Experiment 2: Fluid Dynamics

Purpose: This lab was developed to test Bernoulli's equation. In order to validate this equation, we needed to time how fast a stream of water left a hole in a bucket filled with up to 5 inches in water and then calculate a theoretical time to see if they matched.

Equipment:

• bucket with small hole filled with water
• timer
• 300 mL beaker
• ruler

Set Up/Experiment:

• conduct 6 trials of how fast 300 mL of water is emptied from bucket to beaker
• hole is poked in bucket
• measure diameter of hole
• tape hole closed
• fill bucket with water to 5 inches
• remove tape, let water empty into beaker
• time how long it takes

Data:

Trial #	t (actual)
1	12.2 ± 1.0
2	14.53 ± 1.0
3	15.03 ± 1.0
4	15.3 ± 1.0
5	15.87 ± 1.0
6	14.94 ± 1.0

Calculate:
find t (theroretical) using given equation:

t = V/(A√2gh)


V = 0.016 cu. ft.
A = 3.14E-04 sq. ft.
h = 0.417 ft.
√2gh = (2*32 ft./s/s*0.417 ft.)^(1/2) = 5.17 ft./s


t theoretical = 9.86 seconds

Analyze:

Calculate the error between t_theoretical and t_actual for all test runs.

Compare the theoretical value to the experimental value.  Do they agree within uncertainty? 

Trial #	t (actual)	t (theoretical)	% error
1	12.20	9.86	23.7
2	14.53		47.4
3	15.03		52.4
4	15.30		55.2
5	15.87		61.0
6	14.94		51.5

The lowest percent error is more than 23%. There is a very large propagation of error. Even if the uncertainty in the first trial was off by 1.0 second at 11.2, the % error would still be at about 13.6%.

Assume the diameter you measured isn’t accurate. What is the actual diameter? To solve, rearrange the time-to-drain equation to solve for the diameter of the hole.

t (average) = 14.7 seconds

t = V/(A√2gh) --> A = V/(t√2gh) = 0.016/(14.7*(2*32*0.417)^(1/2)) = 2.11E-04 sq. ft.
A = πr^2 --> r = (2.11E-04/π)^(1/2) = 0.008 ft.
d = 2r = 0.016 ft. = 0.192 inches

What was the percent error in the drill bit’s diameter?

% error = ((actual - theoretical)/theoretical)*100 = ((0.24-0.19)/0.192)*100 = -20.8%

Conclusion:
Using only a timer gave us a high error in all our calculations. The methods for catching the water and timing the water flow are extremely inaccurate. That is why our calculated values are much different from the actual value. The difference between the drill bit diameter calculation was off by 21% and the highest percent error between the theoretical time and the actual time was off by 61%.