble an exponentially decreasing horizontal asymptotic curve. The relationship of the relative energy loss observed in Figure 7 increases from 0.04 to It slightly dips from 0.96 to 0.93 from the relative drop heights of 1.2 d to 1.8 d, respectively. In Figure 8, the relative THL increases almost linearly with respect to relative drop height from 0.32 to 2.79 with respect to the relative drops. This should be expected because THL is mostly affected by the elevation. Figure 9 shows the relationship between the relative sill height and the relative drop height. The diagram illustrates an exponential increase from 0.22 to 0.5 until the 2.4 relative drop height point, then it drops again to In the upward-moving portions of the graph, the sill was raised with each drop height, creating a sufficient hydraulic jump; however, as drop height increased, so did the pressure on the top of the culvert model because of the hydraulic jump. In the case of the 3.0 relative drop, the pressure created by a sill of the same height or taller than the 0.5 relative sill height caused the hydraulic jump to be drowned, which flooded the model. A shorter sill was needed to reduce the amount of pressure created inside the model to allow for proper hydraulic jump formation. Figure 10 shows the relationship between relative sill distance from the end of the culvert and relative sill height. The shape of the graph creates an S-curve starting at 0.28, increases to 0.59, drops to 0.17, and then increases again to SUMMARY AND CONCLUSIONS Formation of a hydraulic jump was used in reducing downstream degradation of BBCs. A BBC is used in areas of high relief and steep topography because it has one or more breaks in the profile slope. The advantage of a culvert is that it allows water to safely pass underneath roadways constructed in hilly topography or on the side of a relatively steep hill. A laboratory model was constructed to represent a 150- BBC. The focus of this research was to evaluate existing BBCs for their effectiveness and for use in the design of new culverts. The evaluation process determined which BBC and sill combination was needed for energy reduction. The concept of energy dissipation has been examined and evaluated in different drops of BBCs. The best method found in this research was to induce a hydraulic jump by way of a sill placed inside the culvert. Data were compiled from several studies on different BBC drop heights. Recommended research for the future should include (1) a computer model for energy dissipation in BBCs for drops of 6 to 30, (2) a numerical model for energy dissipation in BBCs for drops of 6 to 30, and (3) a guidance document on energy dissipation in BBCs for drops up to 30. The data in this research were used to develop a series of dimensionless tables and figures to show the relationship between drop height compared with F r1, efficiency, energy loss, THL, sill height, and sill location. From this research, the following conclusions can be drawn.

10 E163 As relative drop height increases, so does the F r1. As relative drop height increases, efficiency decreases. Overall, energy loss increases with relative drop height. There is a near-linear increase between relative drop height and THL. As relative drop height increases, the sill height increases until it reaches the 2.4 relative drop. It decreases thereaer to the 3.0 relative drop height. The relationship between relative drop height and sill location is variable. ACKNOWLEDGMENT This project was funded by the Federal Highway Administration and sponsored by the Oklahoma Department of Transportation. The authors thank Robert Rusch, bridge division engineer, Oklahoma Department of Transportation, for his active participation in incorporating ideas to make this research more practical to field conditions. In addition, the authors thank Sherry Hunt and Kem Kadavy, hydraulic engineers of the US Department of Agriculture and Agricultural Research Service, who each contributed their ideas in the early stages of this project regarding ways to improve physical construction of the model, as well as students James Brown, Nicholas Johnson, Abdul-sahib Al-madhhachi, Joe Large, Sonal Patil, Marizel Rios Motte, and Taylor Davis whose assistance during some of the project phases and contributions to the research and data collection is greatly appreciated. ENDNOTE 1 Two-dimensional Side-Looking Micro-Acoustic Doppler Velocimeter, SonTek, San Diego, Calif. ABOUT THE AUTHORS Avdhesh K. Tyagi (to whom correspondence may be addressed) is a professor and director of the Oklahoma Infrastructure Consortium, School of Civil and Environmental Engineering, Oklahoma State University (OSU), Stillwater, OK USA; tyagi@ okstate.edu. He has worked in the water resources engineering area at OSU for 35 years. He has also taught at the University of Arizona and the University of Kansas. Tyagi received his doctorate degree from the University of California, Berkeley. Abdelfatah Ali and Matthew Hamilton are research associates at OSU. PEER REVIEW Date of submission: 12/22/2014 Date of acceptance: 09/21/2015 REFERENCES Alikhani, A.; Behrozi-Rad, R.; & Fathi-Maghadam, M., Hydraulic Jump in Stilling Basin With Vertical End Sill. International Journal of Physical Sciences, 5:1:25. Chamani, M.; Rajaratnam, N.; & Beirami, M.K., Turbulent Jet Energy Dissipation at Vertical Drops. Journal of Hydraulic Engineering, 134:10: Chanson, H., Acoustic Doppler Velocimetry (ADV) in the Field and in Laboratory: Practical Experiences. International Meeting on Measurements and Hydraulics of Sewers. n060chanson_revu.pdf (accessed Dec. 16, 2015). Chow, V.T., Open-Channel Hydraulics. McGraw-Hill, New York. Hotchkiss, R.; Flanagan, P.; & Donahoo, K., Hydraulic Jumps in Broken-Back Culverts. Transportation Research Record, 1851:35. org/ / Larson, E., Energy Dissipation in Culverts by Forcing a Hydraulic Jump at the Outlet. Master s thesis, Department of Civil and Environmental Engineering, Washington State University. Lowe, N.; Hotchkiss, R.; & Nelson, J., Theoretical Determination of Sequent Depths in Closed Conduits. Journal of Irrigation and Drainage Engineering, 137:12: Mignot, E. & Cienfuegos, R., Energy Dissipation and Turbulent Production in Weak Hydraulic Jumps. Journal of Hydraulic Engineering, 136:2: dx.doi.org/ /(asce)hy Ohtsu, I.; Yasuda, Y.; & Hashiba, H., Incipient Jump Conditions for Flows Over a Vertical Sill. Journal of Hydraulic Engineering, 122:8: org/ /(asce) (1996)122:8(465). SonTek/YSI Inc., ADVField/Hydra System Manual. edu/soware/instruments/sontek/adv_instruments/advmanual.pdf (accessed Dec. 11, 2015). Tyagi, A.K.; Ali, A.; Johnson, N.; & Hamilton, M., Energy Dissipation in Thirty- Foot Broken-back Culverts Laboratory Models Phase V. Oklahoma Department of Transportation, Stillwater, Okla. Tyagi, A.K.; Ali, A.; Johnson, N.; & Hamilton, M., Energy Dissipation in Twelve-Foot Broken-Back Culverts Laboratory Models Phase IV. Oklahoma Department of Transportation, Stillwater, Okla. Tyagi, A.K.; Ali, A.; Johnson, N.; Motte, M.; & Davis, T., Energy Dissipation in Eighteen-Foot Broken-Back Culverts Laboratory Models Phase III. Oklahoma Department of Transportation, Stillwater, Okla. Tyagi, A.K.; Veenstra, J.; Brown, J.; Ali, A.; & Johnson, N., Laboratory Modeling of Energy Dissipation in Broken-Back Culverts Phase II. Oklahoma Transportation Center, Stillwater, Okla. Tyagi, A.K., A Prioritizing Methodology for Scour-Critical Culverts in Oklahoma. Oklahoma Transportation Center, Stillwater, Okla. Tyagi, A.K.; Brown J.; Al-Madhhachi, A.; Large, A.; Ali, A.; & Patil, S., Laboratory Modeling of Energy Dissipation in Broken-Back Culverts Phase I. Oklahoma Transportation Center, Stillwater, Okla. US Department of Transportation, Federal Highway Administration, Hydraulic Design of Energy Dissipators for Culverts and Channels. Thompson, P.L. & Kilgore, R.T. Hydraulic Engineering Circular No. 14, third ed. FHWA-NHI HEC hydraulics/pubs/06086/hec14.pdf (accessed Dec. 14, 2015). SUGGESTED READING Goring, D. & Nikora, V., Despiking Acoustic Doppler Velocimeter Data. Journal of Hydraulic Engineering, 128:1: (ASCE) (2002)128:1(117). Lowe, N.; Hotchkiss, R.; & Nelson, J., Air Entrainment and Sequent Depths in Horizontal Closed Conduits. World Environmental and Water Resources Congress 2010, ASCE: