I am working through Penney and Edwards Differential Equations and Boundary Value Problems 4th edition.
On section 1.4 Problem 60, I am not getting what they have for an answer, and I am not completely certain that it is my fault as they make their fair share of errors.
The question reads:
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 initially half full of xylene, how long will it take for the liquid to drain completely?
The answer they get is 6 min 3 sec.
I get 8 min 32 sec.
You are supposed to use Toricell's Law which states: A(y)dy/dt = -a * sqrt(2gy) where g is 32ft/sec^2.
To do this, I observed that the area of a cross section A(y) is a constant 9 * pi. a = (1/12) ^ 2 * pi.
After this, it is a routine differential equation. And solving for t in the equation y(t) = 0 yields 162 * sqrt(10) sec or 8 min 32 sec.