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000844-0029 Ding 1Physics Internal Assessment: Experiment Report
An Increasing Flow of Knowledge:
Investigating Torricelli’s Law, or the Effect of Height on Flow Rate
Candidate Name: Chunyang Ding
Candidate Number: 000844-0029
Subject: Physics HL
Examination Session: May 2014
Words: 4773
Teacher: Ms. Dossett
, 000844-0029 Ding 2
If you sit in a bathtub while it is draining, you may notice that the water level seems to
drop quickly initially, but then slows down as the height of the water decreases. Although you
could attribute this time distortion to being impatient and wanting the bathtub clean, it is also
possible that there is a physics explanation for this. This paper will investigate the correlation
between the height of water and the flow rate of the water. Our hypothesis is that as the height of
the water increases, the flow rate of the water will increase linearly.
In order to perform this experiment, we will use a two liter bottle and drill a small hole in
the side. We will fill the bottle with water and allow the water to drain from the bottle. The
independent variable is the height of water above the hole in the two liter bottle, measured in
meters. The dependent variable is the flow rate of water out of the bottle, measured in milliliters
per second. However, these two variables are very difficult to measure directly with a high level
of accuracy. Therefore, for practical purposes, we shall measure the amount of water poured into
the two liter bottle as the independent variable, and the amount of water drained in the duration
of 5.0 seconds as the dependent variable. We can easily convert these values to the units required
for our lab.
One important control for this lab is that the walls of the two liter bottle are very similar
to a perfect cylinder. Otherwise, we could not convert the volume of water in the bottle to the
height of water above the drilled hole. Therefore, instead of drilling the hole at the bottom of the
two liter bottle, where there are irregular shapes created by the “feet” of the two liter bottle, we
will drill the hole roughly 5 cm above the bottom of the two liter bottle, at a region where the
two liter bottle approximates a perfect cylinder.
, 000844-0029 Ding 3
Another control for this lab is the temperature of the water used. Because temperature has
an effect on the density of water, a factor that could potentially affect the experiment, we want to
keep this variable as constant as possible.
A very important control for this lab is the size of the hole drilled. For our experiment,
we will only deal with a single hole of a constant diameter. Because we understand that a larger
hole could potentially increase the flow rate, we choose to not change the diameter of the hole. In
addition, having multiple holes could drain the water much faster than with a single hole, so we
will only have one hole.
Maintaining a constant pressure on top of the water bottle is very important. If we keep
the cap on the two liter bottle, this pressure above the water would change as the water drains.
However, if we leave the cap off the two liter bottle, the pressure on top of the water would be a
constant of 1 atmosphere, or roughly 101325 pascals. In addition, the pressure of the
environment outside of the room should also be kept at a constant of roughly 101325 pascals.
The ranges of volumes of water we wish to fill the two liter bottle are chosen with care.
The minimum value, of 500 mL, was chosen because below that amount, water does not flow
properly from the hole. Rather than spewing out in a constant spray that could be collected by the
beaker, the water would trickle down the side of the two liter bottle. This prevented us from
collecting any data for volumes below 500 mL. The maximum amount of water we chose to fill
the bottle with is 1700 mL because above that level of water, the two liter bottle’s shape begins
to change. The top of a two liter bottle is curved to form a small opening on the top. Therefore,
using more than 1700 mL of water would distort the true purpose of the lab: to investigate the
correlation of height on the flow rate.
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