A large tank of diameter D and open to the atmosphere is draining water through a nozzle of diameter d. where D >>d. The level will decrease slowly from an initial value z= h(0) (tanks initial fill height) down to z=0. At which time the flow will stop. Assuming the Bernoulli equation is a reasonable model over the duration of this process and that there are no dynamic "contraction" effects, estimate the time t until the flow stops.
HINT: Let the water level above the nozzle at any particular time t be h(t). Write additional conservation equation relating the rate of change of water volume within the tank to be volumetric rate of nozzle outflow. Answer should be a function of D,d,h(0), g.