Experiment 2: Fluid Dynamics

Purpose:

The purpose of this experiment is using experiment to prove that the Bernoulli Equation held true in the lab environment and real world.

Procedure:

Using the bucket of 5 gallons water with a small hole drilled in the bottom. Place the small bottle with volume marks beneath the opening hole in the bucket and let the water go. Using the stopwatch measure the time the water leaking out 16 ounces to the small bottle. Record the data, and repeat that 5 more times.

	1st run	2nd run	3rd run	4th run	5th run	6th run
t actual	21.25	21.30	21.46	20.87	20.91	20.95

           

Volume: V =16 oz = = 0.016 ft³

Diameter of the drain hole: D = 0.5 ± 0.025 cm = 0.0164 ± 8.2E-4 ft = 0.1968 ± 9.84E-4 in

Area of the drain hole: A = 𝞹D²/4 = 2.1124E-4 ± 5.2837E-7  ft²

Acceleration: g = 32 ft/s²

Height of water (h) = 3 in = 0.25 ft

t_theoretical =     18.94  s  

with the uncertainty: 18.888 s < t_theoretical < 18.98 s

% error between t_heoretical and t_actual:

1 run	2 run	3 run	4 run	5 run	6 run
11.5 %	11.7%	12.5%	9.7%	9.8%	9.9%

There are still some % error between the theoretical value and experimental values even though the uncertainty is concerned. The % error is from the high of the water in the bucket. We could not use get the time for each run precisely because using the stopwatch.

T_actual  avg =(21.25 + 21.30 +21.46 +20.87 +20.91+ 20.95)/6   = 21.12

Calculation for diameter:

Given diameter	0.25 in
Calculated diameter	0.1863 in
Error	29.2%

Summary:

There is a big %error between the given diameter and calculated diameter of the drill bit. However, the % error between the measured diameter and calculated diameter is acceptable. Therefore, the % error between given and calculated diameter is from the drill bit. There was an error when the hole was being finished.