An underground plastic pipe is to be used to carry water away from a building. As shown in Fig. P11.15, the pipe of diameter D will run downward and have both ends open to the air (pressure P₀). The site requires a drop of H = 2 m over a length L = 40 m. The volume flow rate Q will depend on the weather, but it is supposed that it will not exceed 1 gal/s, or 3.8 × 10⁻³ m³/s (= Q_max). It is desired to choose an appropriate value for D.

(a) Use the engineering Bernoulli equation to calculate the pipe diameter that will exactly accommodate the expected maximum flow. You may assume that the pipe is hydrodynamically smooth.

(b) If D is chosen as in part (a) and Q < Q_max, the pipe will not run full. How would you know that mathematically? 

(c) For the same D, what would happen if ever Q > Q_max? Would the engineering Bernoulli equation still apply to the pipe?

Transcribed Image Text:

a P= Po Figure P11.15 Drainage pipe. L g D H P= Po