A certain part of cast iron piping 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 1,500 m long, while the other branch (pipe B) is 2,100 m long. If the flow rate through pipe A is $0.4 \text{ m}^3/\text{s}$, determine the flow rate through pipe B. Disregard minor losses and assume the water temperature to be $15^\circ\text{C}$. Pipe A has a halfway closed gate valve ($K_L = 2.1$) while pipe B has a fully open globe valve ($K_L = 10$), and the other minor losses are negligible. The density and dynamic viscosity of water at $15^\circ\text{C}$ are $\rho = 999.1 \text{ kg}/\text{m}^3$ and $\mu = 1.138 \times 10^{-3} \text{ kg}/\text{m}\cdot\text{s}$. The roughness of the cast iron pipe is $\varepsilon = 0.00026 \text{ m}$. (Round the final answer to three decimal places.)
The flow rate through pipe B is $\text{m}^3/\text{s}$.
