Factors affecting the Rate of flow of a fluid through a tube
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2. The effect of radius of tube
Once I had found the relationship between the rate of flow and the length of glass tube, I decided to investigate another dimension, the radius of the glass tube. Glass tubes of varying radius were cut to the same length using a glass cutter. The edges of the tubes were smoothed using sand paper for reasons of safety but also to create a smooth edge for the water flow. In order to measure the radius of each glass tube, a travelling microscope was employed. Each glass rod, in turn, was clamped in to a secure position using a boss, clamp and retort stand. The travelling microscope was positioned in front of the opening of the glass tube and focussed so that the cross hair was aligned with the middle of the inside edges. A reading on the scale was taken and the microscope realigned so that the cross hair lay on the opposite inside edge. A second reading of the scale was taken and the difference between the measurements gave the diameter. The measurements for the diameter were halved to obtain the radius values.
The equipment was used to measure the rate of flow of water from the glass tube three times for each radius. The results are shown in Table 3 below.
Table 3
Radius (ml)
Volume of water (ml)
Time (seconds)
Rate (ml/s)
Average rate (ml/s)
1
2
3
1
2
3
1
2
3
0.40
12
12
11
20.11
20.36
20.27
0.60
0.59
0.54
0.58
1.2
66
65
66
10.16
10.15
10.17
6.50
6.40
6.49
6.46
2.2
230
224
230
10.14
9.75
10.12
22.68
22.97
22.73
22.79
3.4
200
198
199
4.98
5.06
5.04
40.16
39.13
39.48
39.59
4.0
198
200
190
3.35
3.33
3.00
59.10
60.06
63.33
60.83
Using these results, the graph "A graph to show the variation of rate of flow with radius" was plotted. This graph shows a clear trend whereby the rate of flow of water increases with the radius of the glass tube. The graph is curved upwards indicating a possible power law. To test this relationship, a graph of rate of flow against radius squared and radius cubed was drawn. The graph "A graph to show the variation of rate of flow with the radius squared" displays a trendline that is a straight line through the origin on the graph. The graph "A graph to show the variation of rate of flow with radius cube" has a curved trendline. This comparison of the graphs has shown that the rate of flow of water is proportional to the radius squared.
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3. The effect of height
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