You are to choose the pipe diameter for the system shown below. The flow rate is Q 1 ft3/s and the pipe is Schedule 40 commercial steel. The total length including an equivalent length allowance for minor losses is L 1800 ft. There is water flowing through the system with density p 62.4 lbm/fts and viscosity w 1 cP. You may assume the elevation change between points C and D on the diagram is negligible and that the pressure at point 2 in the diagram is atmospheric. You are given three pipe sizes to choose from: nominal 4, 5 and 6 inch diameter. The pump performance curve is described by a bQ4 (gpm), (1) AP(psi) where a 32.5 psi and b 6.7747 x 10 ii psi/gpm Proceed in the following manner a) Divide Eqn. (1) by pg and convert units so that you have an equation that provides the pump head pump in feet as a function of the volumetric flow rate in gpm. Graph the h resulting equation as h (ft) vs. Qgpm) with an z-range from Q 0 to the value of Q at which h 0. b) r each of the three pipe sizes, apply the extended Bernoulli\'s equation with losses and work to the system and solve for the system head system (2) hsystem where again head should be in feet and the right-hand side of Eqn. (2) should be a function of Q,in gpm. To determine the value of the friction factor f, use the Colebrook equation and take the limit as the Reynolds number Re oo for each pipe size. (f will then be a constant for each diameter.) Plot Eqn. (2) for the three pipe diameters on the same graph as part a). Find the points of intersection between the system head and the pump head Report each of the three intersection points to three significant figures as (Q(gpm), h(ft) (The actual inner diameters are 4.026, 5.0472, and 6.065 inches, respectively, for Schedule 40,nominal 4, 5 and 6 inch diameter piping.) The graph should be c) Make a recommendation as to which of the pipe diameters you would choose and why.
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