How Does Water Pressure Affect a Submarine at Various Depths?

[biomajor009]

Homework Statement

Your homemade submarine has a circular hole with a diameter of 14 cm in its side. You decide to plug the hole by taping over it with watertight duct tape. This works pretty well while you are exploring the ocean at shallow depths, but you find that as soon as you reach a depth of 9.7 meters the duct tape is dislodged.
(a) What is the pressure of the ocean water at this depth?
(b) What net force was needed to dislodge the duct tape? You may assume that the interior of the sub was at atmospheric pressure.
(c) When the duct tape is dislodged, ocean water begins to shoot into the sub at a speed of 7.1 m/s. You grab something to put over the hole, but all you have handy is a funnel. The large end of the funnel is big enough to cover the hole, while the small end has an opening with a diameter of 2.2 mm. If you place the funnel over the hole, how fast will water shoot out of the small end of the funnel? Would you want to plug up the small end by putting your hand over it?

Homework Equations

The Attempt at a Solution

I'm having trouble getting past the first part of the question. I tried using the equation
P2 = P1 + pgh, but I don't know what P1 should be. Am I even using the right equation?

 

[mjsd]

P1 is the pressure at the surface