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.
Keywords: Bernoulli’s equation; Rainfall intensity; Rainwater harvesting; Sizing; Sustainability.