# Submarine fluid physics problem

cathliccat
Ok, 'A circular window with a 30 cm diameter in a submarine can withstand a maximum force of 5.2x10^5N. What is the maximum depth (in m) in a lake to which the submarine can go without damaging the window round off to the nearest whole number?'

I tried P=F/A=pAhg/A, so I converted 30 cm to meters, solved for P then tried to find h. p=1000, A=pi*.15^2, h=?, g =9.8. So .070 = 9.8h, h=7.21X10^-6. That can't be right because then the submarine wouldn't move at all before the window busted.

Can someone tell me where I went wrong? Thanks!

Staff Emeritus
Gold Member

Originally posted by cathliccat
I tried P=F/A=pAhg/A
This is correct. It seems that somehow you later derived the equation A = g h, since you said "0.70 = 9.8 h." I'm not sure at all where got this! You have the right equation -- just solve it for h.

The pressure at a depth of h meters in a fluid is given by

P = [rho] g h

The force on the window is indeed equal to

F = P A or P = F / A

where A is the area of the window.

Equating these, we get

P = F / A
[rho] g h = F / A

h = F / (A [rho] g)

Does this make sense?

- Warren