Optimum Diameter Exponent of a Pipeline Water Conveyance System

Abstract

The diameter exponent used for evaluating bifurcations of arteries, trees, rivers and so on was introduced to discuss the bifurcation in a pipeline water conveyance system. The relation between the discharge and diameter was discussed using numerical experiments.
1) It was clarified that optimum diameter exponent Δ to reduce construction costs given as a function of the diameter and length was about 2. Therefore, at the bifurcation, the location of each pipeline or water head at the bifurcation point is desired to be given as each velocity is equal. By applying this parameter Δ to a pipeline water conveyance system, the optimum location of each pipeline at bifurcation can be obtainded directly and easily from optimum duty of water.
2) In numerical experiments, it was recognized that the construction costs at each bifurcation was reduced 1.7-14.4% by researching the position of bifurcation point of pipelines. This perecntage was largest in the case that the length of each line was almost the same, and that one of them being at the end of the flow. The locations of each pipeline as a result of this precise calculation and locations easily obtainded by applying optimum diameter exponent Δ showed close agreement.
3) It was recognized that diameter exponent δ given by investigating the general relations between velocities and diameters used for construction was about 2, the same as optimum diameter exponent Δ. Therefore, it was clarified that parameter δ can be used as a condition to obtain the optimum location of pipelines if it is defined as a constant.