Flowing Through Mathematics

In this activity, you will simulate water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. The x-axis represents the time that has passed and the y-axis represents the height of the water in the tube.

You will be using your notes to record your observations:

• First, predict the shape of the graph that will be produced as the water flows from the tube and record this in your notes.

• Next, click Start and observe the graph as the water flows from the tube. Did the graph resemble your prediction? Record why or why not in your notes.
• What point on the graph represents that the tube is empty? Record your answer in your notes.
• Set the diameter of the tube to .5 before answering questions below:

Copy the following statements into your notes, and fill in the blanks to describe the graph. Click on the blanks to see the correct answers.

1. The height of the water in the tube begins at Interactive button. Assistance may be required. _______. 73 cm
2. The water flows out of the tube and is half empty after approximately Interactive button. Assistance may be required. _______ 6 seconds.
3. Just before the tube is empty, the rate the water flows slows down. The tube is finally empty after Interactive button. Assistance may be required. _______ 20 seconds.