| | A straight-walled tank is filled with oil. The oil drains through a horizontal pipe fitted at the bottom of the tank (Movie 1). We observe how the level of oil decreases as a function of time (Figure 1, diagram at center). The measured values closely fit an exponentially decaying function of time. The same experiment can be performed with water (Movie 2). We can see clearly that the water flows more strongly when the level is higher. If a pump is fitted to the end of the pipe, the tank can be filled with oil or water instead (Photo 1). If the pump sets up a constant pressure difference (irrespective of the magnitude of the flow), the filling curves are exponentials again (Figure 1, diagram at right).
Interpretation The outflow is driven by the pressure difference across the pipe which is equal to the pressure difference across the tank. Since the latter is proportional to the level of oil, and since the flow (which is laminar) is proportional to the pressure difference, the flow is proportional to the level. The flow defines the rate of change of oil in the tank. So, in summary, the rate of change of the level of oil is proportional to the level of oil. This leads to the functions observed. | |
