1. Objective

The purpose of this lab is to experimentally prove and demonstrate the fluidal relationship between velocity v and height h.

2. Proof of Torricelli’s Equation

Previously, our AP Physics II class has only come into contact with the relation between fluidal velocity and fluidal height through the abstract formula that constitutes Bernoulli’s Equation:

\[P + \rho \textit{gh} + \frac {\rho\textit v^2}{2} = constant\]

, where \(P\) is fluidal pressure, \(\rho\) is density of the liquid, \(g\) is gravity, otherwise known as approximately \(9.8 m/s^2\), \(h\) is height, \(\textit v\) is the velocity at which the fluid moves, and \(constant\) is the constant, total energy that the system contains. Bernoulli’s Equation is derived from the fact that in fluids, there are three kinds of energy: fluidic (\(P\)), gravitational (\(\rho \textit{gh}\)), and kinetic (\(\frac {\rho\textit v^2}{2}\)) and that if we have a closed system, then it is safe to say that there will be no energy loss or gain, as in the Conservation of Energy. Additionally, since the energy will be constant throughout the system, we may establish two points within the system and set their respective equations equal to one another.