Math Help - fluid force

1. fluid force

Hey guys.

This one's giving me a headache. Could soomeone spare from the shame that my friends think that I'm no good a calculus?

Thanks, here we go...

A circular window on salt-water submarine has a radius of 3ft. The window is "reclining" so that the occupants can see above them, and it makes an angle of 30 degrees with the horizontal. The maximum fluid force this window can withstand is 300,000 lbs. What is the maximum depth to which this submarine can submerge.

2. Re: fluid force

The force on a specific point on the glass depends upon the depth of that point- so consider a line across the window having all points at depth "h". The force thin "rectangle", L by dy, L the length of the line across the wind, dy the "infinitesmal" thickness of the rectangle, on that line is the weight of the water above it which is $\rho hLdy$ where $\rho$ is the density of salt water. Take y measured vertically from the top of the window. What is the width, L(y), of the window at that y? What is the depth, h(y)?

The total force is given by $\rho\int_{y=0}^Y h(y)L(y)dy$ where Y is the distance, vertically, from the top of the window to the bottom. You will need to take that 30 degree angle into account.