Halliday, Resnick & Walker — Fluids: Problem 35

35 Canal effect. Figure 14-35 shows an anchored barge that extends across a canal by distance $d = 30\text{ m}$ and into the water by distance $b = 12\text{ m}$. The canal has a width $D = 55\text{ m}$, a water depth $H = 14\text{ m}$, and a uniform water-flow speed $v_i = 1.2\text{ m/s}$. Assume that the flow around the barge is uniform. As the water passes the bow, the water level undergoes a dramatic dip known as the canal effect. If the dip has depth $h = 0.80\text{ m}$, what is the water speed alongside the boat through the vertical cross sections at (a) point $a$ and (b) point $b$? The erosion due to the speed increase is a common concern to hydraulic engineers.