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

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.

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

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) 73 41.2 18.4 6.8 vs d (cm) 1.5 2 3 5

t vs d for h = 30 cm

t vs 1/d2 for h = 30

t = 164 sec • cm2 • 1/d2

Shortcut t vs d t = 161.8 d-1.97

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) 43.5 23.7 10.5 3.9 vs d (cm) 1.5 2 3 5

t vs d for h = 10 cm

t vs 1/d2 for h = 10 cm

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

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) 26.7 15.0 6.8 2.2 vs d (cm) 1.5 2 3 5

t vs d for h = 4 cm

t vs 1/d2 for h = 4 cm

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

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) 13.5 7.2 3.7 1.5 vs d (cm) 1.5 2 3 5

t vs d for h = 1 cm

t vs 1/d2 for h = 1 cm

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

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?

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.

The relationship is

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

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) 73 43.5 26.7 13.5 vs h (cm) 30 10 4 1

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

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) 41.2 23.7 15.0 7.2 vs h (cm) 30 10 4 1

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) 18.4 10.5 6.8 3.7 vs h (cm) 30 10 4 1

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) 6.8 3.9 2.2 1.5 vs h (cm) 30 10 4 1

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?

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.

The relationship is

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

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.

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 73 1.5 30 10.5 3 10 2.2 5 4 41.2 2 30 3.9 5 10 13.5 1.5 1 18.4 3 30 26.7 1.5 4 7.2 2 1 6.8 5 30 15.0 2 4 3.7 3 1 43.5 1.5 10 6.8 3 4 1.5 5 1 23.7 2 10

The final equation is found by... With the 16 sets of data entered, create the following column. 73 1.5 30 41.2 2 30 18.4 3 30 6.8 5 30 43.5 1.5 10 23.7 2 10 10.5 3 10 3.9 5 10 Then create the values for the column. 26.7 1.5 4 15.0 2 4 6.8 3 4 2.2 5 4 13.5 1.5 1 7.2 2 1 3.7 3 1 1.5 5 1

Graphing t vs h.5/d2

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

That’s all folks!