IOSR Journal of Applied Physics (IOSR-JAP) e-ISSN: 2278-4861.Volume 6, Issue 4 Ver. I (Jul-Aug. 2014), PP 30-34 www.iosrjournals.org www.iosrjournals.org 30 | Page Modeling of the Collect and Discharge Tank for Rain Driven Hydro Power Plant Ohajianya, A. C. 1 , Abumere, O. E. 2 , Chad-Umoren, Y. E. 2 , Osarolube, E. 2 1 (Department of Physics, Federal University of Technology, Owerri, Nigeria) 2 (Department Physics, University of Port Harcourt, Port Harcourt, Nigeria) Abstract: This paper presents a mathematical model of the Collect and Discharge Tank unit of the rain driven hydro power generator currently being designed using the University of Port Harcourt’s faculty of science building at Ofrima, Abuja Campus. The model revealed that over 2.0KW of power can be generated using rain water collected from the building, and that a minimum of 3,751 gallons storage capacity tank is needed to make sure that the unused water accumulated from a 0.6 inches per hour of rainfall is effectively stored if rainfall lasts for 33.33 minutes. This means that for the tank to effectively serve its purpose when rainfall at the rate of 0.6 inches per hour lasts for over 33.33 minutes, a larger capacity size of tank is needed, or the hydro power generating system is redesigned to generate power greater than 2.0KW. Keywords: collect and discharge tank, hydro power generator, mathematical model, rainfall, uniport I. Introduction The collect and discharge tank to be modeled here, is a unit of the rain driven hydro power generator currently being designed using the University of Port Harcourt Faculty of Science building at Ofrima. The tank is to collect water from the roof of the building and then discharge it to an installed Francis turbine on the ground floor in the course of a rainfall and until the unused accumulated water in the tank is exhausted. Rain is liquid water in the form of droplets that have condensed from atmospheric water vapour and then precipitated (that is, become heavy enough to fall under gravity). It is a major component of the water cycle and is responsible for depositing most of the fresh water on the Earth. The major cause of rainfall is moisture moving along three-dimensional zones of temperature and moisture contrasts known as weather fronts. If enough moisture and upward motion is present, precipitation falls from convective clouds (those with strong upward vertical motion) such as cumulonimbus (thunder clouds) which can organize into narrow rain bands [1]. Rainfall intensity is classified according to the rate of precipitation:  Light rain — when the precipitation rate is < 2.5 mm (0.098 in) per hour,  Moderate rain — when the precipitation rate is between 2.5 mm (0.098 in) - 7.6 mm (0.30 in) or 10 mm (0.39 in) per hour,  Heavy rain — when the precipitation rate is > 7.6 mm (0.30 in) per hour, or between 10 mm (0.39 in) and 50 mm (2.0 in) per hour, and  Violent rain — when the precipitation rate is > 50 mm (2.0 in) per hour [2] [3]. For hydro turbine, the power generated from a stream of water is given by P= ƞρghq  (1.1) Where: ƞ = turbine efficiency, ρ = density of water (kg/m 3 ), g = acceleration due to gravity (9.81m/s 2 ), h = net head (m), q  = flow rate (m 3 /s), and the power, P is in J/s or watts [4]. The net head, h=h g − h f − h m (1.2) Where: h g = gross head (total head available, that is, difference of water level between head race and tail race), h f = head loss due to friction in the pipe, h m = other minor losses. A model is a miniature representation of something; a pattern of something to be made; an example for imitation or emulation; a description or analogy used to help visualize something (e.g., an atom) that cannot be directly observed; a system of postulates, data and inferences presented as a mathematical description of an entity or state of affairs [5]. This definition suggests that modeling is an activity, a cognitive activity in which we think about and make models to describe how devices or objects of interest behave. There are many ways in which devices and behaviors can be described. We can use words, drawings or sketches, physical models, computer programs, or mathematical formulas. In other words, the modeling activity can be done in several languages, often simultaneously. If the language used is mathematics, the model is now called mathematical model. A mathematical model can therefore be defined as a representation in mathematical terms of the behavior of real devices and objects.