Fluid Dynamics

In this experiment, we use bernoulli equation to find the variables such as flow rate, velocity of the liquid, and time to empty a given volume.

Volume emptied in our experiment was 500 mL. we deviated from experiment instructions to ease calculations. Height of water in the bucket was kept the same at roughly 3 inches.

We made six runs for time needed to empty 500 mL, here are the data sets:

29.70s
29.21s
29.54s
29.56s
29.50s
29.20s

The theoretical time to empty 500 mL:

Volume emptied: 500 mL = 0.000500 m^3
Area of drain hole: pi*r^2 = 5.67*10^-5
Acceleration: 9.81 m/s
height of water: 3 inches = .8 m

t_theoretical = V/(A*sqrt(2gh))

Calculation & error analysis in MATLAB:

>> properror(t,[v a h],[.000500 5.67*10^-5 .8], [.000001 .01*10^-5 .1])
ans =
    [      26.7100]    '+/-'    [1.6709]
    'Percent Error'    '+/-'    [6.2557]

t_theoretical vs t_actual:

actual	theoretical	percent error
29.7	26.71	11.19%
29.21	26.71	9.36%
29.54	26.71	10.60%
29.56	26.71	10.67%
29.5	26.71	10.45%
29.2	26.71	9.32%

Values do not agree within uncertainty (1.67, 6.25%)

solving for diameter:

2*r=V/(pi*t*sqrt(2*g*h))

r =

v/(2*pi*t*((981*h)/50)^(1/2))

>> properror(r,[v t h], [.000500 26.71 .8],[.000001 .01 .1])
ans =
    [  7.5201e-007]    '+/-'    [4.7025e-008]
    'Percent Error'    '+/-'    [     6.2533]


%error in the drill diameter = given-calculated/calculated
= 48.9% error