Fluid friction from sudden contraction

Friction loss from sudden contraction of cross section. When the cross section of the conduit is suddenly reduced, the fluid stream cannot follow around the sharp corner and the stream breaks contact with the wall of the conduit. A jet is formed, which flows into the stagnant fluid in the smaller section. The jet first contracts and then expands to fill the smaller cross section, and downstream from the point of contraction the normal velocity distribution eventually is reestablished. The cross section of minimum area at which the jet changes from a contraction to an expansion is called the vena contracta. The flow pattern of a sndden contraction is shown in Fig. 5.14. Section CC is drawn at the vena contracta. Vortices appear as shown in the figure. 

Pressure drop on the tube-side of a shell and tube exchanger is made up of the friction loss in the tubes and losses due to sudden contractions and expansions and flow reversals experienced by the tube-side fluid. The friction loss may be estimated by the methods outlined in Section 3.4.3 from which the basic equation for isothermal flow is given by equation 3.18 which can be written as ... 

Only the irreversible frictional pressure drop should be included in the calculation of upstream pressure drop, not the momentum pressure drop required to accelerate the fluid to the velocity at inlet to the valve. The irreversible frictional pressure drop includes both friction in the inlet contraction from the reactor.(K = 0.5 for a sudden contraction1151) and friction in the piping, bends and any fittings. ... 

The viscoelastic fluids represent the 3rd material dass of non-Newtonian fluids. Many liquids also possess elastic properties in addition to viscous properties. This means that the distortion work resulting from a stress is not completely irreversibly converted into frictional heat, but is stored partly elastically and reversibly. In this sense, they are similar to solid bodies. The liquid strains give way to the mechanical shear stress as do elastic bonds by contracting. This is shown in shear experiments (Fig. 1.27) as a restoring force acting against the shear force which, at the sudden ending of the effect of force, moves back the plate to a certain extent. 

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