On the flow of water through pipes and passages having converging or diverging boundaries

Abstract

1. Introduction .—As is well known, diverging boundaries in a passage conveying a fluid tend to unsteadiness of flow with consequent loss of head in eddy formation, the energy loss in such a pipe being greater than in a parallel pipe with the same mean velocity of flow. Converging boundaries, on the other hand, have an opposite tendency, and the present investigation, which was commenced in the engineering laboratories of the Manchester University, and has been completed in the engineering department of University College, Dundee, was undertaken with a view of determining: (1) how this loss depends upon the angle of divergence of opposite sides of a circular pipe with uniformly diverging boundaries; (2) the relative values of the losses in a circular and a square pipe having the same angle of divergence, or increasing in area between the same initial and final limits, in the same length; (3) the effect of a divergence in the one pair of sides of a rectangular pipe, the second pair being parallel; (4) the effect of a variable, as opposed to a regular, rate of divergence of the sides; (5) the loss of head and, if possible, the critical velocity in a circular pipe with uniformly converging boundaries. Twenty-five pipes in all were constructed for use in the experiments. These were very carefully made of wood, finished off with a coating of shellac varnish. They may be divided into three sets. Twenty-five pipes in all were constructed for use in the experiments. These were very carefully made of wood, finished off with a coating of shellac varnish. They may be divided into three sets.