Modelling flow of water in a reservoir using ODEs

This paper aims to establish relationships between the outflow and the inflow of water in a general reservoir in the United Kingdom, through the use of ordinary differential equations. Two proposed models of the inflow-outflow equations include assuming the reservoir as a perfect cuboid, and that it is at 50% of its maximum capacity. The Derwent reservoir in Derbyshire is considered to be an ideal reservoir to model first in this paper and calculations for the daily inflow and outflow give us a rate of change equal to 2.38 × 10 ^-2 m day^-1. Our second model looks more closely into these same factors, taking into account further detail where possible. The Manning-Strickler equation is used to model the inflow of water as a good approximation for open water channels.Assuming a laminar flow, using Hamill’s equation, a function of the height of the reservoir is a good enough fit for the outflow through pipes. Shuttleworth’s modified equation takes into account the temperature in the region to give an approximation for the outflow by evaporation. Taking into account the rainfall between 1980 and 2010, the average precipitation found was 1120 mm equivalent to a flow of 3.55 × 10^-8 ms^-1

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