Experiment 2: Fluid Dynamics

Experiment 2: Fluid Dynamics

Introduction:
The purpose of this experiment is to apply Bernoulli equation to determine the diameter of the hole on the bottom of the bucket.

First, we began the experiment by filling a large bucket with water and then allowed water to flow out of a small hole drilled near the bottom of the bucket. We took 6 trials and record the time took for a 16 ounces of water to exit from the bottom of the bucket. All measurements are in seconds and have an uncertainty of +/- 0.1s.

	1st run	2nd run	3rd run	4th run	5th run	6th run
Time to empty(tactual)	29.1 +/- 0.1s	28.9 +/- 0.1s	28.8 +/- 0.1s	29.2 +/- 0.1s	29.3 +/- 0.1s	28.9 +/- 0.1s
Volume of water before (inch)	3 1/6	3 1/8	3  1/16	3	3	3
Volume fo water after (inch)	2 1/2	2 1/2	2  7/16	2  7/16	2  7/16	2  7/16
Volume emptied (V): 16 ounces = 1.67 × 102 ft3
Area of drain hole (A): πr2 = 4.144 × 10 -4 ft 2
Acceleration due to gravity (g) : 32 ft/s2
Height of water (h): 3 inches = 0.25 ft
ttheoretical: V / A√2gh = (1.601 ×10-2)/ (4.144 × 10 -4)(√2(32)(5.58)) = 25.5 s
% error	1st run	2nd run	3rd run	4th run	5th run	6th run
	14.90%	13.30%	12.94%	14.51%	14.90%	13.33%
taverage : 29.03 s
A theoretical: V / t√2gh = (1.601 ×10-2)/ (29.03)(√2(32)(5.58)) = 0.000292 ft2
Calculated Diameter: 0.588 cm
Given Diameter: 0.700 cm
% error: 16 %

Conclusion:
Compare the experimental value and the theoretical value, we have 16 % error. The 16 % error are due to several uncertainties and unaccounted human errors. First one is during the experiment, when we use stopwatch to catch the time until the beaker reach 16 ounces, there have some time delay. Second, the hole was made with a drill and never properly finished, this would create variations in stream diameter due to roughness around the hole.