How Do You Calculate Net Inward Force on a Submerged Barrel?

[xxxzyon]

Help with fluid mechanics!?

Suppose a cylindrical barrel falls off a ship and sinks to the bottom of the sea at a depth of 1.61 km. Assume that the seawater is incompressible, so that its density at the bottom of the sea is the same at the surface :1020 kg/m^3

If the pressure inside the barrel is 1.00 atm (it was sealed at sea level) and the total surface area of the barrel is 3.50 m^2 , find the NET INWARD FORCE acting on the surface of the barrel when it reaches the bottom of the ocean.

For my attempt, I used the formula Ptot = P surface + ρ density of water x g x h.
The total pressure I got was 116 atm, then I plugged this pressure into P = F/A and got a force of 4. 67 x 10^6 N...

I am not sure what I am supposed to be doing first actually, any guidance would be helpful!

 

[UltrafastPED]

So it is the surface area of the barrel, times the net pressure (116 - 1)=115 atm, pointing inwards.

Net force = pressure x area.

Your hydrostatic pressure formula looks correct: http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html
... so double-check your calculations, and you are all done.