1. Analysis of Water Can Experiment
Created for CVCA Physics by
Dick Heckathorn
30 August 2K+4

2. Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
The time for the can to empty is dependent on two variables. One is the diameter of the opening in the can, the other is the height of the water in the can.

3. Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
To investigate how both height and diameter affect the time for the water to drain out, one must investigate time as a function of either height or diameter keeping the other constant.

4. Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
Let’s begin by plotting time vs diameter keeping the height constant.
time is a function of diameter

5. We will use the time values for
Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
We will use the time values for
h = 30 (cm) vs
d (cm)

6. t vs d for h = 30 cm

7. t vs 1/d2 for h = 30

8. t = 164 sec • cm2 • 1/d2

9. Shortcut t vs d
t = d-1.97

10. Time to Empty Can (sec) We could have used
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
We could have used
h = 10 (cm) vs
d (cm)

11. t vs d for h = 10 cm

12. t vs 1/d2 for h = 10 cm

13. t = 98.0 sec • cm2 • 1/d2 for h = 10 cm

14. Time to Empty Can (sec) Or we could have used
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
Or we could have used
h = 4 (cm) vs
d (cm)

15. t vs d for h = 4 cm

16. t vs 1/d2 for h = 4 cm

17. t = 60.3 sec • cm2 • 1/d2 for h = 4 cm

18. Time to Empty Can (sec) Or we could have used
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
Or we could have used
h = 1 (cm) vs
d (cm)

19. t vs d for h = 1 cm

20. t vs 1/d2 for h = 1 cm

21. t = 29.4 sec • cm2 • 1/d2 for h = 1 cm

22. Yes, it is the values for h = 30 cm.
Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
Is there a preference?
Yes, it is the values for h = 30 cm.
Why?

23. the range of values is large.
Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
The values are large, thus the error measurement is of a lesser percentage
and
the range of values is large.

24. The relationship is

25. Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
Now let’s plotting time vs height keeping the diameter constant.
time is a function of height

26. We will use the time values for
Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
We will use the time values for
d = 1.5 (cm) vs
h (cm)

27. Shortcut t vs h
t = 13.5 sec/cm0.499 • h0.499

28. Time to Empty Can (sec) We could have used
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
We could have used
d = 2 (cm) vs
h (cm)

29. Time to Empty Can (sec) Or we could have used
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
Or we could have used
d = 3 (cm) vs
h (cm)

30. Time to Empty Can (sec) Or we could have used
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
Or we could have used
d = 5 (cm) vs
h (cm)

31. Yes, it is the values for d = 1.5 cm.
Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
Is there a preference?
Yes, it is the values for d = 1.5 cm.
Why?

32. the range of values is large.
Time to Empty Can (sec)
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2
The values are large, thus the error measurement is of a lesser percentage
and
the range of values is large.

33. The relationship is

34. They are combined by multiplication
We Have Found...
and
They are combined by multiplication

35. The final equation is found by...
Plotting
And taking the slope of the line.
To do so, create the following columns and fill in the data.

36. The final equation is found by...
Diameter
Height in (cm)
(cm) 30 10 4 1
1.5 73
43.5
26.7
13.5 2
41.2
23.7
15.0
7.2 3
18.4
10.5
6.8
3.7 5
3.9
2.2

37. The final equation is found by...
With the 16 sets of data entered,
create the following column.
Then create the values for the column.

38. Graphing t vs h.5/d2

39. The Final Equation is...
And with Units...

40. That’s all folks!