You’re a consultant for maple syrup producers. They tap maple trees andcollect sap with plastic tubing that connects to a common pipe delivering the sap to anevaporator. There it’s boiled to produce thick, tasty syrup. The system can be modeled asa pipe with one end, of cross-sectional area A, exposed to atmospheric pressure. The pipedrops through a vertical distance h1 while its area decreases to A/2, as shown in thefigure. A small vertical glass tube extends from the lower portion as shown and is open toatmospheric pressure. You’re asked to provide a formula for the volume flow rate of thesap as a function of the height h2 of the sap in the tube. Express your answer in terms ofknown quantities.
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
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 the 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 the
figure. 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 the sap in the tube. Express your answer in terms of
known quantities.
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