Halliday, Resnick & Walker — Fluids: Problem 32

32 Figure 14-34 shows two sections of an old pipe system that runs through a hill, with distances \(d_A = d_B = 40\text{ m}\) and \(D = 110\text{ m}\). On each side of the hill, the pipe radius is \(2.00\text{ cm}\). However, the radius of the pipe inside the hill is no longer known. To determine it, hydraulic engineers first establish that water flows through the left and right sections at \(2.50\text{ m/s}\). Then they release a dye in the water at point \(A\) and find that it takes \(88.8\text{ s}\) to reach point \(B\). What is the average radius of the pipe within the hill?