Flow of Fluids an
LI/ECI Unit Operations Review
by M u m y Weintraub, Bureau
of Mines, U.S.
Department of the Interior, Pittsburgh, Pa.
Increasing attention is being given to solids transport by fluid power. Recent literature on the flow of fluids emphasizes d eve1o p m ents i n i m m e d i ate engineer i n g ap p I i cat i on s
ACTIYIW
in the many divisions and subdivisions of fluid flow has been maintaincd with the same distribution of interest as in past years. Approximately one third of the material this report summarizes consists of work on theory and application of single phase flow, with another third devoted to multifluid systems, 4% to flow through porous media, and the remainder equally divided between measurement and control and problems of equipment design. Several excellent texts published last year provide both condensed and encyclopedic reviews of the present stare of the art. Studies on similitude. using both physical and mathematical models, describe useful tools for the study of flow in complex systems with emphasis on furnaces. A number of new tools for visualizing flow were described. Several investigators have studied methods of reducing wall friction. or conversely. increasing heat transfer, by such means as artificially roughening walls or modifying the boundary layer by injection or withdrawal of fluid at the wall. Film flow down pipe walls and the limits of stability of Poiseuille flow were also described. I n practical hydraulic system design, the usual numbers of workers have been busy developing graphical shortcuts for pipeline sizing, estimating gas inventory in long-distance lines. and other paperwork simplification. Interesting developments in this area include new measurement of losses in pipe bends, flow over weirs, and studies of fluid energy in oil-well drilling. Non-Newtonian fluids have been studied from several aspects. T h e design of screw extruders for plastics was the subject of several reports, as was the development of new methods for measuring and correlating the flow properties of such fluids. Investigations into turbulent flow of non-Newtonian fluids are particularly noteworthy as they constitute studies in a practically unexplored firld. Unsteady state fluid flow was analyzed in a number of industrially important situations, including surging in blowers, oscillation in flames, and water hammer.
.i\ general sense of progress in equipment design, with no major novelties, is evident in a number of investigations on flow through heat exchangers, turbomachine seals, and similar devices. Studies of jets have shown that a variation of the ratio of heat transfer to momentum transfer occurs within the jet. Toroidal recirculation explains anomalous heat transfer on impact, and other aspects ofjet flow in relation to the operation of ejectors and nozzles have been clarified. The literature on instrumentation has also exhibited steady growth, with the appearance of contributions on mass meters, properties of pitot tubes, application of weirs, and new data on shortpipe orifices. Flow control is represented by reports on transmission line response, choice of valve design and valve sizing, metering pumps, and ejector system control. Simultaneous flow of a gas and a liquid or of two immiscible liquids is of considerable importance in such varied applications as steam generation, liquidliquid extraction, and oil and gas pipelines. Because of the many possible flow regimes-such as bubble, stratified, or wavv-this subject is still only poor117 defined. A reviev of the field has recently been made in a partially successful attempt to interrelate the various analyses vvhich have been reported. .Additional studies reported this year
include measurements of gas-liquid crossflow through tube banks, critical flow for saturated water, and measurements of steam-water mixture flow through Venturi tubes. An increased interest in solids transport by fluid power is evident from the fact that almost half of the publications in the field of practical applications of multiphase flow deal with this topic. Many of these describe specific industrial systems developed by trial-and-error and mechanical devices such as feeders for introducing powders into pneumatic transport systems. The relation between combustion processes and the motion of pulverized coal particles was discussed. A process for preventing water intrusion into well bores promises to permit increasing use of air in place of “mud” as the medium for removing drilling debris from the well bottom. This interest in the direct application of solids transport does not indicate that the scientific aspects have been neglecwd. Several studies dealt \vith fundamental principles and engineering correlations for pneumatic transport, hydraulic transport, and the flow of dry powders under the influence of gravity. Application of fluidization techniques is still only in its infancy, to judge by the number of new chemical processes being investigated at the bench-scale and pilotplant level. Interesting contributions have appeared on heat transfer and
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pressure drop in liquid fluidized beds, on drying, and on the effect of liquid in causing agglomeration in gas fluidized beds. Although the general principles of separation of particles from fluids are independent of the nature of the materials. the order of magnitude of the forces involved differ so greatly that review of the subject is facilitated by classification according to application. Published contributions have included particle size measurement and calculation of terminal velocities; removal of dust from air streams by natural deposition and by water scrubbing; and theory and operation of cyclones for cleaning air; theory and operation of hydraulic cyclones as used in mineral dressing plants. The range of separable particle sizes is increased to larger sizes by a new design of axial flow hydroclone and to smaller sizes by a rotating helical air cyclone. Studies in other fields of fluid behavior which are of great practical importance incIude investigations of bubble formation, pulsations in tray distillation towers, and the formation of spray droplets as in fuel jets and spinning disk atomizers. I n the area of mechanical design, one of the more noteworthy developments this year was the increasing use of plastic pipe. Simplified methods of piping stress analysis have been described, and application of a specific speed index shows promise of widespread utility in comparative studies of rotating machinery. New designs of packaged compressor plants, a new solids handling pump, and a large capacity rotary screw compressor are among developments which should be noted in the files of engineers who have occasion to specify fluid handling equipment. Contributions on trouble-shooting and maintenance of pumps and other equipment will also be found in this year’s literature. Other topics of importance in increasing the effective life of centrifugal pumps are the mechanism of cavitation damage and the means of ensuring satisfaction of the pump characteristic most frequently
ORDER
causing cavitation, the “net positive suction head.”
Single-phase Flow Among a group of reports describing physical models to ease the problems created by maldistribution of flow in furnaces, one ( 6 ) details progress in a research program on the open hearth furnace. The investigation delineated patterns through the furnace and showed the necessity for more symmetrical flow, control of recirculation, control of the impact of the jet on the molten charge. and for more knowledge of droplet dynamics to reduce the damage produced by the spray of flux generated by the jet impact. A modification of the dye injection method for visualizing flows has demonstrated some unexpected characteristics of the turbulent boundary layer (23). Flow near the wall is not two-dimensional. L’ortices generated at the edges of “islands of hesitation” travel down the wall at a slight angle to the surface, moving slowly inward. hlaintenance of stable Poiseuille flow at high Reynolds number was investigated (25). By careful attention to detail laminar flow was attained a t a Reynolds number greater than 20,000. Axially symmetric disturbances as large as 0.001 times the mean velocity were damped out. Transition to turbulent flow occurred whenever the amplitude of the disturbance exceeded some threshold value which decreased with increasing Reynolds number. T h e question of transition from streamline to turbulent flow arose in another form in an attempt (72) t o explain discrepancies in predicted values of heat transfer to vertical falling film systems. I n thin films, even a t high Reynolds number, a significant portion of the fluid is in laminar flow, and another large section is in transition. Integration of Deissler’s equation for eddy viscosity near a boundary led to average heat transfer coefficients which agreed well with experimental data.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
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A number of correlations for pressure loss in curved pipes have been published for laminar flow, but these are not applicable to the industrially more important case of turbulent flow. Friction factors were determined (20) for a series of bends made from 0.6- and 1.4-inch drawn copper tubing covering a range of curvature to tube radius ratio of 16 to 648. These measurements and data from previous investigators were correlated into a single curve showing friction factor as a function of Reynolds number and radius ratio. An interesting fact is the relatively minor change in the correlating parameter for laminar flow that was necessary to secure successful results for turbulent flow. The delivery of energy to the bottom of a rotary drilling pipe string is another problem of applied hydraulics which is becoming of greater importance because of the increasing use of down-hole “mud” operated devices. New drilling developments have included the use of jet action to increase drill penetration rate and the use of “mud-actuated” reciprocating pumps, turbines, and other devices a t the bottom of the hole. Delivery of hydraulic power to the point of use was examined ( 7 ) , with an explanation of how this power is influenced by the pressure-flow characteristics of the devices absorbing the power. A somewhat different engineering problem is the measurement of pressure drops through duct elements such as orifices, valves, or screens at very large mass-flow rates. Such losses can be measured (36) without the use of large quantities of gas by utilizing a simple shock tube technique. Space, Time, and Property Variables. Variation of viscosity with shear rate is probably the most common case of deviation from the elementary laws of fluid flow. Dye injection was used by Shaver and Merrill ( 3 9 ) to relate pressure drops, impact heads, and turbulence. Turbulent flow friction factors were correlated for a series of pseudoplastic fluids by a single equation. Measurements of local velocities showed that for these materials the velocity profiles were sharper than those for viscous flow a t the same Reynolds number, a conclusion which agreed with observations of dye injection dernonstrating the repression of vortex generation even in the turbulent range. I n more extensive theoretical analysis, Dodge and Metzner ( 7 7 ) developed friction factor curves with a Reynolds number modified in a different manner. The friction factor curves of Shaver and Merrill are similar in shape but differ quantitatively by a factor of five. Furthermore, the analysis of Dodge and Metzner leads to prediction of a velocity
an profile of an entirely different shape than that found by Shaver and Merrill. T h e difference may lie in some fluid property not described by the shear stress to shear rate relation. Also both investigators ignored the effect of a discontinuity required by their differential equations on the basis that such discontinuity has been shown to be inconsequential for Kewtonian fluids. -4nother interesting study on nonNewtonian flow ( 3 ) used the MetznerReed modification of Reynolds number to develop an equation for predicting entrance pressure drops and entrance effect length. I t successfully predicted experimental entrance pressure drops even for the solutions of carboxymethyl cellulose which failed to fit the curve of Dodge and Metzner for fully developed turbulence. Where rate of flow is a rapidly changing variable, as in engine exhausts or water hammer, electronic computers are of great assistance in problem solution. Application of computers to the problems of hydraulic transients in large hydroelectric projects was demonstrated (27). In addition to handling the computational work, analog computers are also able to expand the time scale of a transient to values that can be more easily manipulated. Complex Flow Paths. Theoretical and experimental studies of jets flowing in ducts (8) are applicable to problems of mixing and recirculation of flame jets in furnaces. T h e theory predicts the presence and position of a recirculating eddy which forms near the wall under specified flow conditions. Another study on jets (28) provides an explanation of an important phenomenon in high vacuum pumps-the appearance in pump jets of flow rates much higher than critical ones calculated according to gas dynamic equations. T h e cause was not failure of the accepted equation but was due to the appearance of liquid droplets in the gas stream. O n e aspect of vortex flow that has been neglected is the effect of wall friction. A substantial contribution to this problem was made with theoretical work (35) on the cyclone separator. An expression for local tangential velocities, derived as a function of eddy viscosity and wall friction, shows how under certain conditions tangential velocity increases and in other situations decreases toward the center. Conversely, measurements of velocity profiles provide information on eddy motion in the cyclone and hence its loss of particle separating efficiency. Measurement and Control A possibly important source of error in the utilization of the sharp-edged orifice
plate is the development of cavitation. hleasurements have shown ( 3 7 ) that flow at a cavitation number of 0.2 did not introduce any excessive errors in the use of normally calibrated orifice coefficients. T h e same workers suppressed cavitation effects by introducing air, with no deleterious effect on the discharge coefficient. The electromagnetic primary element is no longer a novelty in industrial fluid metering, but a welcome addition to the literature (79) provides details of design and inspection criteria and practical thresholds of electrical conductivity of the fluid as related to a desired instrumental precision. Above the threshold of 20 pmhos per centimeter the flow coefficient is reported to be independent of conductivity and Reynolds number. Another type of primary element, whose operation must probably be restricted to laboratory conditions, is a drag disk (22). Drag forces produced by air velocities as low as 0.2 foot per second 'ivere measured by a sensitive balance. -4utomatic pressure control for ejector vacuum systems has been discussed ( 2 4 ) . Because of the instability characteristics of steam ejectors, the inlet steam pressure is the least desirable parameter to control. Various interconnected streams which comprise a multistage ejector system were analyzed and the different situations which may dictate the choice of the control station were explained. T h e long distances between sensing elements and control devices characteristic of modern centralized chemical plants makes a knowledge of signal attenuation, lag, and phase change of paramount importance when designing a responsive and stable control system. Even with a knowledge of the differential equations of signal transmission, the problem is difficult, for integration of the equations is long and tedious. Expressions have been developed (38) for pneumatic transmission lines which serve the double purpose of assisting in visualizing the response to various signals and of being easily applicable to analog computers for complete solution. T h e analysis utilized the principles of electrical transmission lines and sound propagation, and quantitative results were presented graphically. T h e efficiency of any flow control system is considerably reduced if the final element in the system, the control valve, cannot produce the desired change with a response approximately proportional to the corrective signal. Designing a valve so that a desired relation is developed between valve stem motion and pressure drop must follow different principles for turbulent and viscous flow (9). For turbulent flow the change in pressure drop follows
Unit Operations Review
the change in minimum area throuqh the valve, as in a variable orifice: in laminar flow effective control depends upon shear rate and the total surface of the restriction as in a capillary; henw a long narrow-clearance plug should be specified. For non-h'ewtonian fluids the problem is further complicated because effective viscosity chanqes with shear rate. Methods of incorporating these principles into actual design of valve ports are described.
Flow through Porous Media T h e porous system in which the solids constitute a discontinuous phase appears in the fixed bed catalytic reactor, the deionization bed, and many other types of equipment for solid-fluid contacting. Operation of fixed bed reactors is acknowledged to be seriously affected by axial dispersion in the flowing fluid, but present knowledge is not adequate to permit inclusion of this factor into d i f f w entia1 equations for reactor design. Some progress has been made with a simple diffusion model which works quite well for consolidated beds. Evidence has been presented (5), however, showing that for granular beds of relatively large void dimensions the diffusion model m,2.y not be adequate; a suggested mechanism is based on efficiency of mixing in the voids. Certain aspects of the data are not consistent with either model, and 'in additional mechanism involving a bed capacitance effect is also suggested. Another problem of great importance, because of the magnitude of the economics associated with it. is flow through the blast furnace. Published correlations predict that pressure drop through mixtures of particle sizes should be greater than through the same particles segregated by size and layered. Experimental data was reported ( 3 4 ) at variance with these predictions. Multiphase Flow Interesting new data on liquid-gas flow includes pressure drop measurements for horizontal cross flow through four different arrangements of tube banks (10). Air-water and pentane vapor-pentane liquid systems \+ere studied. Using parameters of the fictitious all-gas pressure drop, the liquid volume fraction and the ratio of fluid densities, the data were correlated to an average deviation of 12% and condensation pressure drops were predicted within a maximum deviation of 3070. A study (33) of Coefficients for floiv of water, steam, and steam-water mixtures through a vertical Venturi tube disclosed that the factors were practically identical for all temperatures and conditions of the fluid. This suggests that if VOL. 52, NO. 3
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the mass flow rate is determined, as by metering of the single-phase flow, the Venturi measurement can be a means of determining steam quality a t high pressures. Solids Transport. I n fluid-motivated transport of solids the primary factor is the interaction of the fluid and solid, which is in some manner related to the drag of fluid on the particle. Several earlier correlations include the drag coefficient estimated from the terminal falling velocity of single particles. An improved generalization of these correlations might be obtained from consideration of a generalized theory (30). Settling velocity in a suspension is shown to be equal to that of a single particle multiplied by the term (1 - c)B where c is the volumetric solid concentration and 6 is a function of particle shape, size distribution, and Reynolds number; 6 apparently has constant values for laminar flow and for fully turbulent flow and varies between these limits in a transition range. Many of the publications on application of hydraulic transport contribute data which dispute previous correlations without providing alternate solutions. An example of this is found in a symposium on hydraulic backfilling of mines ( 4 5 ) comprised of 15 reports dealing with the process of hydraulically moving mine tailings, chiefly sand. O n e of this group states that Durand’s classification of flow regime as a function of particle size will serve for crude estimates, but it is not accurate for size mixtures and does not incorporate the effects of specific gravity and viscosity. Even for relatively homogeneous slurries the Reynolds number is not a n adequate criterion for scale-up similarity. Several equations are offered for safe minimum velocity, but none of the available equations works for all materials. Others in this symposium contribute considerable data on slurry flow, with various conditions of particle size distribution, inclination of pipe, and arrangements of pumps. A review of the experimental work and formulas developed in the U.S.S.R. for hydraulic transport of coal was provided (76). These formulas are accepted as design equations by Soviet engineers, but they differ in several important respects from the correlations which were presented with equal assurance by the French investigators, Durand and Condolios. Perhaps some of the difficulties may be resolved through more fundamental approaches. T h e velocity of individual spheres in turbulent flow was studied (3) as a function of their density ratio and diameter ratio. I t was reported that the mean velocity of spheres with a density
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ratio almost unity was greater than the fluid mean velocity. If the conveying fluid is a gas rather than a liquid, the problems become more complex because of the greater density difference between particle and carrier and the much greater range of solid to gas ratio which is of engineering interest. Thus, it was determined ( 4 3 ) that the power required for air transport approaches a minimum as the solid to air ratio approaches unity. Other workers (46)reported factors which may prove advantageous in transport a t ratios as high as 750. In a study of the energy requirements for the transport of granular materials (27) the pressure drop resulting from particle acceleration and particle “static pressure” was analyzed and confirmed by measurements on solid spheres. A critical solids rate for operability of the conveyor is determined by the slope of the pipe and the air velocity and can be characterized by an average interparticle distance in the conveyor feed section. Fluidization. One of the interesting phenomena associated with fluidized beds is the effect of liquids. When the fluidizing agent is a liquid, the process is referred to as “particulate” because the grains of solid generally move as individual particles. The scale of turbulence of the bed is small, and the fluidization process is easily controlled and relatively easy to treat analytically. Thus, when glass spheres were fluidized with water and ethylene glycol (26), good agreement was obtained with a n equation derived by a simple grouping of terms combined to yield Stokes law for infinitely dilute suspensions and the Kozeny form of equation for fixed bed pressure drop. Experimental determination of the Kozeny constant resulted in a value for fluidized beds that was approximately half that usually found for fixed beds. This may be attributed to rearrangement of the particles in motion. Small amounts of liquid in a gasfluidized bed tend to increase the erratic turbulence of the “aggregative” form of fluidization. O n e report (32) suggests that studies of the effect of moisture may be generalized to correlate the effect of other interparticle forces, such as electrostatic attraction. T h e investigators measured and correlated the amount of water added to an air-fluidized bed with the height of the bed and the heights of the dry fluidized bed and a completely aggregately fluidized one. T h e approach is interesting, but the scatter of the data and the necessity to direct the shape of the curve by choice of three constants make it difficult to assess the hypothesis. T h e nonhomogeneous nature of the
INDUSTRIAL AND ENGINEERING CHEMISTRY
fluidized bed may be the cause of several reported disagreements between investigators of heat and mass transfer ( 7 ) . A capacitance probe was developed for measuring point porosities, and porosities were found to be axially symmetric but to exhibit major variations in radial and longitudinal directions. The radial variation appeared as a wall effect. Longitudinal variation could be represented by three regions: a sieve effect region controlled by entrance design, a constant porosity region dependent upon linear velocity and initial bed height, and a region in which porosity increases steadily to a value of unity. Separation Processes. A novel design of a hydroclone is claimed (47) to be capable of efficiently separating particles of larger diameter than conventional cyclones. T h e device is an axial flow arrangement in which rotary motion is produced by a fixed impeller. The two product streams are separated by an overflow pipe with an air core and a baffle plate to disrupt the vortrs in the annulus. T h e capacity ratio (flow to head) was measured and found to be considerably larger than for conventional cyclones. T h e especially promising nature of this device arises from its present ability and the fact that there is much room for improvement in unexplored geometric factors. At the other end of the particle size scale, miniature hydroclones have separated particles less than 3 microns in diameter. A study (29) showed that equations which have been used for cyclones in the range of 3-inch to 3-foot diameter may be applied with some slight modifications to units as small as 10 mm. T h e common air cyclone can separate particles of about 5 microns diameter. A device has been described (78) which will separate particles down to 0.2 micron. T h e principle used is the superimposing of a rotary motion upon a helical coil through which the suspension flows. Thus, a high centrifugal force is developed although the fluid motion remains laminar. Miscellaneous Multiphase Operations. A number of interesting studies have been published on the generation of sprays by nozzles, a subject of great importance in many processes including spray drying, humidification, and oil combustion. Most of the characteristics of the spray are determined by the interaction between the liquid as it leaves the nozzle and the surrounding air. T h e air flow induced by the liquid has been measured ( Z ) , and various aspects of the penetration of air into the spray cone and of the cone into the ambient air have been studied. I n one of the more comprehensive studies of spray generation (77), the
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an particular interest was swirl nozzles and their suitability for heav) oils. Rate of discharge, spray angle, and fineness of atomization were measured and correlated with viscosity of the liquid and various dimensionless ratios of nozzle dimensions. Charts provide means of designing nozzles for a variety of operating conditions. Mechanical Design
Piping and Valves. In an increasing number of situations advantage is being taken of the low cost, light weight: flexibility, and corrosion resistance of poly(viny1 chloride) (PVC) plastic pipe. Use of PVC has become so frequent, even in the once restricted field of medium pressures, that the pipe may now almost be accepted as a standard engineering material. T h e improvements in plastic, cement, and standardization which led to this acceptance have been reviewed ( 4 2 ) . Piping designers concerned with the evaluation of thermal stresses have, in recent years, been developing more precise and more refined methods of computation for complex systems. An approach to the problem from the opposite direction was presented (74). A less accurate but much simpler and quicker solution is suggested through a criterion which states whether the loading on a specific system is within allowable limits. This criterion is defined by the relation between a dimensionless grouping of the loading factors and another grouping of the geometric parame ters. Pumps. Some novel arrangements of an air-lift pump and its automatic control have been described (75). This system is particularly adaptable to handling hazardous materials or corrosive solutions and abrasive suspensions that would rapidly destroy the more efficient centrifugal or positive displacement types of pumps. T h e design of centrifugal pumps is still enough of an art that comparisons must be made on the basis of an empirical index of performance. Such an index, which is dimensionless and should therefore be the same for different sizes of geometrically similar pumps, is the specific speed. T h e fundamental problems of dynamic similarity of rotary hydraulic machinery have been discussed ( 4 4 ) , especially the universality of specific speed number in its application to both turbines and pumps. After the engineer has determined the type and capacity-pressure specification, he must decide upon the choice of specific units based upon initial cost, operating cost, reliability, and maintenance. This problem has increased in importance with the greater use of small units,
frequently in isolated service such as long-distance gas transmission booster stations. Much of these data are difficult to accumulate, and a valuable service has been performed (73) in a report which correlates a considerable amount of operating cost data on gas compressors in the 50- to 880-hp. class. O n e of the more important causes of pump failure is erosion and corrosion that may be attributed to cavitation. Cavitation is greatly reduced if a minim u m net positive suction head (NPSH) is supplied to the pump. A major problem is the translation of the NPSH value, as measured with a given fluid in a pump operating a t certain conditions, to another fluid and a different set of operating conditions. Some new data for various fluids have been presented ( 3 7 ) , including high temperature water and some hydrocarbons. T h e data were correlated on the basis of vapor to liquid volume ratio. T h e conclusion, however, is that ignorance of the cavitation mechanism and of all the contributing fluid properties makes it desirable to determine NPSH values for each situation directly. A different facet of the application of measured NPSH was attacked (40). There is no close correlation between flow rate as a function of head on the discharge side and on the suction side. T h e effect of suction side geometry on NPSH must be considered. An experimental procedure is described for determining this effect and for applying the measurement to various operating conditions. Acknowledgment Appreciation is expressed to P. R. Sebastian for his efforts in assembling the references on which this review is based, Literature Cited (1) Bakker, P. J., Heertjes, P. M., Brit. Chem. Eng. 3, 240 (1958). (2) Binark, H., Ranz, W. E., Am. SOC. Mech. Engrs. Paper 58-A-284, Annual
Meeting, New York. November-December 195‘8. (3) Binnie, A. M., Phillips, 0. M., J . Fluid Mech. 4. 87 (19581. (4) Bogue, D. ‘C., ’IND.’ENG. CHEM.51, 874f1959). --, (Si Carberry, J. J., Bretton, R . H., A.Z.Ch.E. Journal 4, 367 (1958). (6) Chesters, J. H., Trans. A m . Sac. Mech. Engrs. Ser. A , 81, 361 (1959). (7) Colebrook, R. W., Am. SOC. Mech. Engrs., Paper 58-PET-6, Petrol. Mech. Eng. Conf., Denver, Colo., September 1958. (8) Curtet, R., Combustion and Flame 2, 383 (1958). (9) DeHaven, E. S., IND.ENC. CHEM.51, 63A (July 1959). (10) Diehl, J. E., Ruh, C. H., Am. SOC. Mech. Engrs. Paper 58-HT-20, ASME\ -
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AIChE Heat Transfer Conf., Chicago, August 1958. (11) Dodge, D. W., Metzner, A. B., A.I.Ch.E. Journal 5 , 189 (1959). (121 Dukler. A. E.. Chem. E n e . Proer. 55, ‘ No. io, 62 (1959)’. (13) Edmondson, P. B., Evans, H., Am. SOC. Mech. Engrs. Paper 58-PET-36, Petrol. Mech. Eng. Conf., Denver, Colo., September 1958. (14) Endres, W., Forsch. Gehiete Ingenieurw. 23, No. 1/2, 33 (1957). 115) Fowler, A. H., Jasny, G. R., Chem. En?. Progr. 5 5 , No. 1, 64 (1959). Frolov. A. H.. U ~ o l ’1959. No. 6. 10.
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(l8)-Goetz, A, GeoJis; pura e appl. 36, 49 (1957). (19) Head, V. P., Am. SOC.Mech. Engrs. Paper 58-A-126, Annual Meeting, New York, November-December 1958. (20) Ito, H., Trans. Am. Sac. Mech. Engrs., Ser. D 81, 123 (1959). (21) Jung, R., Forsch. Gebiete Ingenieurw. 24, No. 2 , 50 (1958). (22) Kemp, J. F., J . Sci. Znstr. 34, 411 (1957). 123) Kline, S. J., Runstadler, P. W., ins. A m . Sac, Mech. Engrs., Ser. E 166 (1959). Knight, G. B., Chem. Eng. 66, NO. 6, 171 (1959). (25) Leite. R. J., J . Fluid Mech. 5 , 81 (1959). (26) Loeffler, A. L., Jr., Ruth, B. F., A.I.CI2.E. Journal 5 , 310 (1959). (27) McCaig, I. W., Jonker, F. H., Am. SOC. Mech. Engrs. Paper 58-A-101, Annual Meeting, New York, NovemberDecember 1958: (281 Manov, M. G., Soviet Phys.-Tech. Phys. 3, NO. 2, 289 (1958). (29) Matschke, D. E., Dahlstrom, D. A., Chem. Eng. Progr. 54, No. 12, 60 (19.58); 5 5 , No. 1, 79 (1959). (30) Maude, A. D., Whitmore, R. L., Brit. J . Appl. Phys. 9, 447 (1958). (31) Numachi, F.; Yamabe, M., Oba, R., Am. SOC.Mech. Engrs. Paper 58-A-93, Annual Meeting, New York, NovemberDecember 1958. (32) Parker, H. W., Stevens, W. F., A.I.Ch.E. Journal 5 , 314 (1959). (33) Ratner, A. V., Zelenskil, V. G., Teplocnergetika 5 , 44 (May 1958). (34) Ridgion, J. M., J . Iron Steel Inst. (London) 188, 317 (April 1958). (35) Rietema, K., Krajenbrink, H . J., A#$. Sci. Res. Sec. A 8, 177 (1959). (36) Rudinger, G., Am. SOC.Mech. Engrs. Paper 59-Hyd-13, Hydraulic Conf., Ann Arbor, Mich., April 1959. (37) Salemann, V., Trans. .4m. Sac. Afech. Enms. Ser. D 81. 167 (1959). (38) usamson, J. ’ E., ‘ T r a n s . SOC.Instr. Technol. 10, 117 (1958). (39) Shaver, R. G., Merrill, E. W., A.I.CI2.E. Journal 5 , 181 (1959). (40) Sherzer, A . F., Chem. Eng. Progr. 5 5 , No. 9, 79 (1959). (41) Sineath, H. H.. Dalla Valle, J. M., Ihid.. 5 5 . Go. 11. 59 (1959). (42) Siaudt, F. J., Chem. Eng. 66, No. 11, 115 (1959). (43) Tessari, I., Romano, I., Termotccnico ( M i l a n ) 12, No. 4, 191 (1958). (44) Troskolanski, A . T., Przeglad Mech. 17, 495 (1958). (45) Vine, W. A . , ed., Proc. Symp. Hydraulic Fill, Montana School Mines, May 1958, Montana School of Mines, Butte, Mont., 1958. (46) Wen, C., Simons, H . P., A.I.Ch.E. Journal 5 , 263 (1959). I
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