Chapter 16, Problem 12P

You must design a triangular open channel to carry a waste stream from a chemical plant to a waste stabilization pond (Fig. P16.12). The mean velocity increases with the hydraulic radius $R_h=A/p$, where A is the cross-sectional area and p equals the wetted perimeter. Because the maximum flow rate corresponds to the maximum velocity, the optimal design amounts to minimizing the wetted perimeter. Determine the dimensions to minimize the wetted perimeter for a given cross-sectional area. Are the relative dimensions universal?

FIGURE P16.12