Frictional loss

We used to make wooden knives in Brooklyn, New York, by rubbing a stick on the sidewalk. The wood never got too sharp, but it did get hot. Sometimes it even smelled smoky when I rubbed the wood fast enough. More speed, more friction. Friction makes heat. 

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The potential energy for a conservative system (system without frictional loss) is the negative integral of a displacement times the force overcome. In this case, the potential energy for a displacement a away from Xe, is... 

We have used a common notation from mechanics in Eq. (5-4) by denoting velocity, the first time derivative of a , x, and acceleration, the second time derivative, x. In a conservative system (one having no frictional loss), potential energy is dependent only on the location and the force on a particle = —f, hence, by differentiating Eq. (5-3),... 

Pressure Drop. The pressure drop across a two-phase suspension is composed of various terms, such as static head, acceleration, and friction losses for both gas and soflds. For most dense fluid-bed appHcations, outside of entrance or exit regimes where the acceleration pressure drop is appreciable, the pressure drop simply results from the static head of soflds. Therefore, the weight of soflds ia the bed divided by the height of soflds gives the apparent density of the fluidized bed, ie... 

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. 

Viscous Transport. Low velocity viscous laminar dow ia gas pipes is commonplace. Practical gas dow can be based on pressure drops of <50% for low velocity laminar dow ia pipes whose length-to-diameter ratio may be as high as several thousand. Under laminar dow, bends and fittings add to the frictional loss, as do abmpt transitions. 

Air Cushion Conveyors. Figure 3a shows an air cushion-supported belt conveyor. The belt and material are supported on an air film created by passing air through small holes or slots in a U-shaped trough beneath the belt. The air film reduces the conveying friction losses, resulting in a reduction in requited... 

The actual power requirement is greater than that given by equation 58 or 60 because of the occurrence of frictional losses ia the cascade piping, compressor iaefftciencies, and losses ia the power distribution system. 

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... 

The viscous or frictional loss term in the mechanical energy balance for most cases is obtained experimentally. For many common fittings found in piping systems, such as expansions, contrac tions, elbows and valves, data are available to estimate the losses. Substitution into the energy balance then allows calculation of pressure drop. A common error is to assume that pressure drop and frictional losses are equivalent. Equation (6-16) shows that in addition to fric tional losses, other factors such as shaft work and velocity or elevation change influence pressure drop. 

Note that the total pressure drop consists of 0.5 velocity heads of frictional loss contrihiition, and 1 velocity head of velocity change contrihiition. The frictional contrihiition is a permanent loss of mechanical energy hy viscous dissipation. The acceleration contrihiition is reversible if the fluid were subsequently decelerated in a frictionless diffuser, a 4,000 Pa pressure rise would occur. 

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 ... 

Type of fitting or valve Additional friction loss, equivalent no. of velocity heads, K... 

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). 

FIG. 10 123 Difference in total-power-loss data test minus catalog frictional losses versus shaft speed for 6 X 6 pad doiihle-element thrust hearings. 

In a submerged-tube FC evaporator, all heat is imparted as sensible heat, resulting in a temperature rise of the circulating hquor that reduces the overall temperature difference available for heat transfer. Temperature rise, tube proportions, tube velocity, and head requirements on the circulating pump all influence the selec tion of circulation rate. Head requirements are frequently difficult to estimate since they consist not only of the usual friction, entrance and contraction, and elevation losses when the return to the flash chamber is above the liquid level but also of increased friction losses due to flashing in the return line and vortex losses in the flash chamber. Circulation is sometimes limited by vapor in the pump suction hne. This may be drawn in as a result of inadequate vapor-liquid separation or may come from vortices near the pump suction connection to the body or may be formed in the line itself by short circuiting from heater outlet to pump inlet of liquor that has not flashed completely to equilibrium at the pressure in the vapor head. 

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