Question

A large city waterline pipe has radius 5.7×10^−2 m and feeds ten smaller pipes, each of radius 2.1×10^−2 m , that carry water to homes. The flow rate of water in each of the smaller pipes is to be 6.0 × 10^−3 m3/s, and the pressure is 4.00 × 10^5 N/m2. The homes are 10.5 m above the main pipe. What is the average speed of the water in a smaller pipe? What is the average speed of the water in the main pipe? What is the pressure in the main pipe?

Answer 1

Apply the continuity equation. The flow rate is, dV For the smaller pipe the average velocity of the water is dV dt 6.0x103 m3/s (x(2.1xl01m) = 4.33 m/s For the larger pipe the average velocity of the water is dV dt 10(6.0x101 m/s) (π)(5.7x10-2 m) -5.88 m/:s Use Bernoulli's equation = (10)(4 105 Nr 2)- (10)((43.3)2-(5.87)2)-(103 (9.8)) (10.5 m) -5.02 x106 N/m