A terrible tragedy, averted

Two adult brothers were watching nature programs and saw this image of elephants walking around underwater and using their trunks as snorkels.

Later that day as they were playing with a 100 foot length of garden hose, they thought up a "great" idea. They could use the hose as a super long snorkel. They had enjoyed diving in the nearby disused quarry pond, but had never been able to dive deeper than about 15 feet. So they packed up their hose and took it to the pond.

After a little practice on the edge of the pond, the oldest felt a little light headed, but figured he was just breathing too fast through the hose. He determined to breathe slowly through the hose as he walked into the shallow end. When he had walked out 10 feet from shore, but was still only in knee-deep water, he jerked the hose from his mouth and sat down hard.

Feeling that something was fundamentally wrong with their good idea, the two coiled up the hose on the bank and spent the rest of the day diving and swimming without any assistance from the hose.

Answer the following question.

What is the longest length of hose in centimeters a person could effectively use as a snorkel?State your assumptionsand identify all the variables in your calculation. Show your work.

(Hint: Assume that the hose diameter is 5/8 inch (1.5875 cm). How do you calculate the volume of a cylinder?)

A related problem is how deep could a person dive using a snorkel, assuming they could move a sufficient volume of air through the hose. But that involves the pressure of water on the lungs and we won't get any further into that.