Solved: Youre a consultant for maple syrup producers. They tap maple trees and collect

Chapter 15, Problem 54

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Youre 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 its 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. Youre 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. h2 h1 A 1 2A Figure 15.25 54