Experimental verification of the unsteady Bernoulli's equation using a low-cost apparatus

In this paper we propose a low cost experiment to test the transient behaviour of the water flow from a long pipe connected to a tank, in the time interval between the opening of a valve and the onset of steady state, as predicted by the unsteady Bernoulli equation. Data are collected with the help of the well-known open source video analysis software Tracker, and the experiment is suitable for an undergraduate laboratory project. It is found that the functional form of the velocity vs. time dependence of the flow in the transient stage is well represented by the unsteady inviscid Bernoulli equation, but in order to better understand the details of the parameters involved in the experiment, the Bernoulli equation with losses also becomes useful, thus providing insight into different forms of one of the most important equations in hydrodynamics.