Consider an axially symmetric tank where the shape of the wall is given by f(z) = R(z/H)^n, as shown in the figure. Fluid with density of is drained from a spigot of cross-sectional area, a. Assume that there is no contraction(vena contracta). Please answer following questions.

a. What would be the shape of the vessel, i.e., value of n, so that the level of fluid drops at a constant rate?

b. How much time, t, does it take to empty the tank with liquid filled up to the rim?

c. Calculate t for n = 0 (cylinder) and n = 1 (cone).

R f(z) = R(z/H)" I N spigot cross section area, a