Fluid Dynamics Lab

The purpose of this fluid dynamics lab is to set up the fluid dynamic model by comparing the experimental data and theoretical data. We start the lab by filling bucket with water. We open the hole and let the water from bucket transferred to the small bottle, we put the water from bottle from the bucket and repeat the experiment again.

Volume emptied V = 500 x 10^-6 m³ ± 25 x 10^-6 m³
Height of water to the hole h = 0.145 m ± 0.001 m

We empty the bucket of water for 6 times.

Run	Time to empty (s)
1	17.05 s ± 0.01 s
2	17.34 s ± 0.01 s
3	17.2 s ± 0.01 s
4	16.5 s ± 0.01 s
5	15.51 s ± 0.01 s
6	16.74 s ± 0.01 s

We have the best estimate of actual time to empty volume = 16.72 s ± 0.572 s

Diameter of hole = 0.0052 m ± 0.1 m
Area of drain hole = π(0.0052 m/2 ± 0.1)^2 = 2.123 x 10^-5 m² ± 0.2 m²
Acceleration due to gravity g = 9.81 ms^-2

We have the theoretical time to empty volume:

t_{theoretical = V/(A(2gh)^1/2) = 13.96 s} ± 3.093 s

_{We compare the theoretical time and actual time to empty volume:}

Run	Theoretical time (s)	Actual Time (s)	Does Actual time agress within uncertainty?
1	13.96 ± 3.093	17.05 ± 0.01	Yes
2	13.96 ± 3.094	17.34 ± 0.01	No
3	13.96 ± 3.095	17.20 ± 0.01	No
4	13.96 ± 3.096	16.50 ± 0.01	Yes
5	13.96 ± 3.097	15.51 ± 0.01	Yes
6	13.96 ± 3.098	16.74 ± 0.01	Yes

We need also compare the calculated and given diameter.

The calculated diameter = 0.0052 m ± 1.045 x 10^-3 m
^{The given diameter = 0.0052 m} ± 0.1 m

Conclusion:
By comparing the theoretical time and actual time to empty volume, we have the 4 experimental values agree with the theoretical time out of 6 trials, which means the we can successful approach the theoretical time in the change of 2/3. Also, the calculated diameter is in the range of the given diameter, which shows the set up of experiment approaches the theoretical fluid model. We thus successful set up the fluid dynamic model as the experimental data are closed to theoretical data.