The first thing we need to consider is how many
different variables we have, rather which variables we are measuring and taking
into account, and which we are considering to be constant. The quantities we
assume to be constant are the gravitational acceleration, the surface tension
of materials and their densities. However, in some cases we are more reserved
and we allow certain uncertainties, regarding the density and surface tension
of materials.
The full error analysis will be represented, however
most experiments fall under one of them.
1)
Cylinder:
Since the function for the height of water level has
four variables there are precisely four possible errors. Three of them are
present in all the models, the radius of the orifice, the surface tension and
the density. However it is very difficult to even estimate some of these, so
essentially neither the error of the surface tension nor the error of the
density are the weakest link – in fact they are mostly considered as constants.
2) Cone:
This is the type of container that we used in our
further experiments – and on the cover of the assignment. It is crucial to
determine any possible errors. The three general variables are present here as
well. Additionally we have two more, the radius of the cone i.e. the bigger
radius of the cup, and the total height of the cone (not the cup). It is also
worth mentioning that the error of the total height has its separate error
analysis, as it cannot be measured.
3)
Elliptical
cylinder:
This error estimate is purely
theoretical. The most useful situation where we can have this error estimate is
if there are some inaccuracies in the container.
