Experiment 2: Fluid Dynamics

In this experiment, a bucket with a small hole, bottle with marks, ruler, stopwatch, and some other tools were used.  First, after stopping water come out from the bucket, the height of water was measured to as requested, 3 inches. Then the water was released to flow into the beaker and fill beaker with the assigned volume. When the flowing water reaches the volume, the stopwatch was used to record the reaching time of water. This same process has to be applied six times, and the average taken time will be obtained from these six trials. With the time being obtained and the diameter of the hole being measured, the formula "theoretical time = volume/area*radical(2*gravity*height)" was applied. This formula will then rearranged so the diameter of the hole could be calculated by using this formula. Overall, this experiment was designed for students to get the diameter of the hole on the bucket after recording the time taken for water to flow.

The primary equipment used for this experiment 

the bucket with a hole on it, and the beaker for catching the water flow from the bucket

The time obtained for water to reach the assigned amount

	1st run	2nd run	3rd run	4th run	5th run	6th run
Time to empty(s)	29.7	29.21	29.54	29.56	29.50	29.20
Average (s)	29.45

Volume	500(ml)=16.9(ounces)=0.0169ft
Area of hole	4.1424*10^(-4)
Acceleration	32 ft/ss
Height of water	3inches = 0.25 ft
Theoretical time	10.2 s
Given diameter	7 mm
Calculated diameter	0.162 inches = 4.1148 mm

Hole_diameter =0.35 (cm) ± 0.025 = 0.325(cm)~0.375(cm)

Height_water = 0.25 (ft) ± 0.025 = 0.225(ft)~0.275(ft)

Hole_area = 1/4πd² = 4.1424×10^-4 (ft²) ± 0.0002 = 4.1422×10^-4 (ft²)~ 4.1426×10^-4 (ft²)

Water_volume=0.0169(ft³) ± 0.00045 = 0.01645(ft³)~ 0.01735(ft³)

Time_theoratical=29.45(s) ± 0.025 = 29.425 (s) ~ 29.475 (s)

Equation used : theoretical time : Volume/A*radical(2*gravity*height)
                        diameter: (rearrange the previous formula) A= Volume/time*radical(2*gravity*height)
Then the answers obtained were :
                        theoretical time : 10.2 (s) which is not within the uncertainty
                        diameter: 4.115 (mm) = 0.4115(cm) which is not within the uncertainty
Error:
Time_theoratical= |(10.2(s)-29.45(s))|/29.45(s)x100%=65.37%error
Hole_diameter = |(4.115(s)-7.000(s))|/7.000(s)x100%=41.21%error


The factors that caused such a huge error can be imputed to the hole on the bucket. The used bucket had a plastic hindrance on the hole, which was the hole drilled in the bottom of the bucket. This hindrance made the water go an oblique direction and blocked some amount of water to flow out of the bucket. The other factor which caused such a huge error was the inaccurate measurement of the water height. The water height should be measured three inches up from the hole on the bucket. However, during the experiment, the height   was measured from the bottom of the bucket instead of the hole on the bucket. Therefore, the pressure difference could cause a huge difference in this experiment.