Fluid Friction in PipesFluid Friction in Pipes

CHAPTER 3CHAPTER 3

In Chemical engineering In Chemical engineering processprocess operations, operations,

fluids are typically conveyed through fluids are typically conveyed through pipelinespipelines.. Friction is normally overcome either by means of the pressure Friction is normally overcome either by means of the pressure

generated by a generated by a pumppump or by the fluid falling under or by the fluid falling under gravitygravity from a higher to a lower elevation.from a higher to a lower elevation.

In both cases it is necessary to know what In both cases it is necessary to know what flow rate flow rate or or

velocity velocity can be expected for given driving force. can be expected for given driving force.

For a given flow rate, repetition of the For a given flow rate, repetition of the experimental experimental for different lengths demonstrates that the for different lengths demonstrates that the pressure drop pressure drop ((P1-P2P1-P2) is DIRECTLY ) is DIRECTLY PROPORTIONAL PROPORTIONAL to to L. L.

There are There are three different flow regimes three different flow regimes in the resulting graph:in the resulting graph:

For LOW flow rate, the For LOW flow rate, the pressure gradient is pressure gradient is proportional to the flow proportional to the flow

rate (rate (LAMINARLAMINAR).).

For intermediate flow For intermediate flow rate, the results are rate, the results are irreproducible, and irreproducible, and alternate randomly in alternate randomly in between between

((TRANSITIONTRANSITION))

For HIGH flow rate, For HIGH flow rate, the pressure gradient the pressure gradient is closely proportional is closely proportional to SQUARE of the to SQUARE of the flow rate flow rate

((TURBULENTTURBULENT))

3.2 Laminar Flow3.2 Laminar Flow

In laminar flow the fluid is moving at In laminar flow the fluid is moving at low flow ratelow flow rate..

In order to avoid additional complication of gravity, In order to avoid additional complication of gravity, consider consider flow in flow in horizontal cylinder pipe horizontal cylinder pipe of radius r & length L.of radius r & length L.

Because of the retarding action of the pipe wall, there will be Because of the retarding action of the pipe wall, there will be

shear stress shear stress between the fluid and pipe wall.between the fluid and pipe wall.

Lateral Lateral Momentum Momentum TransportTransport