You\'re asked to provide a formula for the volume flow rate of the sap as a func

Question

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.

Express your answer in terms of the variables A, h1, h2, and gravitational acceleration g.

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 h_1 while its area decreases to A/2, as shown in the given figure. A small vertical glass tube extends from the lower portion, as shown, and is open to atmospheric pressure. (Figure 1) You're asked to provide a formula for the volume flow rate of the sap as a function of the height h_2 of sap in the tube. Express your answer in terms of the variables A, hi, ho, and gravitational acceleration g.

Explanation / Answer

using bernauli's equation b/w point A

and point just below glass tube

p + row * g *h1 +0.5 * row * v^2 = (p + row * g * h2) + 0 + 0.5 * row * (2v)^2

row * g *(h1-h2) = 0.5 * row * (4-1) V^2

2* g *(h1-h2) /3 = V^2

sqrt( 2* g *(h1-h2) /3) = V

volume flow rate = A * sqrt( (2/3)* g *(h1-h2) )  

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