Flows in Bends

Flow in bends and elbow fittings is more turbulent than in straight pipe, thus increasing corrosion and erosion. This can be countered oy selecting a component with greater radius of curvature, thicker wall, or smoother interior contour, but this is seldom economical in miter-elbows. 

FIG. 6-14 Loss coefficients for flow in bends and curved pipes (a) flow geometry, (b) loss coefficient for a smooth-walled bend at Re= 106, (c) Re correction factor, id.) outlet pipe correction factor. (From D. S. Miller, Internal Flow Systems, 2d ed BHRA, Cranfield, U.K., 1990.)... 

Fig. 16-2 Residual stress induced by plastic flow in bending (a) loaded below elastic limit (b) loaded beyond elastic limit (c) unloaded. Shaded regions have been plastically strained.

Anderson combined his love for teaching and interest in students with an active research program. In addition to sediment transport, he was also active in research in such areas as flow in bends, culvert hydraulics, air entrainment by high-velocity flow, or hydraulic structures. He was further active as a consultant for both national and international projects. He also took interest in professional associations, including the International Association for Hydraulic Research lAHR, the American Society of Civil Engineers ASCE, or AWRA. He was the recipient of the 1961 ASCE Norman Medal for the benchmark paper Self-aerated flow, co-authored by Lorenz G. Straub (1901-1963), and the 1965 ASCE J.C. Stevens Award for discussing Sediment transportation mechanics. 

Flow in bends is characterized by the Reynolds number, bend angle and radius. The radius is introduced in the dimensionless Dean number, Dn, which is closely related to Re ... 

A physical picture of what happens to the solids in a gas-solid flow system as they approach and leave a bend is of interest. Assuming the overall flow to be at steady state, as the gas-solid flow approaches a bend the solid and gas flows decelerate. The solid and gas velocities will go to zero if they collide directly with the perpendicular surface of a right-angle turn. Undoubtedly, deflections of the solid particles take place that do not allow the solid velocity go to zero. If the bend is less than 90°, then the degree of deceleration decreases as the angle decreases. Mason and Smith (1972) have provided some interesting photographs of gas-solid flow in bends that show the... 

After the particles have been decelerated by the bend, they must be accelerated to their previous steady-state value (before the bend). The energy loss in flow through a bend is made up of the contributions mentioned above. Little experimental data existed for pressure losses in gas-solid flow in bends and curves until several studies were finally performed Table 5-2 is a compilation of the parameters studied. Schu-chart s (1968) work on bends and curves is quite a complete study. These findings are seeing more acceptance with the increase in the data in the literature. 

CALCULATION OF CAPSULES FLOW IN BEND AND INCLINED SECTIONS... 

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