Fluid Friction in Pipes CHAPTER 3 Fluid Friction in Pipes

In Chemical engineering process operations , fluids are typically conveyed through pipelines, in which viscous action. Such friction is normally overcome either by means of the pressure generated by a pump or by the fluid falling under gravity from a higher to a lower elevation. In both cases it is necessary to know what flow rate or velocity can be expected for given driving force. For a given flow rate, repetition of the experimental for different lengths demonstrates that the pressure drop( P1-P2) IS DIRECTLY PROPORTIONAL to L. There are three different flow regimes in the resulting graph:

For flow rates that are low, the pressure gradient is directly proportional to the flow rate( LAMINAR). For intermediate flow rate, the results are irreproducible, and alternate randomly between extension of regimes 1 and 3( TRANSITION ) For the high flow rate, the pressure gradient is closely proportional to square of the flow rate( TURBULENT )

3.2 Laminar Flow In laminar flow the fluid is moving at low flow rate. In order to avoid additional complication of gravity, consider flow in horizintal cylinder pipe of radius a as shown in figure below. Consider a fluid moving in cylinder with radius r and length L. because of the retarding action of the pipe wall, there will be shear stress  between the fluid and pipe wall