Fluid Dynamics

Purpose
       The purpose of this lab is to determine the time required to empty the water in a bucket using the Bernoulli principle. In this lab, the percent error will also be calculated and will be compared to the true value.

Materials

• Bucket with small hole in the bottom
• Water
• Ruler
• Stopwatch
• Beaker

Experiment

The setup for the experiment

Once the setup is ready, the experiment is conducted and time to empty 16 ounces of water is taken. The following is picture of how the experiment is conducted:

The reason 2 beakers are used is because one beaker can only contain 400mL while we need 450mL. The time taken to empty the 16 ounces was then measured to be:

1st =44.85s

2nd =45.35s

3rd =44.34s

4th =45.67s

5th =46.39s

6th =46.17s

Once the time is recorded, the average of the six run and the standard deviation was calculated and the result appears to be:

      t = 45.46 ± 0.7812s

In step 3 of the experiment, theoretical time is calculated using the following data:

     Volume emptied = 16 ounces / 998.83 ounces/ft^3 = 0.016 ± 0.000845ft^3

     Diameter of drain hole = 0.40 ± 0.005 cm

     Area of drain hole = 0.000135 ± 0.000003375 cm²

     Acceleration due to gravity = 32ft/s²

     Height of water = 1.8 inches = 0.15 ± 0.00417ft

By using the data above, the theoretical time can be calculated using the formula  t=V/A*√2gh.

By using the formula:

    t_th = 38.25 ±7.65 s

The percent error of the time was then calculated and appears to be 18.8%

Some of the error that may happens are the beaker used in the experiment is not an accurate tool to measure the 16 ounces of water. The use of 2 beakers might also contributes to the error since some of the water might actually got spilled instead of being contained. There might also be error contributed through the use of wet beaker instead of the clean and dry one since it change the time by a little bit.

In step 4 of the experiment, the diameter of the drill is actually calculated by deriving it from the formula used for the theoretical time.

The calculated diameter was calculated to be 0.366  ± 0.165 cm

The percent error of the diameter appears to be 9.17%

Through this experiment that Bernoulli equation can be used in an experimental lab since the results show that the the true value lies inside the uncertainty of the experimental value. Since the true value is in the uncertainty and the percent error is fairly low, the data can be concluded to be quite accurate.