Put a Hole in the Bucket Dear Liza...

Experiment 2: Fluid Dynamics

The equation which models the behaviour of a laminar, non-viscous, incompressible fluid flow is as follows:

This equation can be used to determine the theoretical velocity of water exiting a hole in a bucket.

For this experiment, we measured the rate at which water flowed out of a bucket, by recording the amount of time it took to fill a 1000 mL beaker. Data follows:

Bucket Diameter = 25 cm
Initial height of Fluid (above hole) = 12.4 cm
Area of drain hole = .31669 cm^2
Volume emptied = 1000 mL

Trial 1 = 30.01 s
Trial 2 = 29.35 s
Trial 3 = 29.59 s
Trial 4 = 29.39 s
Trial 5 = 29.82 s
Trial 6 = 29.38 s

This data indicates that the time to empty 1000 mL of water should be 29.59 ± .25 seconds. This equates to a flow velocity of:
1000cm^3/.31669cm^2=3157.66cm
3157.66cm/29.59 s=1.06m/s

The predicted velocity, from Bernoulli's equation should be close to the square root of 2*g*height of the water.
that results in a theoretical velocity of:
1.559 m/s

This velocity predicts that the volume of water should be emptied in 20.24 seconds, which represents nearly a 33% deviation from the measured time.
Even if the height of the water is adjusted to reflect the average height over the duration of the experiment, the theoretical time to completion only changes by 1.25 seconds.

These findings lead me to believe that some part of our model is incorrect, for example, the size of the drilled hole may not be exact.
The given data predicts that the cross sectional area of the hole may be in error by as much as 30 percent. This could be caused by the plastic deforming during the drilling process, and leaving a lip which blocked some of the flow.