### HEAD LOSS COMPUTATION IN A DIVERGENT CIRCULAR PIPE

#### Abstract

The head loss in the hydraulic systems falls into two categories, namely major and minor head losses. Major head losses are due to friction while minor head losses are due to components as valves, bends, the abrupt or gradual variation of a section of pipe and many other singularities. The term "minor losses" is a misnomer because, in most practical cases, they are not minor but on the contrary, they represent a significant part of the total head loss. Minor loss can be significant compared to the major loss. As a general rule, major head losses are evaluated using the Darcy-Weisbach relationship while minor head losses are determined using generally an empirical relation. Both relationships are related to kinetic energy which means that head loss is related to the square of the velocity.

In the present study, a rigorous development is proposed for the calculation of major losses along a divergent circular pipe. In the literature, there is no method for calculating friction losses in a divergent circular pipe. In the calculations, these losses are often neglected by the fact that they are insignificant. We will see, through a numerical practical example, that this is not always the case. The theoretical development is based on the integration of the Darcy-Weisbach equation along the divergent pipe. The determination of the exact relationship of the hydraulic diameter was necessary for the calculation of the friction factor according to Colebrook-White relation.

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