Eivind Knudsen Hjertholm, 18 år, Bergen
Skole: Bergen Katedralskole
MODELLING WATER FLOWING THROUGH TWO TANKS
In my project, I have investigated modelling of water flows through two tanks.
The setup was two tanks arranged such that one of them was suspended above the other. There are holes in the bottom of both tanks such that water can flow into the first tank, then from the first to the second tank and then out of the second tank. Initially, before water starts flowing, both tanks are filled with a certain amount of water. I now investigated how I could make an analytical model of the height of the water in each tank relative to time. This means that I wanted to express the height of the water in each tank as a direct function of time.
I built my model from the assumption that the volume flow of water through a hole is proportional to the pressure difference over the hole. For both tanks, this gave a constant of proportionality that I needed to deduce experimentally. This was done by measuring the flow rate out of each tank for a given pressure difference. For each tank, I also got a first order liner differential equation relating the height of the water to time. This differential equation was solved analytically to produce an explicit function for height of time for both tanks.
I tested the model experimentally by measuring the height versus time of the water in each tank for differing inflows and initial water heights. I plotted the data from the experiment together with the predictions by the model. This allowed me to do an analysis of the applicability of the model.
The results were that the functions for both tanks on average gave predictions within an accuracy of 15% for the initial 41% of the time that it took for the water level to reach equilibrium.