Repeat Example 8.7 with a hole size of 10 µm.Example 8.7A small hole is accidentally poked...

Repeat Example 8.7 with a hole size of 10 µm.

Example 8.7

A small hole is accidentally poked in the bottom of an ethanol fuel lank mounted to the side wall of an engine lab. Estimate the size of the ethanol drops that will drip out through the hole.

SOLUTION There is no pressure applied to the fuel and no driving force other than gravity to generate a high mass flow rate. Also, the problem states that the hole is small. Thus we can assume that the flow out the hole will drip in a slow process rather than be atomized. A force balance between a surface tension forceresisting the fluid leaving the tank and a gravity force trying to pull the ethanolout yields

Rearranging to solve for ddrop  gives

So for a hole size of 1.0 mm, the expected drop size is

Note that for such slow dripping processes, where the velocity is so small as to be negligible (different from Rayleigh breakup), the relevant nondimensional parameter is the Bond number:

and so the predicted drop size can be expressed in terms of the Bond number as