Experiment 2: Fluid Dynamics

Objective: 

The purpose of this experiment is to find out measure the diameter of the hole in the bucket using the concept of fluid dynamics. The time to empty 16 ounces of water from the bucket will be measured. Six trials will be done. Students will compare the theoretical time to empty the bucket with the actual time. Diameter of the bucket will be measured and calculated. Percent error will be calculated.

Data:

Step 1: Set up

Diameter measured = 0.52cm±0.005

Step 2: Experiment

Volume emptied = 16 ounces

Height of water = 3 inches

	1st run	2nd run	3rd run	4th run	5th run	6th run
Time to empty (tactual)	23.4s±0.05	23.4s±0.05	22.4s±0.05	22.6s±0.05	23.4s±0.05	23.4s±0.05

Step 3: Calculate:

Volume emptied (V) = 0.016ft³

Area of drain hole (A) = r²π=2.286*10^-4 ft²±8.79*10^-6

Acceleration due to gravity (g) = 32ft/s²’

Height of water= 0.168ft

t_{­theoretical} =V/A(2gh)^0.5

                =21.35s±3.2

                =18.15-24.55s

Step 4: Analyze

Error between t_{­theoretical ­}and t_actual for all test runs:

% error = (actual - theoretical) / theoretical *100%

	1st run	2nd run	3rd run	4th run	5th run	6th run
% Error	9.6%	9.6%	4.9%	5.9%	9.6%	9.6%

t_{­theoretical} =21.35s±3.2=18.15-24.55s

t_{­theoretical ­}and t_actual agree within uncertainty.

r²π=V/t*(2gh)^0.5 

 r=8.19*10^-3ft

 d=0.0164ft

Calculated diameter (inches)=0.0164ft=0.1968inches

Given diameter(inches)	0.2045
Calculated diameter(inches)	0.1968
Error	3.8%

Conclusion

Through using the concept of fluid dynamics, the diameter of the hole in the bucket is calculated to be 0.1968 inches. t_{­theoretical ­}and t_actual agree within uncertainty. Also, the percent errors between t_{­theoretical ­}and t_actual for all test runs are smaller than 10%. Therefore, this experiment is reliable.