**Abstract:**

The principal
objective of this paper is to relate the theoretical amount of water that is
being exerted through three different holes using Bernoulli’s equation. The lab
included measuring the amount of water flow from a hose into a bucket that had
three holes placed at various heights. A second bucket was then used to collect
the water flowing from the holes and then weighed to observe the amount of
water exerted through each hole due to pressure. Only after the water had
reached a certain level, was the water flowing in equal balance with the water
flowing out from the hose. After calculation, the amount of water that was
measured from the three holes should theoretically be the same amount put out
by the hose. We found that the theoretical estimation was very close to the
actual results with only a .36% error, which would have been the result of
errors in measurement.

**Objective:**

The objective of the Water Flow Rate
Lab is to compare the rate the water flowed from the three holes in the bucket
we used with the theoretical amount that should flow out of the same three
holes.

**Procedure:**

Required materials:

The instruments used; first a five
gallon bucket with three holes drilled in it, one at 2.25 inches, another at
4.3575 inches, and the third at 7.125 inches. Our other items were duct tape,
and a bathroom scale as well as another bucket that was free of holes.

Steps:

1.
We began
by measuring the height of each of the holes.

2.
Next we
covered up two of the holes with duct tape, leaving one open.

3.
We then
began flowing water into the bucket and kept it at a certain height in the
bucket to ensure a constant flow rate.

4.
Once a
constant flow rate was achieved, we then placed another bucket under the stream
of water

5.
This was
timed, and once the unaltered bucket was about 2/3 of the way full it was removed.

6.
Then the unaltered
bucket was put on the measuring scale, and the time and weight date was
collected.

7.
Steps 2-6
were repeated for the two other holes in the bucket.

**Results:**

Results:

Mass Flow Rate = .18 lbm/sec

Area of the circle is
.00034 ft

^{2}
H

_{1}= 2.25 in or 0.1875 ft
H

_{2}= 4.375 in or 0.3646 ft
H

_{3}= 7.125 in or 0.5938 ft
V

_{exper.}= 8.48
V

_{Theory}= 8.45
% Error = .36%

C

_{d1}= .54
C

_{d2}= .58
C

_{d3}= .61**Discussion of Results:**

We found our error percentage in the Water Flow Rate lab to
be .36%. There are a few variables that we determined would have led to this
error percentage. The first is that a standard ruler was used to measure the
bucket’s hole placement, the ruler did not provide us with an exact height for
the holes. When measuring, we could have erred in the consistency of where each
measurement was taken. This could affect
the height measurement of the holes. The biggest contributor to the error margin
is that a dial scale was used, instead of a digital one. While using a dial
scale if the reader is at a slight angle then the weight will be read incorrectly,
and it is impossible to record accurate decimals on a dial scale.

There were a few other factors that may have led to the
error percentage, such as drops of water, either from inside the bucket that
splashed out, or extra water that spilled onto the bucket, that would have
increased or decreased the amount of water, depending on how it got there, when
the bucket was being weighed. Another was that the water wasn’t stopped at the
exact time that the timer stopped, meaning that there would have been more
water flowing out than timed for. We decided though that these variables
although noted were too small to play a significant role in the difference
between the actual and estimated water flow.

**Conclusion:**

In this Water Flow Rate Lab experiment we compared the actual
amount of water that flowed out of holes drilled in a bucket, in a certain
amount of time, to the theoretical amount of water that should have flowed out
of the same holes. Using a dial scale we would measure the amount of water in
the bucket, and record that along with the time it took to fill the bucket,
this was repeated for each of the holes for a total of three times. We then calculated these results along with
what should have happened and received an error of .36%. This error percent was
thought to be based on a few different factors, but mostly because we were
using a dial scale, instead of a digital one. With the use of a digital scale,
we think the difference between the theoretical and actual value would have
decreased.

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