Experiment 2: Fluid Dynamics

Introduction: The purpose of this lab is to confirm Bernoulli's equation, specifically the special case of large volumes: Flow Rate = V÷t = A*sqrt(2gh)

Procedure: We took a large bucket with a hole drilled in it and measured the diameter of the hole. We then taped off the hole and filled the bucket with 14cm of water.

 We removed the tape and one of us placed our finger over the hole. Another readied a 500ml beaker.

 The person holding the whole withdrew and started a stopwatch. We timed how long it took to fill the beaker to 300ml.

 When the water level in the beaker reached 300ml, we stopped the time and plugged the hole again.

We then refilled the water level in the bucket to 14cm and repeated five more times.

Data: Hole diameter: 5.1mm, Average time: 13.86 s

Trial	Time
1	14.91s
2	13.86 s
3	13.20 s
4	13.55 s
5	14.26 s
6	13.39 s

 

Analysis: Using t = V÷(A*sqrt(2gh)) we calculated t theoretical to be 8.87 s. Here is the percentage error between actual and theoretical values of t for all trials 

Trial	Percentage Difference
1	68.1%
2	56.3%
3	48.8%
4	52.8%
5	60.8%
6	51.0%

 

Using is the above equation solved for A and the average experimental time, I calculated the theoretical diameter of the hole in the bucket. Using the equation (experimental diameter–theoretical diameter)÷Theoretical diameter x 100%, I found a 25% error. There is a steady error of about 55% between theoretical time and experimental time. The imprecise nature of this data can be explained by our inability to stop the watch at exactly 300mL. We also had uncertainty of about plus or minus a centimeter when measuring the 14cm water level. The inaccurate nature of this data can be explained by the diameter of the hole drilled in the bucket. We could not get a consistent measure on the hole because it was not round. It was irregular and conical shaped. The inaccuracy of our data is much greater than our lack of precision so it can be assumed that our consistent mistake can be attributed to the incorrect measurement of the hole.