Water at 70 degree F flows by gravity from a large reservoir at a high elevation
ID: 2321946 • Letter: W
Question
Water at 70 degree F flows by gravity from a large reservoir at a high elevation to a smaller one through a 120-ft-long, 2-in-diameter cast iron piping system that includes four standard flanged elbows, a well-rounded entrance, a sharp-edged exit, and a fully open gate valve Taking the free surface of the lower reservoir as the reference level, determine the elevation z_1 of the higher reservoir for a flow rate of 10 ft^3/min. A certain part of cast iron piping of a water distribution system involves a parallel section. Both parallel pipes have a diameter of 30 cm, and the flow is fully turbulent. One of the branches (pipe A) is 1000 m long while the other branch (pipe B) is 3000 m long. If the flow rate through pipe A is 0.4 m^3/s, determine the flow rate through pipe B Disregard minor losses and assume the water temperature to be I5 degree C. Show that the flow is fully turbulent, and thus the friction factor is independent of Reynolds number.Explanation / Answer
82 ) velocity of flow = 0.4 / pi * 0.3^2 /4 = 5.659 m/s
Reynolds number = v * D / viscosity = 5.659 * 0.3 / 1.156 * 10^-6
= 1468598.6 (fully turbulent flow)
from moody chart , for complete turbulence rough pipes friction factor is independent of Re and f = 0.078
use bernoullis equation for both pipes
0.5 * rho * Va^2 * (1 + f * La / D) = 0.5 * rho * Vb^2 * (1 + f * Lb / D)
5.659^2 ( 1 + 0.078 * 1000 / 0.3) = Vb^2 ( 1 + 0.078 * 3000 / 0.3)
Vb = 3.2714 m/s
flow rate through B = pi * 0.3^2 * 3.2714 / 4 = 0.2312 m^3/s
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