Equation to estimate droplet volume falling from a needle of a known orifice diameter at a given flow rate I am doing some research to see if there is a simple equation (or an equation that can be simplified) to estimate the volume of a drop of liquid falling due to gravity based upon the approximate flow rate, and perhaps the viscosity/surface tension of the fluid.
Basically this is a drip chamber fluid set for delivering medications. Clinicians routinely calculate fluid flow based upon the number of drops per minute assuming a fixed drop size. However since drop size varies with flow rate. Using a fixed volume size has some amount of inaccuracy. I would like to see if I can be more accurate in determining actual flow rate.
 A: At sufficiently small flow rates, droplets result from a competition between surface tension $\sigma$ and gravity $\rho g$ (with $\rho$ the mass density, and $g$ the gravitational acceleration). The ratio between $\sigma$ and $\rho g$ defines a surface area: $\frac{\sigma}{\rho g}$. For water-air surface tension at room temperature ($\sigma = 7 \ 10^{-2} \ J/m^2$) it follows that water droplets are typically described by a capillary length scale $\sqrt{\frac{\sigma}{\rho g}} \approx 3 mm$. 
Flow rates can be brought into the description via the capillary number, which measures the competition between viscous forces and surface tension: $\mu v/\sigma$. Here $\mu$ is the viscosity of water, and v the average velocity of the water leaving the orifice (volume per second divided by orifice area).
For not too high flow rates (under conditions where inertial forces are negligible) plotting $\rho g r^2/\sigma$ vs $\mu v/\sigma$ should suffice to capture the droplet radii $r$ resulting from the measurements.
Predicting sizes requires an analysis going beyond these dimensional considerations, and should involve contact angles, etc.
