A pipe system consists of a gate valve, wide-open (K_v = 0.2), in line A and a globe valve, wide-open (K_v = 10), in line B. The cross-sectional area of pipe A is half of the cross-sectional area of pipe B. The head loss due to the junction, elbows, and pipe friction are negligible compared with the head loss through the valves. Find the ratio of the discharge in line B to that in line A.