The Torricelli model for the draining bucket is based on two physical concepts:

- The Bernoulli relationship between pressure, , density,
and speed, for fluid along a streamline:

- The hydrostatic relationship between changes in pressure over the
height of a fluid column and gravity (acceleration ), fluid density
and the height of the column:

Equating these two gives a relationship between height of the
fluid above
the hole and the speed at which it spews forth,

The because the volume lost of fluid in the bucket must equal the flux of fluid through the bucket's hole (with area ),

and using the fact that (for a bucket with regular sides and constant cross section in height) ,

Substituting in the relationship from above gives a differential equation for height of the fluid, , as a function of time:

2000-07-30