(Part B) Machinerys Handbook 31st Edition Pages 1484-2979

FLOW OF COMPRESSED AIR IN PIPES Machinery's Handbook, 31st Edition

2779

W = weight in pounds of one cubic foot of entering air L = length of pipe in feet

Flow in Branched (Parallel) Pipes.— Pipe systems commonly have parallel sections to allow some fluid to bypass a component. The principle of continuity dictates that in a steady flow situation, total flow into a branched system is equal to total flow exiting the branched system. The following are the governing equations for branching pipe systems. Q i A 1 v 1 A 2 v 2 = + where Q i is the total flow rate entering the branching system. A 1 and v 1 are the cross sec­ tional area and flow velocity of the first branch, and subscript 2 refers to the second branch. Head loss is equal in all branches and equal to the total head loss across the network: h L h L 1 h L 2 = = Energy Loss in Pipes.— As fluid moves through straight pipe and tube, some energy is lost to friction. The relationship between pressures and velocities at two ends of a pipe is governed by Bernoulli’s equation: p 1 γ 1 --- v 1 2 2 g --- z 1 + + p 2 γ 2 --- v 2 2 2 g --- z 2 = + + where p is pressure, v is velocity, z is elevation, and g is acceleration due to gravity. For inviscid, incompressible liquid flow moving through a pipe, Bernoulli’s equation simplifies because the specific weight of the fluid is assumed to be the same at both points of interest. Darcy-Weisbach Equation and the Moody Diagram: This equation can be used to calcu­ late friction loss in Newtonian liquids for all flow regimes. It requires the use of a friction factor, which is dimensionless and can be determined using the equation for laminar flow, the Colebrook equation for turbulent flow, or graphically through the use of the Moody diagram (Fig. 1). The Darcy-Weisbach equation is: h L fLv 2 2 gD = ------ where h L is head loss in units of length, L is pipe length, v is average fluid velocity, D is inside diameter of the pipe, and f is the friction factor.

64 R e = --- . The Colebrook equation for turbulent

The friction factor for laminar flow is f

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flow is 1 f --- where e is the pipe roughness, and D is the inside diameter. This applies when the pipe is completely full of fluid. Calculators are available online for this factor, or it can be solved numerically. 2 = – log ε 3.7 D ------ 2.51 R e f + ------- 10 Moody’s diagram was generated experimentally. A chart of surface roughness of com­ mon pipe and tube materials can be found in Table 22 for use with the turbulent flow equa­ tion and Moody diagram.

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