Acertain part of cast iron piping (ε =0.00026 m) of a water distribution system involves a parallel section. both parallel pipes have a diameter of 30 cm, and the flow is fully turbulent. one of the branches (pipe a) is 1000 m long with a halfway-closed gate valve (k =2.1) while the other branch (pipe b) is 3000 m long with a fully open globe valve (k = 10). if the flow rate through pipe a is 0.4 m3/s, determine the flow rate through pipe b. do not disregard minor losses and assume the water temperature to be 15 °c. also, show that the flow is fully turbulent, and thus friction factor is independent of reynolds number. assume that the density and viscosity of water to be 1000 kg/m3 and 1.138 x10-3 pa. s.