posted by sam .
Through a pipe of diameter 16cm, water is pumped from the Colorado River up to Grand Canyon Village, on the rim of the canyon. The river is at 564m elevation and the village is at 2096m elevation.
a) At what minimum pressure must the water be pumped to arrive at the village? The acceleration of gravity is 9.8m/s^3
b)If 4800m^3 are pumped per day, what is the speed of water in the pipe?
c) What additional pressure is necessary to deliver this flow? You may assume that the free-fall acceleration and the density for air are constant over this range of elevations.
a) (density)*g*(elevation change)
= 1.00*10^3 kg/m^3*9.8 m/s^2*1532 m = 15.0*10^6 Pascals
That is about 150 atmospheres.
b) Velocity = (Volume flow rate)/Area
c) Add (1/2)*(density)*V^2 dynamic pressure to the answer in (a)
The density here is the density of water . Air has a neglible effect on the difference between inlet and outlet pressure