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Report of Experiment #7
Fluid Flow
TA: Yasamin Masoumi Sefidkhani
11/18/2022
Abstract:
In this experiment, we looked at fluid flow and Poseuille's law. There were two inquiries in it. We
employed one capillary in the initial investigation, and three distinct capillaries in the subsequent
investigation. We measured the duration of the water's passage through the capillaries. The
fluid's flow rate was then determined using the data. This fluid's flow rate can be influenced by
size and pressure. This pace can be affected by pressure and size. In experiment 1, the
apparatus' reservoir's height was modified to vary the pressure, and in experiment 2, the
capillaries' diameter was varied to change the pressure.
Introduction:
To acquaint and validate Poiseuille's Law, this experiment is being conducted. We
investigated how fluid flow rates and several types of flow relate to one another. Using
capillaries of varied sizes and a flow rate monitor as characteristics. We timed how long each
capillary took to fill a graduated cylinder to a specified mark to calculate the flow rate. Next, we
calculated the results’ average. We did this several times with different pressures and capillary
sizes to understand the link between the flow rate and each.
Investigation 1:
Using a capillary with a 1.25 mm (about 0.05 in) diameter, we first assembled the
equipment as seen in Figure 1 to start this experiment. The capillary’s height was modified so
that the graduated cylinder rests directly beneath it. Once the capillary was attached to the
system and water could flow to remove air bubbles, the plastic bottle's height was adjusted. We
timed how long it took the device to fill the graduated cylinder to the 50-cc mark after it was
positioned beneath the capillary. We refreshed the water in the bottle so that its level stayed at
our predetermined baseline to maintain a constant pressure. To obtain two sets of time data, we
later calculated the average flow rate and its error at the current
pressure. The pressure was then raised three millimeters each
time, and we timed how long it took the graduated cylinder to fill to
the 50-cc mark three more times. To understand the correlation
between pressure and flow rate vs. pressure, we make use of this
data. By displaying the data’s best fit line, the relationship between
pressure and flow rate was made clear. By including additional data
points where the source of the pressure is ambiguous. The more
meticulously we measured, the closer our line is to the origin. This
is accurate because our measurements of the two heights
completely determined the pressure readings. Our findings support
a section of Poiseuille’s Law, which states that flow rate is (at least
somewhat) influenced by pressure. Since flow rate and pressure
and proportional flow rate increase so does the pressure.
Figure 1-
Experiment Apparatus
Table 1-
Heights 1&2, Time 1&2, Diameter of Capillary, Average Time, Average Flow Rate
Trail
h1
h2
∆𝑝
t1
t2
t avg.
avg.
δ
time
δ𝑎𝑣𝑔. ?𝑖𝑚𝑒
𝑎𝑣𝑔. ?𝑖𝑚𝑒
avg Q
(
)
𝑐𝑚
3
?
δ𝑄
𝑄
δ𝑣
(𝑐𝑚
3
)
∆ 𝑄
Trail 1
32. 75
43. 8
11
98. 9
97. 3
98. 12
0. 005
0. 6886
0. 510
0. 6886
0. 05
0. 351
Trail 2
32. 75
46. 8
14
88. 4
83. 3
85. 86
0. 005
0. 6886
0. 582
0. 6886
0. 05
0. 401
Trail 3
32. 75
49. 8
17
73. 5
73. 5
73. 50
0. 005
0. 6886
0. 680
0. 6886
0. 05
0. 468
Trail 4
32. 75
52. 8
20
57. 5
66. 3
61. 88
0. 005
0. 6886
0. 808
0. 6886
0. 05
0. 556
Graph 1-
Average Flow Rate vs. Pressure
Investigation 2:
We compared the flow rates via four capillaries of various diameters for this portion of
the experiment. We timed how long it took the capillary to fill the graduated cylinder to the 50-cc
mark three times without altering the height of the capillary or reservoir. We repeated this
process using capillaries of various diameters. Since the flow rate would be incredibly sluggish
for the capillary with the smallest diameter (0.5 mm), we adjusted the pressure and utilized a
10-cc graduated cylinder. However, none of the capillaries our group tried to use to collect data
worked properly. Since the pressure, in this case, was changed we needed to calculate the
correct flow rate so we can compare it to the other capillaries. This was done by dividing our
flow rate (Q) by 2.5. We then obtained the logarithms of d and Q by deriving an equation from
Poiseuille’s Law
.
Then, since neither of these variables has units, we generated a
𝐶 =
∆𝑝
128δη𝐿
graph of lnQ vs lnd. After plotting the best fit line, we used the IPL Calculator to determine its
slope and slope error: 2.63658±1.521759. Our values were within the allowable error limits, the
slope should have been in the 4 range which in still case with margin of error it was roughly 4.
This graph demonstrates the relationship between flow rate and diameter.
Table 2-
Data for Investigation 2
Capillary
diameter
(d)
h1
h2
∆𝑝
t1
t2
t3
t avg.
avg.
δ
time
δ𝑎𝑣𝑔. ?𝑖𝑚𝑒
𝑎𝑣𝑔. ?𝑖𝑚𝑒
avg Q
(
)
𝑐𝑚
3
?
δ𝑄
𝑄
δ𝑣
(𝑐𝑚
3
)
1. 5𝑚𝑚
32. 75
52. 8
20
31. 4
31. 0
31. 47
31. 28
0. 005
0. 6886
1. 598
0. 689
0. 5
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