Abstract
This paper is a continuation of the second half of the problem involved in the writer’s 1933 paper on pipe flow and Prof. Lewis F. Moody’s 1944 paper. The pipe-flow situation is shown to be in satisfactory condition; the main attention is on bends and fittings.
It has been customary in the past to rate the losses in bends and fittings as a function of velocity head. Another old method, less used, was to rate the loss in equivalent length of pipe. In the case of bends and fittings two types of loss are superposed, i.e., skin friction or pipe-loss type, and bend loss. The methods of test are less accurate than for pipe as they involve getting the difference between two much larger readings. Consequently the test data are much poorer than for pipe, for several reasons: one given above; another that the pipe fittings are not geometrically similar; and the test data are very much less than those on pipe. It seems clear that a rational formulation, however, could be attempted if we can establish some picture of the factors involved in the losses. Up to the present time bend and fitting losses have been taken from a range of factors unconnected with size, roughness, or velocity of flow. This formulation, on the basis of the tests, endeavors to show that there is a true bend loss for smooth fittings underlying the superposed losses due to roughness and Reynolds number. The final formulation involves an evaluation of the true bend loss and an evaluation of the roughness and Reynolds number effects paralleling the friction factor in pipe. The final conclusion is that the equivalent pipe length is by all means the most reliable and convenient method of tabulating losses in different kinds of fittings and bends. The final formulation is . This formulation has been checked against the test results and while it is obvious that the factors will be both plus and minus over a considerable range, the general correlation of the test data appear to be as good as our present test information will permit.
