Fluid Dynamics

In this experiment we filled a bucket with water and recorded the time elapsed as the water drained from a small hole at the bottom of the bucket. Then, calculated the theoretical time elapsed and compared both results.

Experiment: The bucket was filled with water 2.3 inches above the small hole, the hole had a diameter of approximately 0.6 centimeters. We ran six trials and recorded the time it took for 473 mL (16 ounces) of water to flow out of the bucket.




Volume emptied (V) = 16 ounces = 473 mL
 Height of water (h) = 2.3 in = 0.192 feet
 Area of drain hole (A) = pi*(.3cm)^2 = .28 cm^2 = 0.0003014 ft^2
 Acceleration due to gravity (g) = 32 ft/s^2

Trial #   time (t_actual)
1            25.06 s
2            24.85 s
3            25.24 s
4            25.36 s
5            25.17 s
6            26.09 s

The average of the six trials was 25.30 seconds. We then calculated the theoretical time by using the Flow rate equation, Continuity equation and Torricellis Theorem, which relates the speed of fluid flowing out an opening to the height of fluid above the opening.

R = V/t = Av  &  v = sqr(2gh)  ----->  V/t = A[sqr(2gh)]  ----> t(theoretical) = V/A[sqr(2gh)]    

                                                         

                                                         t (theoretical) = 15.14 s

Calculate Error:    |theoretical - actual|/theoretical x 100 = % error

                              |25.3s - 15.14s|/15.14 x 100 = 67% error

Comparing our measured value with the theoretical value gave us a 67% error. This does not agree within uncertainty. We then assumed that the measured diameter was inaccurate and decided to solve for the actual diameter using the same equations and the data recorded.

    

     v = sqr(2*32*0.192) = 3.505 ft/s,      R = V/t = (0.0160 ft^3)/25.30s = 6.324*10^-4 ft^3/s

                          V/t = A[sqr(2gh)] --- >  6.324*10^-4 ft^3/s = pi*r^2*3.505

                           r = 0.0076 ft = 0.28 cm, diameter = 0.56 cm

                          |0.6cm - 0.56cm|/0.6 x 100 = 6.67 % error

Here we see that our diameter should had been 0.56 cm. To check our result we compared both the calculated and measured diameters, this gave us a percent error of 6.67% which is within our uncertainty. This proves that our measurements were correct but there is still an unknown source that altered our results drastically.

There may be a few reasons why our result for our time had a big error. It is possible that we did not measured the height of the water correctly since we did not have a good angle reading the measurement while looking into the bucket. The increments on the beaker were not small enough to read exactly 473 mL, it was an approximate. Having better measuring equipment would had definitely lowered the error on our results.