Fluid Dynamics Lab

Objective: Use Bernoulli equation to figure out the time it takes to drain an amount of water from a bucket with a hole in the bottom and use this to examine experimental error.

Equipment:

• A bucket with a small hole drilled into the side
• Tap water
• Graduated cylinder
• Ruler 
• Stopwatch

Bernoulli"s equation work:

To find the time to empty a volume of water we need to find the rate of flow.

Set up:
First the bucket's hole was taped over. Then the bucket was filled with water and the water level in the bucket was measured with the ruler.

Procedure:
 To get  an idea of the procedure a pilot test was run. The tape was peeled off as the timer was started and the drained water was caught in the graduated cylinder. Once the graduated cylinder was filled to 100 mL then the stopwatch was stopped and the drain hole was covered. Our Pilot run had a time of 
5.23 (+/-) 0.10 s. 

Six official trials were run with the results as listed below. The measurements of the radius of the drain hole and height of the water in the bucket are also listed.

Run	1	2	3	4	5	6
Time to empty (tactual),s ±0.10	5.83	6.35	6.43	6.23	6.04	6.3
Diameter of Drain Hole,  mm	5.8±0.2
Height of Water, cm	15.0±0.2

     Some calculations with the measured values showed that the time to drain the water should have been 2.21s

     Since this is drastically different then the times recorded during the experiment, the equation was rewritten to find the radius of the drain hole needed to empty the same amount of water in the calculated time.

This radius of 3.5mm was different from the measured 5.8mm. This is most likely due to the fact that the calculated 2.2s came from measurements with their own uncertainties. The one measured with a caliper had the direct uncertainty of measurement while the time uncertainty was dependent on 3 other measurements. Since both values of the radius of the drain hole came from measurements the best way to calculate the percent error is as follows.

    The diameter of the whole was said to be a quarter inch (6.35 mm). Comparing this to the measured 5.8±0.2mm gives an error of 9.1% error using the above method.

    The reason this method is used here instead of the %error where the difference is divided by the "True" value is because there is no real True value since both methods depend on measurements with uncertainty.