Water is pumped through a pipe of diameter 13.0 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 2311 m.(a) At what minimum pressure must the water be pumped to arrive at the village? (in MPa)b) If 4300 m3 are pumped per day, what is the speed of the water in the pipe? (in m/s)(c) What additional pressure is necessary to deliver this flow? Note: You may assume that the free-fall acceleration and the density of air are constant over the given range of elevations.( in kPa)I have tried this over and over but i know B it is 3.75 m/s please help if you know to do this THANKS!!!!!
a) Pressure is the weight of a 1 meter square column of water. The height of the pipe is 2311-564 = 1747 m volume is 1747 m? density of water is density of water at 20C = 0.998 g/cm? = 998 kg/m? mass of water is 1747 m? x 998 kg/m? = 1744000 kg weight of water is 1744000 x 9.8 = 17090000 N Pressure is 17090000 N/m? or 17.09 MP b) Cross sectional are of pipe is A = πr? A = π(.065)? = 0.0133 m? one meter of pipe has a volume of .0133 m? 4300 m? are pumped per day The water in that one meter of pipe has to be changed 4300 / 0133 = 324000 times per day to handle the flow That is 324000 / (24*3600) times per second or 3.75 times per second. Since the section of pipe is is 1 meter, that is 3.75 meters per second.
