Rate of Dripping of tube My original problem was to discover the rate at which leaking taps dripped, and its relation with the tap's size, radius, etc. However, I have no clue how taps work, so I simplified the problem. 

In the above case, there is a cylinder of small radius $R$ filled with fluid of a density $\rho$ to a height of $H$. The coefficient of surface tension of the fluid is $\gamma$. The problem of calculating the period of dripping SEEMS a lot easier now, but I still have no clue how to do it, so instead I approach it with dimensional analysis, and get the following (plausible) result:
$$ T = k \frac{\sqrt{\gamma}}{g\sqrt{\pi\rho H}} $$
where $T$ is the time period for a drop to fall down, $k$ is an unknown dimensionless constant, and $g$ is the gravitational acceleration. Interestingly, the equation does not seem to depend upon the radius of the cylinder. What I'd like to get pointers toward is a) is my equation marginally correct and b) how do I even approach this problem using physics? 
 A: You're calculating the rate of liquid flow through a tube under a specified pressure gradient. The rate of flow changes depending on whether the flow is laminar or turbulent. Laminar flow is described by the Hagen-Poiseuille equation:
$$ \Delta P = \frac{8\mu\ell V}{\pi r^4} $$
where $\Delta P$ is the pressure drop, $\mu$ is the viscosity of your saline solution, $\ell$ is distance along the pipe, $r$ is the pipe radius and $V$ is the volume flow rate.
For turbulent flow there is no simple analytic treatment, but there is an empirical equation called the Darcy–Weisbach equation:
$$ P - P_0 = f_D \frac{l}{2r} \frac{\rho V^2}{2} $$
where $V$ is the flow velocity and $f_D$ is an empirically measured constant called the friction factor.
Note that the HP equation includes the viscosity but not the density of the liquid, while the DW equation includes the density not the viscosity. That's because in fluid dynamics there are always two effects to consider, viscous forces and inertial forces. At the low flow rates where the HP equation applies the viscous forces dominate. At the high flow rates where the DW equation applies the inertial forces dominate.
(I suppose this isn't strictly true as viscous forces get rolled into the friction factor, but it is basically correct.)
