# Effect of Changing the Shape and Size of Inlet Area of Grates on the Hydraulic Efficiency of Urban Rainstorm Drainage Systems

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Dimensional Analysis

_{o}, W

_{o}, H

_{g}, A

_{g})

_{i}/Q), Q is the total discharge, q

_{i}is the intercepted discharge, L

_{o}is the relative grate length (L

_{g}/L), L

_{g}is the length from beginning of flume to the grate position, L is the length of the flume, W

_{o}is the relative grate width (W

_{g}/W), W is the channel width, W

_{g}is the water spread beside every grate, H

_{g}is the relative grate height (h

_{g}/h

_{u}), h

_{g}is the water depth at grate upstream, h

_{u}is the water depth at flume upstream, A

_{g}is the relative grate area (a

_{o}/a

_{g}), a

_{o}is the grate inlet area, a

_{g}is the grate area, g

_{1}, g

_{3}, g

_{5}refers to the grate’s position, and h

_{d}is the water depth at flume downstream.

## 3. Experimental Work

## 4. Results and Discussion

#### 4.1. The Effect of Changing the Grate Shape on the Efficiency of Urban Rainstorm Drainage Systems

#### 4.2. The Effect of Changing the Inlet Area of Grates on the Efficiency of Urban Rainstorm Drainage Systems

#### 4.2.1. The Effect of Changing the Inlet Area of Grates on the Discharge Efficiency

#### 4.2.2. The Effect of Changing the Inlet Area of Grate on the Relative Grate Water Height

#### 4.2.3. Effect of Changing the Inlet Area of Grate on the Relative Water Width

## 5. Prediction of the Discharge Efficiency

_{g}+ 0.134

_{g}is the relative grate area, Q is the flume discharge (L/s), and £ is the system discharge efficiency.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Asfaw, B. Assessment of Storm Water Drainage System in Kemise Town. Master’s Thesis, School of Graduate Studies Addis Ababa Institute of Technology, Addis Ababa University, Addis Ababa, Ethiopia, 2016. [Google Scholar]
- Čarnogurská, M.; Příhoda, M.; Zeleňáková, M.; Lázár, M.; Brestovič, T. Modelling the Profit from Hydropower Plant Energy Generation Using Dimensional Analysis. Pol. J. Environ. Stud.
**2016**, 25, 73–81. [Google Scholar] [CrossRef] - Zeleňáková, M.; Čarnogurská, M.; Slezingr, M.; Słys, D.; Purcz, P. Model based on dimensional analysis for prediction of nitrogen and phosphorus concentrations at the river station Ižkovce, Slovakia. Hydrol. Earth Syst. Sci.
**2013**, 17, 201–209. [Google Scholar] [CrossRef] - AASHTO. A Policy on Geometric Design of Highways and Streets. Task Force on Geometric Design. American Association of State Highway and Transportation Officials. 2001. Available online: https://sjnavarro.files.wordpress.com/2011/08/aashto-2001.pdf (accessed on 15 March 2022).
- Magdi, M.E.Z. The Impacts of Poor Drainage on Road Performance in Khartoum. Int. J. Multidiscip. Sci. Emerg. Res.
**2014**, 3, 901–907. [Google Scholar] - Singh, R.R.; Navpreet, K.; Goyal, E.N. Drainage on roads. Int. J. Prog. Civ. Eng.
**2014**, 1, 2394–4684. [Google Scholar] - Owuama, C.O.; Uja, E.; Kingsley, C.O. Sustainable Drainage System for Road Networking. Int. J. Innov. Manag. Technol.
**2014**, 5, 83–86. [Google Scholar] [CrossRef] - Izzard, C.F. Tentative results on capacity of curb opening inlets, with discussion. Highw. Res. Board
**1950**, 11, 36–54. [Google Scholar] - Mostkow, M.A. Theoretical study of bottom type water intake. Proceeding of Sur le calcul des grilles de prise d’eau, La Houille blanche, Grenoble. 2011, pp. 570–580. Available online: https://doi.org/10.1051/lhb/1957048 (accessed on 15 April 2022).
- Mustafa, Z. An Experimental Investigation of the Hydraulics of Street Inlets. Ph.D. Thesis, University Teknologi Petronas, Seri Iskandar, Malaysia, 2003. [Google Scholar]
- Gahin, H.Ġ. Examination of Grate Inlets within Urban Stormwater Drainage. Master’s Thesis, Istanbul Technical University, Ġstanbul, Turkey, 2006. [Google Scholar]
- Michael, B.; Jianqing, Y. Combined hydraulic and black models for forecasting in urban drainage systems. J. Hydrol. Eng.
**2006**, 11, 589–596. [Google Scholar] - Carvalho, R.F.; Leandro, J.; David, L.M.; Martins, R.; Melo, N. Numerical Research of the Inflow Into Different Gullies Outlets. In Proceedings of the Computing and Control for the Water Industry, Exeter, UK, 5–7 September 2011. [Google Scholar]
- Lopes, P.; Leandro, J.; Carvalho, R.F.; Páscoa, P.; Martins, R. Numerical and experimental investigation of a gully under surcharge conditions. Urban Water J.
**2013**, 13, 468–476. [Google Scholar] [CrossRef] - Sezenöz, B. Numerical Modeling of Continuous Transverse Grates for Hydraulic Efficiency. Master’s Thesis, Middle East Technical University, Ankara, Turkey, 2014. [Google Scholar]
- Manuel, G.; Joan, R.; Beniamino, R.; Eduardo, M. Assessment of inlet efficiency through a 3D simulation: Numerical and experimental comparison. Water Sci. Technol.
**2016**, 74, 1926–1935. [Google Scholar] - Wakif, S.; Sabtu, N. Hydraulic Performance of Vertically Depressed and Non-Depressed Grate. Urban Water J.
**2019**, 16, 554–563. [Google Scholar] [CrossRef] - Cosco, C.; Gómez, M.; Russo, B.; Tellez-Alvarez, J.; Macchione, F.; Costabile, P.; Costanzo, C. Discharge coefficients for specific grated inlets. Influence of the Froude number. Urban Water J.
**2020**, 17, 1–13. [Google Scholar] [CrossRef] - Gómez, M.; Russo, B.; Tellez-Alvarez, J. Experimental investigation to estimate the discharge coefficient of a grate inlet under surcharge conditions. Urban Water J.
**2019**, 16, 85–91. [Google Scholar] [CrossRef] - Guo, S.; Chen, L.; Chen, G.; Zhang, W.; Ma, Y. Experimental Study of the Hydraulic Performance of Continuous Transverse Grates. J. Irrig. Drain. Eng.
**2021**, 147, 06021007. [Google Scholar] [CrossRef] - Aranda, J.; Beneyto, C.; Sánchez-Juny, M.; Bladé, E. Efficient Design of Road Drainage Systems. Water
**2021**, 13, 1661. [Google Scholar] [CrossRef] - Buckingham, E. On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev.
**1914**, 4, 345–376. [Google Scholar] [CrossRef]

**Figure 7.**Relationship between discharge efficiency and passing discharge for different types of grate shapes.

**Figure 10.**Relationship between discharge efficiency and passing discharge for different inlet areas.

**Figure 12.**Relationship between relative water height of grate and relative grate distance for different grate inlet areas at (Q = 1.2 L/s).

**Figure 13.**Relationship between relative grate water height and relative grate distance for different grate inlet areas at (Q = 6.0 L/s).

**Figure 14.**Relationship between relative width and relative grate distance for different grate inlet areas (Q = 1.2 L/s).

**Figure 15.**Relationship between relative width and relative grate distance for different grate inlet areas (Q = 3.3 L/s).

Types of Grate Shape | Shape of Slots | Length of Total Slot (cm) | Width of Slots (cm) | Inlet Area (cm^{2}) | % Inlet Area | Number of Longitudinal Bars | Number of Transverse Bars | Number of Diagonal Bars | (£) from Q (6.0–1.0) L/s |
---|---|---|---|---|---|---|---|---|---|

Grate type (1) | Trapezium | 104.8 | 0.2 | 21 | 27% | 15 | 0 | 0 | 34.4% to 75.5% |

Grate type (2) | Trapezium | 104.8 | 0.2 | 21 | 27% | 0 | 15 | 0 | 64.2%to 73.3% |

Grate type (3) | Trapezium | 104.8 | 0.2 | 21 | 27% | 0 | 0 | 15 | 33.7% to 73.9% |

Grate type (4) | Trapezium | 103.8 | 0.2 | 20.8 | 26% | 1 | 0 | 24 | 34.6% to 75.6% |

Grate type (5) | Circle | ــــــ | 0.4 | 21.7 | 28% | 173 circles with diameter 0.4 cm | 32.5% to 70% |

Types of Grates | Length of Total Slots (cm) | Width of Slots (cm) | Inlet Area (cm^{2}) | % Inlet Area | Number of Longitudinal Bars | Number of Transverse Bars | Number of Diagonal Bars | (£) From Q (6.0–1.0) L/s |
---|---|---|---|---|---|---|---|---|

Grate type 4 | 103.8 | 0.2 | 21 | 26% | 1 | 0 | 24 | 34.6% to 75.6% |

Grate type 4 | 168.4 | 0.2 | 40.32 | 51% | 1 | 0 | 44 | 35.5% to 77.6% |

Grate type 4 | 201.6 | 0.3 | 50.52 | 64% | 1 | 0 | 36 | 26.8% to 78.7% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Fathy, I.; Abdel-Aal, G.M.; Fahmy, M.R.; Fathy, A.; Zeleňáková, M.; Abd-Elhamid, H.F.; Nassar, M.A.
Effect of Changing the Shape and Size of Inlet Area of Grates on the Hydraulic Efficiency of Urban Rainstorm Drainage Systems. *Water* **2022**, *14*, 2541.
https://doi.org/10.3390/w14162541

**AMA Style**

Fathy I, Abdel-Aal GM, Fahmy MR, Fathy A, Zeleňáková M, Abd-Elhamid HF, Nassar MA.
Effect of Changing the Shape and Size of Inlet Area of Grates on the Hydraulic Efficiency of Urban Rainstorm Drainage Systems. *Water*. 2022; 14(16):2541.
https://doi.org/10.3390/w14162541

**Chicago/Turabian Style**

Fathy, Ismail, Gamal M. Abdel-Aal, Maha Rashad Fahmy, Amira Fathy, Martina Zeleňáková, Hany F. Abd-Elhamid, and Mohamed A. Nassar.
2022. "Effect of Changing the Shape and Size of Inlet Area of Grates on the Hydraulic Efficiency of Urban Rainstorm Drainage Systems" *Water* 14, no. 16: 2541.
https://doi.org/10.3390/w14162541