For the tank shown, derive a relationship for the time needed to discharge the liquid from height h to height h$.$ Assume the density of the liquid is constant. The liquid is fed at a flow rate $=$ F; and leaves the tank at a rate $=$Sh$,$ where S is discharge coefficient which is constant. The volume of a cylinder $==$ r r$3$ h and the volume of the cone $=1/3$ r$^3$ h$.$