A cylindrical tank with length 5 ft and radius 3 ft is situated with its axis horizontal. If a circular bottom hole with a radius of 1 in is opened and the tank is half full of xylene, how long will it take for the liquid to drain completely?


I know to use Torricelli's Law in the version A(y)dy/dt=-a*sqrt(2gy) where A is the cross sectional area of the tank, y is the depth of the liquid, a is the area of the drain, and g is gravity. I have the problem set up in full except for A(y). I know this will be a rectangle with varying width. How do you find this varying width? I know it changes in relation to the circular bases of the horizontal cylinder, but i am stumped on how to express the value mathematically. ANy and all help is appreciated! Thank you!