A bag house is to be designed to handle 1000 m$$^3$$/min of air. The filtration takes place at constant pressure so that the air velocity through each bag decreases during the time between cleaning according to the relation $$u = \frac{1}{0.267 + 0.08t}$$ where,u is in m/min of cloth and t is the time in min. The bags are shaken in sequence row by row on a 30 mincycle. Each bag is 20 cm in diameter and 3 m height. The bag house is to be square in cross-section with 30 cm spacing between bags and 30 cm clearance from the walls. Calculate the minimum number of bags required