Aqueducts for Least Cost Conveyance of Water

Models of the cross section of a tunnel, a pipeline and a canal are designed showing the relative sizes of all dimensions. These relative sizes are all related to some one important dimension. The construction costs and the costs to make up the loss due to fluid friction are then expressed in terms of the one important selected dimension and added. By differential calculus the optimum size of the one important dimension is then found from which all the other characteristics of the most economical aqueduct are obtained. Equations are derived for size, maximum velocity of flow, maximum energy gradient, construction cost per unit length, annual construction cost per unit length, annual cost to overcome fluid friction per unit length, and conveyance cost per unit volume.