Question

Discuss a case study of control volume analysis inside a piping system. A variation in flow direction should be considered in the analysis.

Answer 1

A control volume is defined as a finite region with open boundaries, the region allows the flow of mass, momentum, and energy through the boundaries. The analyst who creates a control volume for analysis of a system makes a balance sheet for incoming and outgoing fluid and the resultant changes in the properties of fluid that include power output, net heat transfer, and momentum of fluid.

         We will discuss a problem of the flow of viscous fluid through a circular pipe and will consider a control volume section inside the pipe. We need to keep this in mind that control volume analysis does not focus on fluid characteristics with in the volume, it basically details the incoming and outgoing fluid characteristics. The continuity and Bernoulli principle can also be applied to a control volume as they are applied to any section for a fluid flow problem.

Continuity equations is the total mass of fluid contained in the control volume must be invariant with time. Therefore, there will ban exact balance between total rate of flow into the control volume and out to the control volume. And the Bernoulli’s equation states that the total energy (pressure energy, kinetic energy, and datum) of an incompressible steady one-dimensional fluid will be equal in all parts of the system.

Several case studies report control volume analyses inside a piping system considering variation in flow direction of which one case study I found useful for requirement of this question: Analysis of water hammer with different closing valve laws. Most analysis of flow in pipelines and networks has assumed the flow to be at steady state conditions. this means that the flow does not change with time at any location in the pipeline system. With the assumption of uniform flow, the analysis becomes simpler and solutions are easy to obtain. pipeline flows are frequently in unsteady state due to the sudden opening and closing of valves. Transient flow can be defined as the flow fluctuation when the velocity and pressure of a fluid or gas flow change over time due to changes in the system.
Water hammer is a kind of transient phenomenon that occurs when rapid valve closure suddenly blocks the flow in pipelines. It depends on the fluid compressibility where there are sudden changes in pressure. Understanding water hammer is very important in order to prevent excessive pressure build up in pipeline which cause pipeline damage.

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