Flow, frictional loss

Centrifugal pumps, 181 Discharge systems, 187 Example calculation, 186 Flow friction losses, 185. 186 Friction losses, pipe, see Chapter 2 Friction, 188 Pressure head, 184—186 Static head, 184-186 Suction head, 184, 185 Suction lift, 184, 185 Suction systems, 186 Hvdroclones, 265—267 Application system, 267 Ignition, flammable mixtures, 493 Impellers, centrifugal, reducing diameter, 203 Impellers,... 

For non-Newtonian fluids in slow flow, friction loss across a square-woven or full-twill-woven screen can be estimated by considering the screen as a set of parallel tubes, each of diameter equal to... 

For non-Newtonian fluids in slow flow, friction loss across a square-woven or full-twill-woven screen can be estimated by considering the screen as a set of parallel tubes, each of diameter equal to the average minimal opening between adjacent wires, and length twice the diameter, without entrance effects (Carley and Smith, Polym. Eng. Set, 18, 408-415 [1978]). For screen stacks, the losses of individual screens should be summed. 

Flow friction losses me assumed negligible and pL and pH are the light and heavy densities, respectively. 

Beck, C., Laminar Flow Friction Losses through Fittings, Bends and Valves , J. Am. Soc. Naval Engrs. 56 235-271 (1944). 

Further reductions in reservoir pressure move the shock front downstream until it reaches the outlet of the no22le E. If the reservoir pressure is reduced further, the shock front is displaced to the end of the tube, and is replaced by an obflque shock, F, no pressure change, G, or an expansion fan, H, at the tube exit. Flow is now thermodynamically reversible all the way to the tube exit and is supersonic in the tube. In practice, frictional losses limit the length of the tube in which supersonic flow can be obtained to no more than 100 pipe diameters. 

The upward flow of gas and Hquid in a pipe is subject to an interesting and potentially important instabiHty. As gas flow increases, Hquid holdup decreases and frictional losses rise. At low gas velocity the decrease in Hquid holdup and gravity head more than compensates for the increase in frictional losses. Thus an increase in gas velocity is accompanied by a decrease in pressure drop along the pipe, a potentially unstable situation if the flows of gas and Hquid are sensitive to the pressure drop in the pipe. Such a situation can arise in a thermosyphon reboiler, which depends on the difference in density between the Hquid and a Hquid—vapor mixture to produce circulation. The instabiHty is manifested as cycHc surging of the Hquid flow entering the boiler and of the vapor flow leaving it. 

From equation 60 one can obtain a theoretical power requirement of about 900 kWh/SWU for uranium isotope separation assuming a reasonable operating temperature. A comparison of this number with the specific power requirements of the United States (2433 kWh/SWU) or Eurodif plants (2538 kWh/SWU) indicates that real gaseous diffusion plants have an efficiency of about 37%. This represents not only the barrier efficiency, the value of which has not been reported, but also electrical distribution losses, motor and compressor efficiencies, and frictional losses in the process gas flow. 

Eig. 11. Power saving for variable speed drives. Power input for variable speed adjusts with flow to naturally match the frictional losses. FIC = flow... 

Example 8 Compressible Flow with Friction Losses. 6-25... 

Expansion and Exit Losses For ducts of any cross section, the frictional loss for a sudden enlargement (Fig. 6-13c) with turbulent flow is given by the Borda-Carnot equation ... 

For laminar flow, data for the frictional loss of valves and fittings are meager. (Beck and Miller,y. Am. Soc. Nav. Eng., 56, 62-83 [194fl Beck, ibid., 56, 235-271, 366-388, 389-395 [1944] De Craene, Heat. Piping Air Cond., 27[10], 90-95 [1955] Karr and Schutz, j. Am. Soc. Nav. Eng., 52, 239-256 [1940] and Kittredge and Rowley, Trans. ASME, 79, 1759-1766 [1957]). The data of Kittredge and Rowley indicate that K is constant for Reynolds numbers above 500 to 2,000, but increases rapidly as Re decreases below 500. Typical values for K for laminar flow Reynolds numbers are shown in Table 6-5. 

The correclion (Fig- 6-14rZ) accounts for the extra losses due to developing flow in the outlet tangent of the pipe, of length L. The total loss ror the bend plus outlet pipe includes the bend loss K plus the straight pipe frictional loss in the outlet pipe 4fL /D. Note that = 1 for L /D greater than the termination of the curves on Fig. 6-14d, which indicate the distance at which fully developed flow in the outlet pipe is reached. Finally, the roughness correction is... 

TABLE 6-4 Additional Frictional Loss for Turbulent Flow through Fittings and Valves ... 

This is pressure drop (including friction loss) between run and branch, based on velocity in the mainstream before branching. Actual value depends on the flow split, ranging from 0.5 to 1.3 if mainstream enters run and from 0.7 to 1.5 if mainstream enters branch. 

For friction loss in laminar flow through semicircular ducts, see Masliyah and Nandakumar AlChE J., 25, 478-487 [1979]) for curved channels of square cross section, see Cheng, Lin, and On ]. Fluids Eng., 98, 41-48 [1976]). 

Example 8 Compressible Flow with Friction Losses Calculate the discharge rate of air to the atmosphere from a reservoir at 10 Pa gauge and 20 G through 10 m of straight 2-in Schedule 40 steel pipe (inside diameter = 0.0525 m), and 3 standard radius, flanged 90 elhows. Assume 0.5 velocity heads lost for the elhows. 

Vanes may be used to improve velocity distribution and reduce frictional loss in bends, when the ratio of bend turning radius to pipe diameter is less than 1.0. For a miter bend with low-velocity flows, simple circular arcs (Fig. 6-37) can be used, and with high-velocity flows, vanes of special airfoil shapes are required. For additional details and references, see Ower and Pankhurst The Mea.surement of Air Flow, Pergamon, New York, 1977, p. 102) Pankhurst and Holder Wind-Tunnel Technique, Pitman, London, 1952, pp. 92-93) Rouse Engineering Hydraulics, Wiley, New York, 1950, pp. 399 01) and Joreensen Fan Engineerinp, 7th ed., Buffalo Forge Co., Buffalo, 1970, pp. Ill, 117, 118). 

Ideal (Frictionless) Flow in Nozzles The flow path in well-formed nozzles follows smoothly along the nozzle contour without separating from the wall. The effects of small imperfections and small frictional losses are accounted for by correcting the ideal nozzle flow by an empirically determined coefficient of mscharge. The acceleration of a fluid initially at rest to flowing conditions in an ideal nozzle is given by ... 

The economics would depend upon the smoother flow of fluid without exce.ssive friction loss. A smaller section of pipe may not only require a higher h.p. for the same suction and lifting head due to greater frictional losses, but may also cause the pipe to deteriorate quickly as a result of the additional load on its surface. Losses due to bends ami valves should also be added in the total friction loss. 

This formula is another variation on the Affinity Laws. Monsieur s Darcy and VVeisbach were hydraulic civil engineers in France in the mid 1850s (some 50 years before Mr. H VV). They based their formulas on friction losses of water moving in open canals. They applied other friction coefficients from some private experimentation, and developed their formulas for friction losses in closed aqueduct tubes. Through the years, their coefficients have evolved to incorporate the concepts of laminar and turbulent flow, variations in viscosity, temperature, and even piping with non uniform (rough) internal. surface finishes. With. so many variables and coefficients, the D/W formula only became practical and popular after the invention of the electronic calculator. The D/W forntula is extensive and eomplicated, compared to the empirieal estimations of Mr. H W. 

Skin friction loss. Skin friction loss is the loss from the shear forces on the impeller wall caused by turbulent friction. This loss is determined by considering the flow as an equivalent circular cross section with a hydraulic diameter. The loss is then computed based on well-known pipe flow pressure loss equations. 

Stator prof ile and skin friction loss. This loss is from skin frietion and the attaek angle of the flow entering the stator. 

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