Torricelli’sTank Lab Project

ANALYSIS

Ananalysis of this data shows that the flow rate out of the vessel isdirectly proportional to the orifice area. We can also see from thegraph of time against level of water drained to be a smooth curve,where time increases steadily with the drop on the level of waterdrained. In the tables are collected data from two trial experimentswith same starting level, the same orifice area, but with differentoutlet levels and all done in the same cylindrical tank. Note that inthe first trial it takes 529.58 sec to drain the tank from an initiallevel of 19.5 cm to 18 cm when the outlet is at 15 cm. When theoutlet is lowered to 5 cm it takes less time that is 153 sec to drainthe tank from the initial level of 19.5 to 18 cm.

Onthe second trial experiment the outlet is lowered by a 10 cm but theinitial level is maintained, thus increasing the volume that must bedrained and yet it took less time to complete the process. Lookingeven more closely at tabulated data, we note that in the sameexperiment at which the initial level was 19 cm, when the out letlevel is lowered to5 cm, it takes only 514.11 sec to drain 4.5 cm ofthe tank level. But when the outlet level is at 15 cm it takes moretime529.58 sec to drain 1.5 cm of the tank to level.

Experimentally,the residual height R of the water in the bottle can be obtainedthrough the plot V ^{2}versus H and the total time (t_{0})needed to drain off the bottle, can also be obtained through the plotof V versus T. Alternatively, the dynamical variables that depends onthe time T during the flow are: H and V for both our experiment.However, neither the expressions of these dynamical variables asfunctions of the time nor the mathematical relation betweenthemselves would depend on the particular geometry of the cylindricalbottles and pin-holes actually used in the experiments.

REFERENCES

HenryC. Foley, 2007: Introductionto Chemical Engineering Analysis Using Mathematica. Available from

 https://books.google.co.ke/books?id=zGB1ZKfKCnUC&pg=PA116&lpg=PA116&dq=course+work+on+Torricelli%E2%80%99s+Tank+experiment&source=bl&ots=p6ZSl1frMm&sig=clJLXhVPPNKIQ8LaMnuYxBo02UI&hl=en&sa=X&redir_esc=y#v=onepage&q=course%20work%20on%20Torricelli%E2%80%99s%20Tank%20experiment&f=false

PauloMurilo Castro de Oliveira, 2000: Pin-Hole Water Flow from CylindricalBottles *PhysicsEducation 35, 110*(March 2000). Available from

http://arxiv.org/pdf/cond-mat/0005428.pdf