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By C. A. Brebbia and A. J. Ferrante (Auth.)

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This is based on the experimental observation that turbulence increases with distance from the wall. 3 we approach the smooth pipe limit and for R* = 60 the rough pipe. The engineer can now obtain the k coefficient for a wide range of Re numbers and different roughnesses. 1 presents some experimental results showing the effective roughness k to be expected in different pipes. 7. 1. 8) showing the relationship between k, Re and k/D. 4 Empirical formulae Empirical formulae of exponential type are frequently used in engineering to estimate head losses in pipes.

4) is an unstable zone and, depending on perturbations, we may have there laminar or turbulent flow. 3 Effect of rugosity in turbulent flow Blasius investigated the effect of rugosity on turbulent flow and determined that for smooth walls viscosity effects are dominant, and the friction coefficient X depends only on the Re number. If the roughness increases, however, the flow is influenced by a roughness coefficient as well as by Re number. 27) where c is a constant. The formula has been confirmed experimentally for values of Re in the range 4000 < Re < 105.

For an ideal fluid the drag is zero, as the pressure forces are in perfect equilibrium around the body. This paradox is due to the fact that the viscosity is zero and therefore drag cannot exist. The drag forces can be computed by integrating the pressure and shear components around the body. 72) Note that these forces are resisted by the pressure or form drag and the skin friction or viscosity drag. Usually, form drag is the more important and sometimes aerodynamic profiles are adopted to diminish it.

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