Fluid flowing through a pipe encounters resistance because of resistance offered by the pipeline, viscosity of the fluid, and the roughness present in the pipeline’s interior surface. The main energy loss in a pipeline is because of friction as the pipeline has usually long length (Sawhney 2011, p629). The pipeline’s total energy decreases based on the direction of the flow. Fluid flowing through a pipe encounters resistance because of the resistance offered by the pipefittings, fluid viscosity, and the roughness present in the pipeline’s interior surface. Turbulence is generated in fluid flow because of resistance leading to loss of pressure and energy head (Sawhney 2011, p630). The decline in fluid flow energy (generally expressed as units of feet) as the fluid flows through the system is referred to as head loss (Wolf Creek Nuclear Operating Corporation 2004, p2). Head loss in pipeline can be variable head loss due to changing cross-section and constant velocity head loss. The constant velocity head loss occurs because of the kinetic energy loss as the fluid flows out of the pipeline having some velocity at the exit and due to the friction in the pipe. The head loss because of friction occurs because of the resistance given by the pipe’s surface roughness when the fluid layer glides over the pipeline’s wall. It also occurs because of the resistance given by the fluid layers to one another (Sawhney 2011, p630). When the length of the pipe is 500 times larger than its diameter, the pipeline is referred to as a long pipeline. Such a pipeline experiences head loss because of friction as the major loss. Fluid flowing at the exit of the pipeline has a particular velocity, which is the head loss because of the kinetic energy flowing out of the fluid. This is considered a minor loss. Variable velocity head loss occurs because of the variable velocity leading into a pipeline each time a change happens inside the pipeline’s cross-section. For instance, changes in cross-section can occur due to sudden enlargements, many pipe fitments, sudden contractions, and pipe entrance (Sawhney 2011, p630-631). Flow in Pipes (Darcy’s Formula) Henry Philibert Gaspard Darcy (1803-1858), a French scientists made significant contributions to hydraulics. One of his significant contributions was the experimental development of pipes’ pressure-loss formula. Using the equation below (equation 1) one can arrive at the formulation Darcy had. The formula is from friction coefficient formula substituted with shear stress from the definition of Cf. This form of relationship suggests that if the friction coefficient is identified, then the calculation of the pressure drop is possible. Assuming that one is using long circular pipes, can be used instead of where L is the pipe’s length: The above formula can be rearranged to a form that was used several years ago: Generally, the formula is close to that of Darcy’s; however, he made use of the pipe diameter (D) rather than 2R, and a friction factor f as an alternative to the friction coefficient (which is 4 times larger) Using the equation for laminar flow one gets The Darcy’s pressure-drop formula can be written if the average velocity in the pipeline is known: Following the original formula, g was added to both sides of equation. This is generally a one-dimensional model since the average
Head Loss Fluid Mechanics Introduction Fluid flowing in pipes is usually turbulent. The flow is considered turbulent if the Reynolds value is greater than 4000. During the turbulent flow, the velocity distribution is relatively the same (or uniform) and the velocity profile is flatter in comparison to the laminar flow…
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