Suppose I want to pump 80 gallons of air per second (at sea level) through a hose or pipe that runs to a depth of 20 feet, and then let the air (in its natural form -- i.e. not channeled through any kind of diffuser) bubble up from 20 FT deep to sea level. Using the assumptions & questions below, how would a person accurately calculate the following:

Note: I prefer the methods/calculations in lb-ft system; however, feel free to use metric units & calculations if that is easier or more convenient for you.

Assumptions:
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1. sea water density = 63.9 lbs/ft^3
2. pressure @ sea level = 14.7 psi
3. water temperature = 88 degrees F
4. air temperature = 100 F
5. motor/pump efficiency = 85%

What would be the best way to accurately calculate the following:
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1. pressure (psi) @ 20 FT deep = ? (inside the hose/pipe & outside the hose/pipe)
2. air volume @ 20 FT deep = ? (80 gal @ sea level = ? Gal @ 20 FT deep?)
3. the optimal hose diameter & motor size (hp) to minimize power consumption =?
4. optimal operating hose pressure (psi) = ?
5. electrical power (kWh) needed per operating hour to drive the motor/pump = ?
6. motor size (hp) required = ?
7. the time it would take for a bubble (80 gallon @ sea level) to reach sea level = ?

Thanks in advance to those who will help me!

Hello zeffur

This seems more a homework question. There is a specific board for that. See Home - Education - Homework help.

As to the various questions :

To pump air to a certain depth in water, you have to replace the water in the tube with air, i.e. you have to overcome the weigth of that column of water by air pressure first to get air to the bottom of the tube.
On top of that you get the requirements to pump 80 gallons of air per second.

Using the provided assumptions it must be easy to get to the required answers!