Chris Todd Johnson - Lab 8
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How investigating a simulated fluid pressure water tank proves the relationship between the total pressure of a fluid and depth
Introduction:
The data collected while observing a simulated fluid pressure water tank allows the comparison of the dependency of the total value of Pressure (P) on a fluid to different test values for depth (h). Given that the simulation of a fluid pressure water tank allows for the input of multiple values, including different test values for depth (h), it is possible to determine the dependency of each value on the total value of Pressure (P).
An observer would notice that the total value of Pressure (P) is called the dependent variable because it will be the variable that may or may not depend on the change in another variable and is located on the y-axis of the graphs. The Pressure (P) may be calculated by the following equation: Pressure (P) = Force (F) / Area (a).
The effect of depth (h in meters) on the total pressure of a fluid (P in Pascals) may be calculated by the following equation: Pressure (P) = [(density (ρ) X gravity (g)] X depth (h) + atmospheric pressure (P
o
).
The accepted value for the pressure of the atmosphere at sea-level which is 101,350 Pascals.
The accepted value for the acceleration of gravity is 9.8 m/s
2
.
The accepted value for the density (ρ) of water is 1000 kg/m
3
.
Procedure:
1.
Start the simulation 2.
list 15 different test values for depth (h) to input into the simulation to determine its dependency on the value of the water pressure (P)
Trial #
X = Depth (meters)
1
0.2 meters
2
0.4 meters
3
0.6 meters
4
0.8 meters
5
1.0 meters
6
1.2 meters
7
1.4 meters
8
1.6 meters
9
1.8 meters
10
2.0 meters
11
2.2 meters
12
2.4 meters
13
2.6 meters
14
2.8 meters
15
3.0 meters
3.
input the first test value for depth (h) into the simulator and observe its dependency on the value of the pressure (P), then repeat the process for the fourteen remaining test values
4.
perform comparative analyses
Results:
Trial #
Y = Pressure (Pascals)
X = Depth (meters)
1
103200 Pascals
0.2 meters
2
105300 Pascals
0.4 meters
3
107100 Pascals
0.6 meters
4
109100 Pascals
0.8 meters
5
111000 Pascals
1.0 meters
6
113100 Pascals
1.2 meters
7
115100 Pascals
1.4 meters
8
117000 Pascals
1.6 meters
9
119000 Pascals
1.8 meters
10
120900 Pascals
2.0 meters
11
122800 Pascals
2.2 meters
12
124900 Pascals
2.4 meters
13
126800 Pascals
2.6 meters
14
128700 Pascals
2.8 meters
15
130500 Pascals
3.0 meters
100000
105000
110000
115000
120000
125000
130000
135000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
f(x) = 0 x − 10.35
Pressure (P) vs. Depth (h)
h = Depth (meters)
P = Pressure (Pascals)
Data from the table, input into the graph, shows that when different test values for depth (h) are input into the simulator, the value for pressure (P) rises as the value for depth (h) does. Data from the table and graph also show that the slope of the “Pressure (P) vs. Depth (h)” graph is constant and forms a diagonal line. One may observe that values of the pressure of a fluid and the depth are directly proportional.
Data from the simulation screenshot allows an observer to view one of the 15 trials for different values of depth (h), and the resulting total pressure (P) value. One may observe that during the current screenshot of trial #8, the value of depth (h) was set to 1.6 meters (m) and the resulting value for total pressure (P) was 117,000 Pascals (P).
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Final comparative analysis:
The equation: Pressure (P) = [(density (ρ) X gravity (g)] X depth (h) + atmospheric pressure (P
o
) allows one to observe how the effect of depth (h in meters) on the total pressure of a fluid (P in Pascals) may be calculated. One may observe the following calculations, of the first 4 trials of the experiment.
One may observe that the following calculations based on values of Pressure (P), from both observations
and strictly math calculations, show that all of the final values of Pressure are very similar.
Trial #
Pressure (P) experimental
X = Depth (meters)
Pressure (P) calculated
Experimental Error (%)
1
103200 (P)
0.2 (m)
103310 (P)
0.11%
2
105300 (P)
0.4 (m)
105,270 (P)
0.03%
3
107100 (P)
0.6 (m)
107,230 (P)
0.12%
4
109100 (P)
0.8 (m)
109,190 (P)
0.08%
5
111000 (P)
1.0 (m)
111,150 (P)
0.13%
6
113100 (P)
1.2 (m)
113,110 (P)
0.01%
7
115100 (P)
1.4 (m)
115,070 (P)
0.03%
8
117000 (P)
1.6 (m)
117,030 (P)
0.03%
9
119000 (P)
1.8 (m)
118,990 (P)
0.01%
10
120900 (P)
2.0 (m)
120,950 (P)
0.04%
11
122800 (P)
2.2 (m)
122,910 (P)
0.09%
12
124900 (P)
2.4 (m)
124,870 (P)
0.02%
13
126800 (P)
2.6 (m)
126,830 (P)
0.02%
14
128700 (P)
2.8 (m)
128,790 (P)
0.07%
15
130500 (P)
3.0 (m)
130,750 (P)
0.19%
One may observe that the formula for calculating experimental error is:
Percentage error = [(Actual value − Experimental value) / Experimental value] x 100
From the table, one may observe that the experimental percentages of error are very small in value, ranging from the lowest value recorded of 0.01% to the highest value recorded of 0.19%.
Conclusion:
The data collected while observing a simulated fluid pressure water tank allowed the comparison of the dependency of the total value of Pressure (P) on a fluid to different test values for depth (h). Given that the simulation of a fluid pressure water tank allowed for the input of multiple values, including different test values for depth (h), it was possible to determine the dependency of each
value on the total value of Pressure (P).
For the experiment, 15 different test values for depth (h) were input into the simulation to determine its
dependency on the value of the water pressure (P). Data from the table, input into the graph, shows that when different test values for depth (h) are input into the simulator, the value for pressure (P) rises as the value for depth (h) does. Data from the table and graph also show that the slope of the “Pressure (P) vs. Depth (h)” graph is constant and forms a diagonal line. One may observe that values of the pressure of a fluid and the depth are directly proportional.
Finally, one may observe that the formula for calculating experimental error, Percentage error = [(Actual value − Experimental value) / Experimental value] x 100, was used for each trial of the experiment. From the table, one may observe that the experimental percentages of error are very small in value, ranging from the lowest value recorded of 0.01% to the highest value recorded of 0.19%.
One might observe that this experiment shows a simple way to use a simulation to prove a physics point. However, since an electronic simulation was used to obtain the data, instead of obtaining them from a real-life situation, an improvement that could be made to this experiment would be to plan
and perform real-life tests and compare the results of each.
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