Fluid Dynamics with a Bucket

Materials: 

•            Bucket with a small hole drilled at the bottom
•            About 5 gallons of Tap Water
•            Graduated Cylinder
•            Ruler 
•            Stopwatch

In this experiment we will be testing the effectiveness of Bernoulli's Equation for a fluid flowing pipe. 

In order to set up for this experiment we put a bucket on the side of the table with a piece of duct tape covering the hole. We filled up the bucket to about 16.3 cm from the bottom. Using the graduated cylinder it was necessary to try to find the right angle to catch the water. Once set up we were able to find a good enough posittion. Because the flow rate of the water coming out of the bucket was so fast, it was necessary to use the larger graduated cylinder and mark with a piece of duct tape the point where we would stop. 

In an attempt to acquire great results we did 6 runs timing how long it took to the graduated cylinder to be filled with water.

Time to Empty: 11.01s, 11.5s, 11.29s,10.63s, 10.1s, 11.18s
Time to Empty (Mean): 10.95 + .5s

To compare the accuracy of our data we want to calculate the theoretical amount of time it will take to fill up that cylinder. Because our cylinder is larger and has no marks, we just decided to measure the mass of the water inside the cylinder. With the mass we are able to calculate the volume of the water being emptied out. 

Volume Emptied Out; 3.83*10^-4 + .1 m^3
Area of Exit Hole: 6.63 * 10^-5 m^2
Acceleration of gravity: 9.81 m/s^2
Height of Water: 0.14 + .02 m

Analyse:

Our mean time was 10.95 + .5s while our theoretical time was 6.37s. Complete difference!
The theoretical value and experimental value of the time do not agree with the uncertainty for many reasons. One, is the duct tape clogging the whole isn't the greatest parchment device in the world, because of this we are always losing a bit of water throughout the experiment. But if you think about it, losing a cm or two of water from a bucket is a lot, considering the diameter of the bucket is well over a foot long. Also the diameter of the exit hole is hard to calculate, the digital calliper may be useful but we have to consider the hole was made by a drill controlled by a human hand. 

In order to solve for the diameter we just rearranged the equation for the theoretical time. Comparing both diameters we have:

Theoretical Diameter: 6.8mm

Calculated Diameter: 6.88 + .02 mm

With this given information we are able to see that our percentage error was 11.7% for the diameter.