An Essay on Energy Losses in Pipe Flows

The transportation of fluids is key in the world we live in today. Whether it is the movement of sewage waste from the home to treatment plants, the transit of the worlds most most valuable commodity in crude and petroleum product pipelines, to the transportation of water in homes, pipe systems are integral in civilization. In order to ensure the efficient, cost effective and required volume of flow of fluids in theses systems, the dynamics of the energy losses must be understood. This essay explores the methods of calculating energy losses for incompressible flow in pipes and the causes of these energy losses. Energy losses in pipe flows occur due to two main factors. Losses occur where there is a change in the velocity of flow, which can be caused by expansion/contractions or due to, bends or valves in the pipe. These changes in velocity result in turbulence that disrupts the flow. These types of losses are usually described as minor losses as they can be considered as negligible in systems where the length of pipe is relatively long or Local losses as they occur in specific parts of the system.
Energy losses also occur due to frictional forces within the pipe, which cause shearing effects near the walls of the pipe, these are usually described as major losses or global losses as they often account for large portions of energy losses in a system and occur throughout. In order to understand energy losses we must first be able to define the nature of energy within pipe flows. The total energy within a pipe flow can be defined using the Bernoulli principle, which is derived from conservation of energy. The Bernoulli equation represents the value of energy within the flow at a point in terms of head. This is convenient as it is easy to measure in experimental conditions. Head is determined by dividing the total energy in joules by the unit weight. There are three types of energy within pipe flows. The first is kinetic energy, which is a function of the velocity, the second is pressure energy which is the work done per unit weight acting on the liquid and the third is potential energy which is the height of the liquid from the surface. Bernoulli principle states that in a given streamline the total energy remains constant and therefore a reduction in the velocity results in an increase in pressure. It is known that during flow there will be losses that occur. Using Bernoulli’s principle we can state that the total energy at a point is equal to the total energy at a second point along the flow plus the energy losses incurred between the two points. In a horizontal pipe this energy loss can be measured directly as a head loss, which is caused by a decrease in the pressure. Given that the pressure drop is caused by the work done by friction between the internal surface of the pipe and the fluid and since the fluid is at a constant velocity, the total value of shear must be equal to and therefore can be represented by the acceleration caused by the pressure difference. The force of acceleration caused by the pressure difference can be calculated by multiplying the pressure difference between the two points by the cross-sectional area of the pipe. With expressions for the both forces found, they can be equated and solved dividing through by density and gravity to determine a general solution for the head loss, bearing in mind that shear can be expressed as a function of the friction factor, the velocity and density of the liquid. The result of the steps outlined gives an expression for head losses due to friction, which is known as the Darcy-Weisbach equation shown below.

Where: Head loss Friction factor Length of Pipe Diameter of Pipe Pipe Velocity Acceleration due to gravity

This equation indicates the ways in which global head loss can be minimized in order to reduce energy costs of transporting fluids. The