Curved pipes

The concepts behind the analysis are not difficult. The piping system is simply a stmcture composed of numerous straight and curved sections of pipe. Although, for straight pipe, elementary beam theory is sufficient for the solution of the problem, it is not adequate for curved pipe. However, by the iatroduction of a flexibiUty factor, to account for iacreased flexibiUty of curved pipe over straight pipe, and a stress intensification factor, /, to account for... 

Miller Internal Flow Systems, 2d ed.. Chap. 13, BHRA, Cranfield, 1990) gives the most complete information on losses in bends and curved pipes. For turbulent flow in circular cross-seclion bends of constant area, as shown in Fig. 6-14 7, a more accurate estimate of the loss coefficient K than that given in Table 6-4 is... 

Curved Pipes and Coils For flow through curved pipe or coil, a secondary circiilation perpendicular to the main flow called the Dean effect occurs. This circulation increases the friction relative to straight pipe flow and stabilizes laminar flow, delaying the transition Reynolds number to about... 

In laminar flow, the friction factor for curved pipe/ may be expressed in terms of the straight pipe friction factor/= 16/Re as (Hart, Chem. Eng. ScL, 43, 775-783 [1988])... 

FIG. 6-14 Loss coefficients for flow in hends and curved pipes (a) flow geometry, (h) loss coefficient for a smooth-waUed hend at Re = 10, (c) Re correction factor, (d) outlet pipe correction factor (From D S. Millet] Internal Flow Systems, 2d. ed., BHRA, Cranfield, V.K., 1990.)... 

Acceptable comprehensive methods of analysis are analytical, model-test, and chart methods, which evaluate for the entire piping system under consideration the forces, moments, and stresses caused by bending and torsion from a simultaneous consideration of terminal and intermediate restraints to thermal expansion and include all external movements transmitted under thermal change to the piping by its terminal and intermediate attachments. Correction factors, as provided by the details of these rules, must be applied for the stress intensification of curved pipe and branch connections and may be applied for the increased flexibihty of such component parts. 

Bogen-lampe, /. arc lamp, -lampenkohle, /. arc carbon, -licht, n. arc light, -linie, /. curved line, -mass, n. circular measure, -rohr, n., -rBhre, /. bent or curved pipe or tube, -schweisaung, /. arc welding, -skala, /. curved scale, -spektrum, n. arc spectrum. Stiic n. curved piece (Brewing) return bend,... 

While the modified energy equation provides for calculation of the flowrates and pressure drops in piping systems, the impulse-momenlum equation is required in order to calculate the reaction forces on curved pipe sections. I he impulse-momentum equation relates the force acting on the solid boundary to the change in fluid momentum. Because force and momentum are both vector quantities, it is most convenient to write the equations in terms of the scalar components in the three orthogonal directions. 

White, C.M., "Streamline Flow through Curved Pipes", Proc. Royal Soc., A 123, 645 (1929)... 

Figure 2.13 2-D Cartesian (left) and body-fitted grid (right) defined on a curved pipe.

Dean, W. R., The stream-line motion of fluid in a curved pipe, Philos. Mag. 5 (1928) 673-695. 

Figure 11.9. Schematic representation of flow in curved pipes (a) Axial velocity distribution (b) Velocity distribution in the shedding layer (c) Notations of pipe cross section.

Let / b be the radius of curvature of the pipe axis and R4 be the radius of the circular cross section of the pipe. Define U as the axial velocity component and (=/ d — r) as the distance normal to the wall. Denote 0 as the angle in the transverse plane with respect to the outward direction of the symmetry line and 4> as the angle measured in the plane of the curved pipe axis, as shown in Figs. 11.9(a) and (c). Assume that the changes of the flow pattern along the axis of the bend can be neglected. Thus, the momentum integral equations... 

Thus, an expression for the friction factor of a curved pipe can be obtained from its definition given below... 

When a dilute gas-solid suspension flow passes through a curved pipe, the particle velocity is lowered by the wall friction, the effects of gravitation, and collision with the wall. The analysis of flows in pipe bends may be represented by three typical arrangements of bends ... 

Trp Particle relaxation time the curved pipe axis, defined... 

Tubular type equipment Long and slender straight pipe or a coiled pipe or a U-shaped curved pipe. The flow direction is considered to be only along the axial direction. 

---