## P

The character of the flow is determined through the Reynolds number, Re = pwD/^, where ^ is the viscosity of the fluid. This nondimensional grouping represents the ratio of dynamic to viscous forces acting on the fluid.

Experiments have shown that if Re < 2300, the flow is laminar. For larger Re the flow is turbulent. Figure I.16 shows how the friction factor depends upon the Re of the flow. Note that for laminar flow the f vs. Re curve is single-valued and is simply equal to 16/Re. In the turbulent regime, the wall roughness e can affect the friction factor because of its effect on the velocity profile near the duct surface.

If a duct is not circular, the equivalent diameter De can be used so that all the relationships developed for circular systems can still be used. De is defined as

P is the "wetted" perimeter, that part of the flow cross section that touches the duct surfaces. For a circular system De = 4(nD2/4nD) = D, as it should. For an annular duct, we get

Fig. I.16 Friction factors for straight pipes.

Fig. I.16 Friction factors for straight pipes.

where f is the friction factor for the tubes (a function of the Re), N the number of tube rows crossed by the flow, and Fd is the "depth factor." Figures I.17 and I.18 show the f factor and Fd relationship that can be used in pressure-drop calculations. If the fluid is air, the pressure drop can be calculated by the equation p=M ft

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