Consider a right cylinderical hot tub. Radius = 5 feet; Height = 4 feet; placed on one of its circular ends. water is draining from the tub through a circular hole in the base of the tub 5/8inches in diameter.
k = .6; using Torricelli's Law v = [2*g*h(t)]^1/2 and the equation
dV/dt = -kAv
where A is the area of the drain
V is the volume of water in the hot tub at time t
Find: a) find the rate at which the depth of water is changing
b) find the time required to drain the tub if it is initially full
c) find the time required to drain the upper half and then the lower half of the tub
Solving Differential Equations by Separation of Variables is investigated. The solution is detailed and well presented.