# Occlusion in Bottom Intakes with Circular Bars by Flow with Gravel-Sized Sediment. An Experimental Study

^{1}

^{2}

^{*}

## Abstract

**:**

_{50}, is close to the spacing between the bars. An experimental campaign including 24 tests, each repeated time times, with six different longitudinal slopes from 0 to 35% and four different specific incoming flow rates, q

_{1}, in the range of 0.115 to 0.198 m

^{3}/s/m, is presented. The results show the inefficiency of circular profiles in comparison with T-shaped bars. No important influence of rack slope is found that could help to reduce clogging. This works confirms the importance of the selection of bar profile to reduce maintenance labor. A comparison of results with previous works with gravel sediment in T-shaped bars is considered. A methodology to calculate the wetted rack length considering occlusion due to flow with sediment transport is proposed, and the results are compared with those in the bibliography.

## 1. Introduction

^{3}/s from the Mazar River and 3.0 m

^{3}/s from the Pindilig River [3]. Maintenance works at San Antonio SPH become necessary as parts of the trash rack are obstructed by wedged stones, leaves, or branches, meaning that the collection of the minimum amount of water through the bottom rack can no longer be ensured. This situation is shown in Figure 2.

_{1}; their width, b

_{w}; the longitudinal slope; and the bar profile adopted. The optimum bar profiles differ when dealing with clear water as compared to when transported sediments are included. In the latter situation, clogging needs to be considered in order to minimize maintenance and operation labor. This has been stated by several authors [1,2,5,6,7]. The optimum bar profiles are presented in Figure 3. This figure presents the optimum profiles for, on the one hand, maximizing derived flow without considering sediments (Figure 3a) [5,8,9], and on the other, minimizing the sediment trapped in the slits of the bars (Figure 3b) as suggested in Reference [2] and the present work. It can be observed that some of the optimum profiles in the case of clear water diversion are less efficient in the case of sediment transport. This fact is related to the length of contact between embedded gravels and profiles. Figure 3c presents how rounded profiles with a higher radius, such as circular bars, present a larger length of gravel–bar contact than other crest-rounded bars with a lower radius, which are more efficient. The length of gravel–bar contact is proportional to the drag force needed to remove gravels embedded in the slit between two bars. Conversely, Brunella et al. [10] conducted an experimental work for clear water diversion with circular profiles and recommended those to avoid clogging. This contrasts with other authors’ experiences [2,6]. No experimental measurements were found related to circular bar profiles in bottom intakes considering sediment transport.

_{1}; longitudinal rack slope, tanθ; or rack length to take into account clogging and/or the consideration of an obstruction factor. As an example, the equation proposed by Krochin [6] to calculate the wetted rack length to derive an incoming flow includes an obstruction coefficient to take into account occlusion in the bottom intake design:

_{1}is the incoming flow; C

_{q}is the discharge coefficient; k is the obstruction parameter defined as $k=\left(1-f\right)m;$ m is the void ratio, which is calculated as the void area divided by the total area of the rack; and f is the percentage of rack that is considered to be occluded (Krochin recommended adopting a value between 0.15 and 0.30).

_{50}, of 22.0 mm, and with four different incoming flows and six longitudinal rack slopes. The analysis of clogging effects in the diverted flow and a comparison of the results with those presented previously using T-shaped bars by Castillo et al. [7] are included. The methodology to calculate the length of rack needed to consider the clogging phenomenon is also included and compared with literature recommendations such as those of Krochin [6] and Drobir [5].

## 2. Experimental Setting

#### 2.1. Physical Device

^{3}/s/m to assure that the gravels were transported by the flow. The inlet total flow was measured with an Promag 53-W electromagnetic flowmeter of 125 mm (Endress Häuser, Reinach, Basel, Swizterland) with an accuracy of 0.5%. Tests were performed with six different longitudinal rack slopes. In all cases, the approximation flow regime was subcritical, changing to supercritical near the bottom racks. Further details of the model can be found in References [7,16,17,18,22]. The rejected flow was measured by a 90-degree V-notch weir.

#### 2.2. Sediment Experimental Tests with Racks Made of Circular Bars (m = 0.28)

_{50}= 22.0 mm (the sieve curve is almost uniform) and which presented rounded faces. At the coarse part of the sieve curve, d

_{90}= 35 mm and d

_{max}= 40 mm. At the finest part, d

_{min}= 10 mm, while d

_{10}= 16 mm. Considering the spacing between bars, b

_{1}= 11.7 mm, few materials will go through the rack for the tested gravel. Zingg’s shape classification [18] for this gravel is presented in Table 3.

_{1}= 114.6, 138.3, 155.5, and 198.0 l/s/m) and six rack slopes (tanθ = 0%, 10%, 20%, 30%, 33%, and 35%) were tested. Twenty-four tests, with each test repeated three times, were conducted in the laboratory.

_{1}= 114.6 and 138.3 l/s/m, the duration of the test was approximately 12 min, whilst for the high flow rates the duration of the test was approximately 8 min. At the end of each test, the solid weight of each of the three parts (derived, rejected, and trapped sediment) was quantified. Gravels were drained for a period of 30 min before being weighed.

#### 2.3. Previous Studies of T-Shaped Bottom Rack Occlusion by Flow with Gravel-Sized Sediment

_{50}: 8.3 mm (gravel 1), 14.8 mm (gravel 2), and 22.0 mm (gravel 3). The first type of gravel was tested with a T-shaped flat rack with a void ratio of m = 0.22, while the two remaining types of gravel were used for the T-shaped flat bar with m = 0.28. They were tested with three incoming flows (114.6, 138.3, and 155.5 l/s/m) and five different slopes (0%, 10%, 20%, 30%, and 33%). Further details about that study can be obtained in References [7,18]. As a result of the experiments in the laboratory, the following was obtained:

- Reduced void ratio according to rack occlusion, termed the effective void ratio, m’.
- Visualization of preferential occlusion area related to the streamline curvature.
- The most efficient longitudinal rack slope, which in T-shaped bars was 30%.
- Finally, a methodology was proposed to obtain the wetted rack length, taking into account the sediment transport and occlusion as well as its comparison with the lengths proposed by Krochin [6].

_{50}= 14.8 mm and 22.0 mm, respectively.

#### 2.4. Methodology to Define the Effective Void Ratio

_{qH}is the discharge coefficient; H

_{0}is the energy at the beginning of the rack considered equal to the minimum energy; θ is the angle of the rack with horizontal; and h

_{c}is the critical depth (Figure 5). The numerical computation interval for x is 0.05 m, until it reaches the total rack length of 0.90 m.

_{1}m; and the wetted rack length in the slit of two bars, considering the effective void ratio, L

_{1}m′. m′ denotes the effective void ratio that takes into account the reduction of the original void ratio due to the occlusion of the rack as a result of gravel deposition.

## 3. Results and Discussion

#### 3.1. Sediment Tests with Circular Bars

#### 3.1.1. Deposition of Gravels over Racks

_{1}− q

_{2})/q

_{1}, which is the percentage of the derived flow. The values for the clear water case are also included. In Figure 6, it can be observed that the increase in the slope does not suppose a remarkable increase in the efficiency, as was expected in view of the results of other racks, such as those with T-shaped bars [7]. In the case of racks made with circular bars, the adopted form between two bars enabled the possibility that gravels of sizes even larger than the space between bars can be embedded (Figure 3c). Moreover, the surface of the gravel–bar contact reached when gravel was trapped was greater than that in other bar types. This means that the drag force exerted by the water to prevent the deposition of gravel was not high, enough even with large longitudinal slopes such as 35%. The difference between the percentage of derived flow from the lowest and the highest slope adopted in the laboratory facility was in a range of 6% for q

_{1}= 138.3 l/s/m, and 11% for q

_{1}= 198.0 l/s/m. These values are also summarized in Table 4, which presents the mean value of the three tests for each case. In this table, the efficiency is also shown to decrease with the increase in the incoming flow as the rack has a constant length of 0.90 m.

#### 3.1.2. Effective Void Ratio

#### 3.2. Relation between Hydraulic Parameters at the Beginning of the Rack with Ratio m’/m

_{0}is the velocity at the beginning of the rack; d

_{50}the median diameter of the gravels; υ the kinematic viscosity of the water; ρ the density of the water; and C

_{D}is the drag coefficient of the gravel that adopts the value of 0.45.

_{D}

_{0}, the velocity was proposed to be used to calculate the m′/m ratio, as the velocity can be obtained in an easier way in practice. Garcia et al. [23] proposed a relation between the incoming flow and the initial flow depth, h

_{0}. Once the velocity at the beginning of the rack can be calculated from the incoming flow, the reduction of the void ratio can be obtained, which supposes a useful relation that can be used in the design of bottom intake systems.

_{0}, we used measurements previously reported in Garcia et al. [23], wherein the relation ${h}_{0}=a\left({q}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)$ was achieved for each longitudinal slope. Taking into account that ${h}_{c}={\left(q/\sqrt{g}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$, the previous relation can be presented as $\frac{{h}_{0}}{{h}_{c}}=a\left({\sqrt{g}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)$. Values of $\frac{{h}_{0}}{{h}_{c}}$ are presented in the case of circular bars and the void ratio m = 0.28 is employed for several longitudinal slopes. A linear regression is proposed in Figure 15 and collected in Equation (4) that relates $\frac{{h}_{0}}{{h}_{c}}$ to the longitudinal rack slope, with a correlation coefficient of R

^{2}= 0.85. Once $\frac{{h}_{0}}{{h}_{c}}$ is calculated, we can obtain U

_{0}from the equation ${U}_{0}=q/\left[{\left(q/\sqrt{g}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{(\frac{{h}_{0}}{{h}_{c}})}_{regression}\right]$.

#### 3.3. Comparison of Occlusion in Racks with Circular and T-Shaped Flat Bars

_{50}= 14.80 mm with fractured faces material (named gravel 2) or a grain size of d

_{50}= 22.00 mm with rounded faces (named gravel 3). In the present work, the same gravel with d

_{50}= 22.00 mm was used. Efficiencies are presented in Figure 16, and it can be seen that the highest percentage of derived flow in each case corresponds to the tests carried out with the T-shaped bars, while the lowest values are presented with the circular bar test. It can be observed that in terms of flow derivation capacity between the racks with circular bars and those with T-shaped bars, the circular bars presented the lowest efficiency. The values presented in Castillo et al. [7] were reviewed in the case of gravel with a grain size of d

_{50}= 14.80 mm.

_{1}= 138.3 l/s/m in Figure 18. It can be observed that this quantity was higher in the case of circular bars, which makes maintenance more difficult.

#### 3.4. Methodology to Calculate the Effective Wetted Rack Length, Lm’, for the Design of Bottom Intakes Considering the Gravel-Sized Sediments

_{0}, which can be calculated as explained in Section 3.2.

_{50c}is the diameter that corresponds to the smallest of the three axes of the ellipsoid, which represents 50% of the weight of the gravels embedded in the rack at the end of each test; W is the mean weight of the materials embedded in the rack. The values of these parameters in the case of circular bars were d

_{50c}= 19.5 mm and W = 10.2 g. The correlation coefficients of Equations (6) and (7) were 0.85 and 0.71, respectively.

- Calculate L
_{1}m, the wetted rack length in the slit of two bars, considering the initial void ratio, m, by using Equation (2) coupled with Equation (3) in the case of circular bars or with Equation (8) in the case of T-shaped bars [17]:$$\text{}{C}_{qH}\approx \frac{0.58{e}^{-0.75\left(\frac{x}{{h}_{c}}m\right)}}{\left(1+0.9tg\theta \right)};\text{}$$ - Calculate the effective void ratio from the proposed Equations (6) and (7) depending on the rack slope and velocity at the beginning of the rack, U
_{0}; - Calculate L
_{1}m′, the wetted rack length in the slit of two bars, considering the effective void ratio that takes into account the clogging effects obtained, m, by using Equation (2) coupled with Equation (3) in the case of circular bars, or with Equation (8) in the case of T-shaped bars; - Calculate Lm, i.e., the wetted rack length over a bar using the methodology of Garcia et al. [23].$$\text{}Lm=\frac{q}{\overline{{C}_{qH}}m\sqrt{2g{H}_{min}}},\text{}$$$$\text{}\overline{{C}_{qH}}=\frac{am{C}_{q0}}{\left(1+tan\theta \right)}{q}^{b},\text{}$$
_{min}is the minimum energy head calculated as 1.5 h_{c}, with h_{c}being the critical depth in reference to the plane of the rack. Constants a and b in the case of the void ratio m = 0.28 adopted the values 1.45 and 0.05, respectively, in the case of circular bars, and 1.50 and 0.05 in the case of T-shaped bars [23]. Figure 5 presents the scheme of the different lengths described.

_{c}of 11.30 and 9.5, respectively). The effective wetted rack lengths show that circular bars are less effective than T-shaped bars for the same gravel tests in the case of 30% slope, considered as the recommended design slope. Depending on the incoming flow to the rack, we can also conclude that lengths are near to the length proposed by Krochin [6] with f = 30%, or near to the value of f = 15% for higher incoming flows.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Notations

a, b | constant of adjustment depending on the shape of bars and the space between them in Equation (10) |

b_{1} | space between bars |

b_{w} | bar width |

C_{D} | drag coefficient of gravels |

$\overline{{C}_{qH}}$ | mean discharge coefficient for energy head |

C_{qH} | discharge coefficient for flow depth |

C_{q}_{0} | static discharge coefficient |

d_{50}, d_{90}, d_{10}, d_{min}, d_{max}, d_{50c} | characteristic diameters of gravels |

f | percentage of rack occluded |

g | gravitational acceleration |

H_{0} | energy head at the beginning of the rack in reference to the rack plane |

H_{min} | minimum energy head obtained when the Froude number equals the unity, and there is critical depth |

h_{c} | critical depth |

h_{0} | flow depth at the beginning of the rack |

k | obstruction parameter defined as k = (1 − f) m |

Lm | wetted rack length |

Lm′ | effective wetted rack length considering rack occlusion |

L_{1}m | wetted rack length in the slit of two bars, considering the initial void ratio |

L_{1}m′ | wetted rack length in the slit of two bars, considering the effective void ratio |

m | void ratio |

m’ | effective void ratio considering rack occlusion |

q_{1}, q_{2} | specific approaching and rejected flow, respectively |

U | mean velocity of the flow over the rack |

U_{0} | mean velocity of the flow at the beginning of the rack |

W | mean weight of the gravels deposited over the racks |

x | longitudinal coordinate along the rack |

υ | kinematic viscosity of water |

ρ | density of water |

θ | angle of the rack plane with the horizontal |

${F}_{D0}$ | drag force |

R_{e}_{0} | Reynolds number calculated at the beginning of the rack |

## References

- Lauterjung, H.; Schmidt, G. Planning of water intake structures for irrigation or hydropower. A Publication of GTZ-Postharvest Project. In Deutsche Gesellschaft für Technische Zusammenarbeit (GTZ) GmbH; GTZ: Bonn, Germany, 1989. [Google Scholar]
- Andaroodi, M.; Schleiss, A. Standardization of Civil Engineering Works of Small High-Head Hydropower Plants and Development of an Optimization Tool (No. LCH-BOOK-2008-026); EPFL-LCH: Lausanne, Switzerland, 2006. [Google Scholar]
- CELEC EP. Proyecto Mazar-Dudas (2003). Available online: https://www.celec.gob.ec/hidroazogues/proyecto (accessed on 6 July 2018).
- PROAGRO, Programa de Desarrollo Agropecuario Sustentable. Tirolesas Serie de Investigación Aplicada N
^{o}1 Criterios de Diseño y Construcción de Obras de Captación para Riego—PDF (2010). Available online: https://docplayer.es/20552716-Tirolesas-serie-de-investigacion-aplicada-no-1-criterios-de-diseno-y-construccion-de-obras-de-captacion-para-riego.html (accessed on 6 July 2018). (In Spanish). - Drobir, H. Entwurf von wasserfassungen im hochgebirge. Österr. Wasserwirtschaft
**1981**, 33, 243–253. [Google Scholar] - Krochin, S. Diseño Hidráulico; Escuela Politécnica Nacional: Quito, Ecuador, 1978. (In Spanish) [Google Scholar]
- Castillo, L.G.; García, J.T.; Carrillo, J.M. Experimental and numerical study of bottom rack occlusion by flow with gravel-sized sediment. Application to ephemeral streams in semi-arid regions. Water
**2016**, 8, 166. [Google Scholar] [CrossRef] - Frank, J.; Von Obering, E. Hydraulische untersuchungen für das tiroler wehr. Bauingenieur
**1956**, 31, 96–101. (In German) [Google Scholar] - Frank, J. Fortschritte in der hydraulic des sohlenrechens. Bauingenieur
**1959**, 34, 12–18. (In German) [Google Scholar] - Brunella, S.; Hager, W.; Minor, H. Hydraulics of bottom rack intake. J. Hydraul. Eng.
**2003**, 129, 2–10. [Google Scholar] [CrossRef] - Ract-Madoux, M.; Bouvard, M.; Molbert, J.; Zumstein, J. Quelques réalisations récentes de prises en-dessous à haute altitude en Savoie. La Houille Blanche
**1955**, 6, 852–878. (In French) [Google Scholar] [CrossRef] - White, J.K.; Charlton, J.A.; Ramsay, C.A.W. On the design of bottom intakes for diverting stream flows. In Proceedings of the Institution of Civil Engineers; ICE Publishing: London, UK, 1972; Volume 51, pp. 337–345. [Google Scholar]
- Simmler, H. Konstruktiver Wasserbau; Technische Universität Graz, Institut für Wasserwirtschaft und konstruktiven Wasserbau: Graz, Austria, 1978. (In German) [Google Scholar]
- Bouvard, M. Mobile Barrages & Intakes on Sediment Transporting Rivers; International Association of Hydraulic Engineering and Research (IAHR) Monograph: Rotterdam, The Netherlands, 1992. [Google Scholar]
- Raudkivi, A.J. Hydraulic Structures Design Manual; International Association of Hydraulic Engineering and Research (IAHR): Rotterdam, The Netherlands, 1993; pp. 92–105. [Google Scholar]
- Carrillo, J.M.; García, J.T.; Castillo, L.G. Experimental and numerical modelling of bottom intake racks with circular bars. Water
**2018**, 10, 605. [Google Scholar] [CrossRef] - Castillo, L.G.; García, J.T.; Carrillo, J.M. Influence of rack slope and approaching conditions in bottom intake systems. Water
**2017**, 9, 65. [Google Scholar] [CrossRef] - García, J.T. Estudio Experimental y Numérico de los Sistemas de Captación de Fondo. Doctoral These, Universidad Politécnica de Cartagena, Cartagena, Spain, 2016. (In Spanish). [Google Scholar]
- Ahmad, Z.; Kumar, S. Estimation of trapped sediment load into a trench weir. In Proceedings of the 11th International Symposium on River Sedimentation, University of Stellenbosch, Stellenbosh, South Africa, 6–9 September 2010; pp. 1–9. [Google Scholar]
- Bina, K.; Saghi, H. Experimental study of discharge coefficient and trapping ratio in mesh-panel bottom rack for sediment and non-sediment flow and supercritical approaching conditions. Exp. Therm. Fluid Sci.
**2017**, 88, 171–186. [Google Scholar] [CrossRef] - Noseda, G. Correnti permanenti con portata progressivamente decrescente, defluenti su griglie di fondo. Ricerca sperimentale. L’ Energia Elettrica
**1956**, 6-June, 565–581. (In Italian) [Google Scholar] - Carrillo, J.M.; Castillo, L.G.; García, J.T.; Sordo-Ward, A. Considerations for the design of bottom intake systems. J. Hydroinf.
**2018**, 20, 232–245. [Google Scholar] [CrossRef] - García, J.T.; Carrillo, J.; Castillo, L.G.; Haro, P.L. Empirical, dimensional and inspectional analysis in the design of bottom intake racks. Water
**2018**, 10, 1035. [Google Scholar] [CrossRef] - Castillo, L.G.; García, J.T.; Haro, P.; Carrillo, J.M. Rack length in bottom intake systems. Int. J. Environ. Impacts
**2018**, 1, 279–287. [Google Scholar] [CrossRef] - Drobir, H.; Kienberger, V.; Krouzecky, N. The wetted rack length of the tyrolean weir. In Proceedings of the IAHR-28th Congress, Graz, Austria, 22–27 August 1999. [Google Scholar]

**Figure 1.**Mountain River at Sincholagua Paramo, Ecuador, approximately 4000 meters above sea level, MASL. (

**a**) Type of solids transported by the river; (

**b**) location in Ecuador (without scale).

**Figure 2.**Mazar–Dudas Hydroelectric Project: (

**a**) San Antonio bottom rack intake embedded in a weir—cleaning tasks and repairing process after a flood in the Mazar River, Ecuador (Image courtesy of Corporación Hidroeléctrica del Ecuador-CELEC EP Hidroazogues) [3]; (

**b**) project location in Ecuador (without scale).

**Figure 3.**Scheme of optimum bar profiles: (

**a**) clear water flow; (

**b**) flow with sediments; (

**c**) comprehensive sketch to visualize the influence of the profile radius on the length of gravel–bar contact.

**Figure 6.**Percentage of derived flow for a specific inlet flow: (

**a**) 114.6 l/s/m; (

**b**) 138.3 l/s/m; (

**c**) 155.5 l/s/m; (

**d**) 198.0 l/s/m.

**Figure 7.**Top view of occluded bottom racks with circular bars for m = 0.28, q

_{1}= 138.3 l/s/m, and diverse longitudinal slopes: (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; (

**d**) 30%; (

**e**) 33%; and (

**f**) 35%.

**Figure 8.**Top view of occluded bottom racks with circular bars for m = 0.60, dividing the rack into four parts, with the void ratio calculated from occluded areas: (

**a**) q

_{1}= 155.5 l/s/m and 10% longitudinal slope and (

**b**) q

_{1}= 198.0 l/s/m and 35% longitudinal slope.

**Figure 9.**Flow over the occluded circular bars bottom rack and formation of wakes for rack slopes: (

**a**) 20%; (

**b**) 30%.

**Figure 11.**Water profiles over the rack measured in the laboratory and calculated for q

_{1}= 138.3 l/s/m and slopes (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; and (

**d**) 30%.

**Figure 12.**Water profiles over the rack measured in the laboratory and calculated for q

_{1}= 155.5 l/s/m and slopes (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; and (

**d**) 30%.

**Figure 13.**Water profiles over the rack measured in the laboratory and calculated for q

_{1}= 198.0 l/s/m and slopes (

**a**) 0%; (

**b**) 10%; (

**c**) 20%; and (

**d**) 30%.

**Figure 14.**Velocity at the beginning of the rack, U

_{0}, as a function of the ratio between the effective and the initial void ratios, m’/m.

**Figure 16.**Comparison between percentage of derived flow for bottom racks with T-shaped bars (gravel 2 and gravel 3) and circular bars (gravel 3) for specific inlet flows: (

**a**) 114.6 l/s/m; (

**b**) 138.3 l/s/m; and (

**c**) 155.5 l/s/m.

**Figure 17.**Comparison of effective void ratio, m′, for circular bars and values previously presented for T-shaped bars [7]. All cases have a void ratio of m = 0.28.

**Figure 18.**Comparison of effective void ratio, m′, for circular bars and values previously presented for T-shaped bars [7].

**Figure 19.**Linear adjustment of the ratio m′/m ratio as a function of the values U

_{0}, d

_{50c}/b

_{1}, and W.

**Figure 20.**Calculated rack length necessary to derive the total incoming flow when sediment transport is presented for different rack slopes.

Author | Bar Space, b_{1}(m) | Longitudinal Rack Slope (%) | Increment of Rack Length (%) | Obstruction Factor (%) | Bar Profile |
---|---|---|---|---|---|

Ract-Madoux et al. [11] | 0.100 | 20 | – | – | Thick trapezoidal, rail-type, round head (next to circular) |

White et al. [12] | 0.030–0.076 | 20 | – | – | Prismatic heptagon |

Krochin [6] | 0.020–0.060 | 20 | – | 0.15–0.30 | Prismatic |

Simmler [13], Drobir [5] | 0.150 (d_{95} = 0.060) | 20–30 | 0.50–1.00 | – | Several rounded profiles (next to circular) |

Lauterjung and Schmidt [1] | – | 9–70 | 0.20 | – | Same as Reference [13] |

Bouvard [14] | 0.100–0.120/0.002–0.03 SHP | 30–60 | 0.50–1.00 | – | Same as Reference [11] |

Raudkivi [15] | >0.005 | 20 | – | – | Trapezoidal, inverted railway tracks |

Andaroodi and Schleiss [2] | 0.020–0.040 SHP | 84–100 | 0.20 | – | Bulb-ended, round head |

Castillo et al. [7], Carrillo et al. [16], Castillo et al. [17], García [18] | 0.006–0.045 | 30 | – | 0.30 | T-shaped |

_{95}is the diameter where 95% percent of the distribution has smaller particle size.

Description | Rack Length (m) | Rack Width (m) | Bar Type (mm) | Width of the Bars, b_{w} (mm) | Direction of the Bars | Spacing between Bars, b_{1} (mm) | Void Ratio $\text{}\mathit{m}=\frac{{\mathit{b}}_{1}}{{\mathit{b}}_{1}+{\mathit{b}}_{\mathit{w}}}\text{}$ | Longitudinal Slope (%) |
---|---|---|---|---|---|---|---|---|

Present work | 0.90 | 0.50 | O30/30 | 30 | Longitudinal | 11.7 | 0.28 | 0, 10, 20, 30, 33, and 35 |

Previous works [7] | 0.90 | 0.50 | T30/25/2 | 30 | Longitudinal | 8.5 | 0.22 | 0, 10, 20, 30, and 33 |

T30/25/2 | 11.7 | 0.28 |

d_{50} (mm) | Blade | Disc | Rod | Sphere |
---|---|---|---|---|

22.0 | 8% | 30% | 19% | 43% |

Incoming Flow (l/s/m) | Percentage of Derived Flow (%) | |||||
---|---|---|---|---|---|---|

Longitudinal Slope (%) | ||||||

0 | 10 | 20 | 30 | 33 | 35 | |

114.6 | 76 | 77 | 78 | 81 | 80 | 84 |

138.3 | 69 | 71 | 74 | 76 | 76 | 75 |

155.5 | 64 | 68 | 71 | 73 | 72 | 74 |

198.0 | 56 | 62 | 66 | 67 | 67 | 67 |

Incoming Flow (l/s/m) | Effective Void Ratio | |||||
---|---|---|---|---|---|---|

Longitudinal Slope (%) | ||||||

0 | 10 | 20 | 30 | 33 | 35 | |

114.6 | 0.070 | 0.069 | 0.069 | 0.073 | 0.073 | 0.077 |

138.3 | 0.071 | 0.073 | 0.077 | 0.079 | 0.080 | 0.078 |

155.5 | 0.071 | 0.075 | 0.079 | 0.083 | 0.083 | 0.085 |

198.0 | 0.072 | 0.080 | 0.088 | 0.091 | 0.092 | 0.092 |

**Table 6.**Summary of lengths calculated to obtain the effective wetted rack length considering gravel-sized sediments.

Case | q_{1} (m^{3}/s/m) | L_{1}m (m) | L_{1}m′ (m) | Lm (m) | Lm − L_{1}m (m) | Lm − L_{1}m + L_{1}m′ (m) | Lm′/h_{c} (m) |
---|---|---|---|---|---|---|---|

T-shaped bars, 10% slope | 0.100 | 0.62 | 1.18 | 0.82 | 0.20 | 1.38 | 13.75 |

0.200 | 1.02 | 1.32 | 1.26 | 0.24 | 1.56 | 9.78 | |

0.300 | 1.32 | 1.72 | 1.62 | 0.30 | 2.02 | 9.66 | |

0.400 | 1.64 | 2.06 | 1.94 | 0.30 | 2.36 | 9.29 | |

0.500 | 1.90 | 2.36 | 2.22 | 0.32 | 2.68 | 9.11 | |

T-shaped bars, 30% slope | 0.100 | 0.66 | 0.94 | 0.97 | 0.31 | 1.25 | 12.45 |

0.200 | 1.08 | 1.08 | 1.49 | 0.41 | 1.49 | 9.34 | |

0.300 | 1.44 | 1.44 | 1.92 | 0.48 | 1.92 | 9.15 | |

0.400 | 1.76 | 1.76 | 2.29 | 0.53 | 2.29 | 9.02 | |

0.500 | 2.04 | 2.04 | 2.63 | 0.59 | 2.63 | 8.92 | |

Circular bars | 0.100 | 0.35 | 1.03 | 0.65 | 0.30 | 1.32 | 13.14 |

0.200 | 0.56 | 1.40 | 0.99 | 0.43 | 1.83 | 11.44 | |

0.300 | 0.74 | 1.66 | 1.28 | 0.54 | 2.20 | 10.49 | |

0.400 | 0.895 | 1.88 | 1.52 | 0.63 | 2.51 | 9.89 | |

0.500 | 1.04 | 2.07 | 1.75 | 0.71 | 2.78 | 9.44 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Garcia, J.T.; Castillo, L.G.; Haro, P.L.; Carrillo, J.M.
Occlusion in Bottom Intakes with Circular Bars by Flow with Gravel-Sized Sediment. An Experimental Study. *Water* **2018**, *10*, 1699.
https://doi.org/10.3390/w10111699

**AMA Style**

Garcia JT, Castillo LG, Haro PL, Carrillo JM.
Occlusion in Bottom Intakes with Circular Bars by Flow with Gravel-Sized Sediment. An Experimental Study. *Water*. 2018; 10(11):1699.
https://doi.org/10.3390/w10111699

**Chicago/Turabian Style**

Garcia, Juan T., Luis G. Castillo, Patricia L. Haro, and Jose M. Carrillo.
2018. "Occlusion in Bottom Intakes with Circular Bars by Flow with Gravel-Sized Sediment. An Experimental Study" *Water* 10, no. 11: 1699.
https://doi.org/10.3390/w10111699