Experiment 2: Fluid Dynamics

Purpose:
To experimentally measure what effects the height of water above a hole has on the flow rate of water out of that hole.  This  will be conducted six times with varying heights and the results compared.

Equipment:

• Bucket with small hole near bottom
• Beaker
• Meter Stick
• Stopwatch
• Tape
• Water

Experiment:

 

Measure and record the dimensions of the hole in the bucket.  Place bucket above the beaker so that the stream of water exiting the hole enters the beaker.  Place tape over the hole so that water does not leak out.  Fill the bucket to a certain depth and record the water height above the hole.  Remove the tape and allow 300 mL to flow into the beaker from the bucket while recording the time that it takes using a stopwatch. 

 

Below is the data that was recorded from the six trials.

 

0.0072	±	0.0005	Hole Diameter (m)
4.072E-05	±	0.000006	Hole Area (m^2)
0.0003	±	0.000025	Water Removed (m^3)
0.02	±	0.0075	Hole Above Bottom (m)
Trial		Initial Height (m)			Final Height (m)			Avg Height Above Hole (m)			Time (s)
1		0.080	±	0.005	0.074	±	0.005	0.057			9.8	±	0.2
2		0.080	±	0.005	0.076	±	0.005	0.058			9.6	±	0.2
3		0.073	±	0.005	0.063	±	0.005	0.048			10.8	±	0.2
4		0.069	±	0.005	0.060	±	0.005	0.045			11.1	±	0.2
5		0.065	±	0.005	0.055	±	0.005	0.040			11.9	±	0.2
6		0.094	±	0.005	0.086	±	0.005	0.070			9.0	±	0.2

The data below shows the calculation of the theoretical times that it would take to drain the same amounts of water for trials one through six.  In addition, the % error was calculated for each trial.

3.506E-05	Min Hole Area (m^2)
4.637E-05	Max Hole Area (m^2)
0.000275	Min Water Removed (m^3)
0.000325	Max Water Removed (m^3)
0.013	Min Hole Above Bottom (m)
0.028	Max Hole Above Bottom (m)
Experimental					Theoretical
Trial	Min Height (m)		Max Height (m)		Min Time (s)	Max Time (s)		Theoretical Time(s)			% Error
1	0.045		0.070		5.1	9.9		7.5	±	2.4	30.7%
2	0.046		0.071		5.0	9.8		7.4	±	2.4	29.3%
3	0.036		0.061		5.4	11.1		8.3	±	2.8	30.5%
4	0.032		0.057		5.6	11.7		8.7	±	3.0	28.3%
5	0.028		0.053		5.8	12.6		9.2	±	3.4	28.9%
6	0.058		0.083		4.7	8.7		6.7	±	2.0	34.4%

 

The data below shows the calculations of how big the hole should theoretically by in order to drain the water in the time experimentally measured plus the % error associated. 

0.0003	±	0.000025	Water Removed (m^3)
0.02	±	0.0075	Hole Above Bottom (m)
Experimental								Theoretical
Trial		Time (s)			Height (m)			Min Hole Diameter (m)			Max Hole Diameter (m)			Hole Diameter (m)			% Error
1		9.8	±	0.2	0.057	±	0.013	0.0055			0.0068			0.0061	±	0.00066	17.4%
2		9.6	±	0.2	0.058	±	0.013	0.0055			0.0068			0.0062	±	0.00066	16.7%
3		10.8	±	0.2	0.048	±	0.013	0.0054			0.0068			0.0061	±	0.00072	17.6%
4		11.1	±	0.2	0.045	±	0.013	0.0054			0.0069			0.0062	±	0.00075	16.7%
5		11.9	±	0.2	0.040	±	0.013	0.0053			0.0069			0.0061	±	0.00080	17.3%
6		9.0	±	0.2	0.070	±	0.013	0.0055			0.0067			0.0061	±	0.00059	18.8%

Conclusion:



The experimental values obtained for time to drain are higher than the theoretical values calculated but are the same within the experimental error.   The drill bit calculations show that the hole diameter should be about 0.0061 meters with some error.  The hole size is within the error but the average comes out smaller than the measured valued of the hole.