Chapter 15, Problem 54P

You’re a consultant for maple syrup producers. They tap maple trees and collect sap with plastic tubing that connects to a common pipe delivering sap to an evaporator. There it’s boiled to produce thick, tasty syrup. The system can be modeled as a pipe with one end, of cross-sectional area A, exposed to atmospheric pressure. The pipe drops through a vertical distance h₁ while its area decreases to A/2, as shown in Fig. 15.25. A small vertical glass tube extends from the lower portion, as shown, and is open to atmospheric pressure. You’re asked to provide a formula for the volume flow rate of the sap as a function of the height h₂ of sap in the tube.

FIGURE 15.25 Problem 54