Fluid Dynamics

The objective of the experiment is to observe of behavior of a fluid (in this case, water) and the Bernoulli Equation as it exists through a small opening.

Procedure:
See Physics 4C Lab Manual (Martin Sydney Mason), Experiment 2.





































Data and Observations
Volume of Water Emptied: 300 mL

	Trial 1	Trial 2	Trial 3	Trial 4	Trial 5	Trial 6
Height of water (m)	0.080	0.080	0.073	0.069	0.065	0.094
Time to empty (s)	9.8	9.6	10.8	11.1	11.9	9.0

Calculations:
Volume Emptied: 300 mL*(1 cm^3/1 mL)*((1 m)^3/(10^2 cm)^3)= 3.0*10^-4 m^3
Area of Hole: d=7.2 mm= 7.22 *10^-3 m, r= 0.0036 m; A= πr^2= 4.07*10^-5 m^2

time(theoretical) = Volume/(Area*sqrt(2*g*height))
Calculated Theoretical Times

	Trial 1	Trial 2	Trial 3	Trial 4	Trial 5	Trial 6
Time (s)	5.88	5.88	6.16	6.34	6.53	5.43

Analysis
Error between calculated and theoretical times: % error = (|Exp -Theo| / Theo) x 100

	Trial 1	Trial 2	Trial 3	Trial 4	Trial 5	Trial 6
% Error	66.7	63.3	75.3	75.1	82.2	65.7

The average percent error is 71.8%, and the experimental values are not within the degree of uncertainty (±0.2 seconds to account for human reaction time).

Diameter: A=V/tsqrt(2gh), πr^2=V/tsqrt(2gh), r= sqrt(V/πtsqrt(2gh)), d= 2sqrt(V/πtsqrt(2gh))

	Trial 1	Trial 2	Trial 3	Trial 4	Trial 5	Trial 6
Diameter (m)	0.0056	0.0056	0.0054	0.0054	0.0053	0.0056
% Error	28.6	28.6	33.3	33.3	35.8	28.6

Using the formula for percent error (% error = (|Exp -Theo| / Theo) x 100), the values result in an average percent error of 31.4%.

Summary 
Fluid dynamics are very unpredictable. In addition, since this experiment is rather crude, large errors are not unexpected. This is the most probable explanation for large discrepancies between the measured and calculated times and diameter.