Can some one help me with this material balance question?
3-14a. When full, a bathtub contains 25 gallons of water and the depth of the water is one foot. If the empty bathtub is filled with water from a faucet at a flow rate of 10 liters per minute, how long will it take to fill the bathtub?
3-14b. Suppose the bathtub has a leak and water drains out of the bathtub at a rate given by Torricelli’s law.
Qleak=Cd Ao root(2gh)
Here h is the depth of water in the bathtub, and Cd represents the discharge coefficient associated with the area of the leak in the bathtub, Ao. Since neither Cd nor Ao are known, we express
Qleak= k root(h)
in which k=CdAoroot(2g). To find the value of k we have a single experimental condition given by
Experiment: Qleak=33.16x10^-5 m^3/s, h=.10m
Given the experimental value of k, assume that the cross section of the bathtub is constant and determine how long it will take to fill the leaky bathtub.