Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria.
Faculty of Engineering and Built Environment, University of Johannesburg, Johannesburg, South Africa.
Environ Monit Assess. 2019 May 3;191(6):338. doi: 10.1007/s10661-019-7434-z.
Bernoulli's equation was applied to a section of hopper collector to determine the appropriate dimensions of the hopper for rainwater harvesting. Also, the hopper surface area (SFA) for a given volume was minimized by differentiating it in relation to the slant angle (SA). Combining the rational formula-Manning's equation and the best hydraulic section criteria-expressions were obtained for the optimum sizes of rectangular and circular gutters. Minimum hopper SFA for a given volume was found to occur at an optimum hopper SA of 35.282°. With the optimum conditions, design charts were produced for the hopper, circular, and rectangular roof gutters. The ratio of hopper larger radius to the smaller radius designated as (α) gave hopper dimensions with excessively wide upper radius for values of 0.1 ≤ α ≤ 0.2. Alpha (α) values of 0.8 and 0.9 gave values of R and Z which are almost too close to be distinguished. The valid range of α for hopper design was found to be 0.292 ≤ α ≤ 0.8. The study revealed that roof plan area has more effect on hopper dimensions than gutter slope. In addition, the case of excessive long gutters can be addressed by placing the hopper at the lateral epicenter of the eaves. In this regard, regions with abundant rainfall can solve water scarcity issues if proper design parameters of RWH components are considered in order to avoid waste of water through the overflow of water collection systems.
伯努利方程应用于料斗收集器的一段，以确定适合雨水收集的料斗尺寸。此外，通过相对于倾斜角（SA）对其进行微分，使料斗的表面积（SFA）最小化。结合合理的公式-曼宁方程和最佳水力剖面标准-得出了矩形和圆形排水沟最佳尺寸的表达式。发现给定体积的最小料斗 SFA 出现在最佳料斗 SA 为 35.282°时。在最佳条件下，为料斗、圆形和矩形屋顶排水沟制作了设计图表。料斗较大半径与较小半径的比值指定为（α），对于 0.1≤α≤0.2 的值，给出了具有过大上半径的料斗尺寸。α（α）值为 0.8 和 0.9 给出了 R 和 Z 的值，它们几乎太接近而无法区分。发现料斗设计的有效 α 范围为 0.292≤α≤0.8。研究表明，屋顶平面面积对料斗尺寸的影响大于排水沟坡度。此外，可以通过将料斗放置在屋檐的横向震中，来解决排水沟过长的问题。在这方面，如果考虑适当的 RWH 组件设计参数，就可以解决水资源短缺问题，避免通过集水系统的溢流浪费水。
