Water is pumped through a pipe of diameter 15.0 cm from the Colorado River up to Grand Canyon Village, on the rim of the canyon. The river is at 564 m elevation and the village is at 2096 m. a. At what minimum pressure, Pmin, must the water be pumped to arrive at the village? (In other words what pressure is needed at the bottom to get the water to the top with exactly no pressure remaining?) b. If 4500 m3 are pumped per day, what is the speed, vvillage, of the water in the pipe in the village? If the people at the top are seeing water move through the pipe, there has to be SOME pressure, therefore there must be more pressure pushing from the bottom, Pactual, than what you calculated in part (a). c. What ADDITIONAL pressure, Pextra, is necessary to deliver this flow? (Pactual = Pmin + Pextra)
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.
Water is pumped through a pipe of diameter 15.0 cm from the Colorado River up to Grand Canyon Village, on the rim of the canyon.
The river is at 564 m elevation and the village is at 2096 m.
a. At what minimum pressure, Pmin, must the water be pumped to arrive at the village? (In other words what pressure is needed at the bottom to get the water to the top with exactly no pressure remaining?)
b. If 4500 m3 are pumped per day, what is the speed, vvillage, of the water in the pipe in the village?
If the people at the top are seeing water move through the pipe, there has to be SOME pressure, therefore there must be more pressure pushing from the bottom, Pactual, than what you calculated in part (a).
c. What ADDITIONAL pressure, Pextra, is necessary to deliver this flow?
(Pactual = Pmin + Pextra)
[Note: You may assume that the free-fall acceleration and the density of air are constant over the given range of elevations.]
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