Water at 70 degree F flows by gravity from a large reservoir

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.

Solution

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