Water is pumped up from the Colorado River to supply Grand
Canyon Village, located on the rim of the canyon. The river is at
an elevation of 564 m, and the village is at an elevation
of 2,095 m. Imagine that the water is pumped through
a single long pipe 20.0 cm in diameter, driven by a
single pump at the bottom end.
(a) What is the minimum pressure at which the water must be
pumped if it is to arrive at the village?
MPa
(b) If 4,600 m3 of water is pumped per
day, what is the speed of the water in the
pipe? Note: Assume the free-fall acceleration
and the density of air are constant over this range of elevations.
The pressures you calculate are too high for an ordinary pipe. The
water is actually lifted in stages by several pumps through shorter
pipes.
m/s