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, P_min, 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 m³are pumped per day, what is the speed, v_village, 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, P_actual, than what you calculated in part (a).

(derivation comes straight from continuity. use definition of the area of a circle in terms of diameter not radius)

c. What ADDITIONAL pressure, P_extra, is necessary to deliver this flow? (P_actual= P_min+ P_extra)

(this derivation comes straight from bernoulli.. question is asking for additional pressure.)