Chemical Engineering Volume 1: Coulson and Richardson’s

Hydraulic jump
If a liquid enters a channel under a gate, it will flow at a high velocity through and just
beyond the gate and the depth will be correspondingly low. This is an unstable condition,
and at some point the depth of the liquid may suddenly increase and the velocity fall.
This change is known as the hydraulicjump, and it is accompanied by a reduction of the
specific energy of the liquid as the flow changes from rapid to tranquil, any excess energy
being dissipated as a result of turbulence.
If a liquid is flowing in a rectangular channel in which a hydraulic jump occurs between
sections 1 and 2, as shown in Figure 3.23, then the conditions after the jump can be
determined by equating the net force acting on the liquid between the sections to the
rate of change of momentum, if the frictional forces at the walls of the channel may be
neg 
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  1. INDEX 883 LURlE, M. 650, 656 Mass transfer coefficients, overall in terms of film 620 LYLE, O. 252, 272, 557, 566 wet bulb temperature 742 LYNWORTH, L. C. 267, 273 counter- and co-current flow 623 countercurrent in a column 623 MA AMEN, H. R. E. VAN 280, 311 — distillation 576 McADAMS, W. H. 417, 418, 428, 475, 486, 563, 564 drops 652 McCORMICK, R. H. 211,229 examples 580, 585, 606, 608, 621, 628, 643, Mach number 175 644,645 McKELVEY, J. M. 306,312 — film-penetration theory 614 McKELVEY, K. K. 765, 786 — flow in pipe 732 McLEMAN, M. 217, 219, 220, 229 — — from liquid to gas, inside vertical tube 647 McNELLY, M. J. 492, 565 further reading 654 MAFFETT, J. 209,228 — humidification 738 Magnetic flow meter 265 in a column 623 Magnus principle 215 example 585 MAISEL, D, S, 650, 656 — fluidised beds 654 MANDHANE, J. M. 184,185, 227 packed beds 654 MANGELSDORF, H. G. 466, 467,468, 469, 564 vertical tubes 647 Manometer 234 wetted-wall columns 647 — example 252 mechanisms, example 606, 608 — inclined 235 nomenclature 656 — inverted 236 — — penetration theory 600, 602 — two-liquid 236 plane surfaces and pipe walls 723 — well type 234 _ practical studies 646 Marangoni effect 619 references 655 MARCHELLO, J. M. 600, 614,655 through stationary gas 577, 578 MARKS, W. M. 433,563 to a sphere 617, 652 MARRUCCI, G. 113,116,131,139 surface 726 Mars pumps 319 _ _ buffer zone 719 MARSHALL, P. 316,326,376 surface of particles 651 MARSHALL, W. R. 652,653,656 . __ — turbulent zone 719 MARSLAND, R. H. 516,565 — — turbulent 717 MARTIN, M. W. 189,227 two-film theory 600 MARTINELLI, R. C. 186,188, 227, 727, 735 unsteady state 591 MASHELKAR, R. A. 293, 301, 312 • velocities 586 Mass 2,4, 7, 8 with bulk flow 578, 725 — and heat transfer coefficients 695 — chemical reaction 626 — density 1 __ catalyst pellet 634 — flowrate, compressible flow 159 . example 628 maximum 162 , . steady state 626 — heat and momentum transfer related 700 _ _ unsteady state 631 — simultaneous 717 Mathematical tables 815 — inertial 21 MATHUR.M. P. 217,229 — quantity 21 Maximum flow and critical pressure ratio 154 — transfer 571, 573, 696 — -— conditions 161, 172 across a phase boundary 599, 646 ideal gas, isothermal flow 145 and reaction in sphere, example 643 — — non-isothermal flow 147 at plane surfaces 649 — flowrate 167 boundary layer 691 — heat flux to boiling liquids 483,486 — — bulk flow, Reynolds analogy 727 film boiling 486 coefficients 577. 582, 620, 646, 647, 723, 724, MAXWELL, J. C. 594,655 725 Maxwell model 116 driving force in molar concentration 577 Maxwell's law for binary systems 594 mole fraction 577 multicomponent mass transfer 595 _ partial pressure 577 of diffusion 594 example 732 MEADOWCROFT, D. B. 759, 786 in boundary layer 692 Mean beam length 466,468 terms of heat transfer coefficient 727 — various geometries 468 _„„ , „. theories 619 — free path of molecules 574, 697,698, 700, 702 _ water cooling towers 774 —- radius, heat conduction through thick tube wall 392 liquid phase 597 — residence time, C.S.T.R. 310
  2. INDEX 885 Multipass exchangers, mean temperature difference Nomenclature, flow of multiphase mixtures (Chapter 5) 510 079 Multiphase systems, solids, liquids and gases 181 — heat transfer (Chapter 9) 566 Multiple stage pumps, vacuum, producing 365 — humidification and water cooling (Chapter ! 3) 787 Multistage compression 353 — liquid mixing (Chapter 7) 312 number of stages 354 — mass transfer (Chapter 10) 656 MYLER, C. A, 214,224,229 — momentum heat and mass transfer (Chapter 12) 735 NAG AT A, S. 288, 293, 310, 311, 312 — pumping of fluids (Chapter 8) 377 NAGLE, W. M. 477, 511, 564, 565 — the boundary layer (Chapter 11) 692 Nash Hytor pumps 346 — units and dimensions (Chapter 1) 22 Natural convection. 414, 435 Non-circular ducts, hydraulic mean diameter 87 — — between coaxial cylinders 433 — sections, heat transfer in 433 surfaces 435, 437 Non-coherent systems of units 6 - from a horizontal pipe, example 437 Non-condensable, condensation in presence of, - — heat transfer coefficients, example 437 example 479 horizontal pipe 435 — gas, effect on heat transfer 479 surfaces 435 Non- ideal gas 34 — gases, liquids 435 Non-isentropic compression across Shockwave 177 - — streamline 435 Non-isothermal flow 159 - - - turbulent 435 ideal gas, horizontal pipe 169 organic liquids 435 Non-Newtonian and viscous liquids, impellers 288 streamline and turbulent flow 433, 435 behaviour 58, 104 - - vertical, cylinders 435 flocculated suspensions 196 plates 435 — characteristics 196 — - — surfaces 435 — flow 103, 191 - air 435 example 129 . liquids 435 -—fluids 31, 103, 181 water 435 — characterisation 118 — draught water cooling towers 762, 765 flow in pipes and channels 121 example 766 melts 121 NEIL, D. S 550, 566 mixing 277, 286 NELSON, W. L. 554, 566 Net positive suction head 337 pumps, centrifugal 342 Network design 516 —— single phase systems 121 Neutrally buoyant particles, solids-liquid flow 210 time-dependent, mixing 288 NEWTTT, D. M. 200, 201, 203, 210, 217, 218, 228, • turbulent flow 136. 187 229 two-phase systems 191 Newton 3, 4, 7 — properties 136 Newtonian and non-Newtonian behaviour 52 — shear-thinning suspensions 187 — behaviour, disperse suspensions 196 two-phase flow, streamline 191 — flow, pipe, circular cross-section 75, 76 — time-dependent, non-viscoelastic 282 — fluid behaviour 58 viscoelastic 282 — fluids 31,61 — turbulent flow 136, 187 high viscosity, mixing 288 Normal stress differences 117 laminar or turbulent flow 187 — stresses 117 — — low viscosity, mixing 282 NORWOOD, K. W. 300,312 mixing 277 No-slip condition 671 pressure drop for turbulent flow 75 Notch 244,261 -— liquids, multiphase flow 181 — coefficient of discharge 262 NlENOW, A. W. 274, 280, 288, 293, 298, 300, 307, — end contractions 262 310,311,312 — Francis formula 262 NJKURADSE, J. 63. 705, 715, 717, 735 — rectangular 262 NISHIKAWA, M. 293,312 — triangular 263 NISHIWAKI, N. 436, 563 NOVAK, V. 293,312 Nomenclature, flow and pressure measurement Nozzles 143, 172, 244, 246, 254 (Chapter 6) 272 — coefficient of contraction 254 in pipes and channels (Chapter 3) 140 — converging/diverging, flow 156 of compressible fluids (Chapter 4) 179 ideal gas 154 fluids, energy and momentum relationships — exit and back pressure comparison 155 (Chapter 2) 56 — flow measurement 246
  3. INDEX 887 Pneumatic conveying 211 Power law fluids i 34 blockage 21S laminar flow 191 dense phase 213, 222 -index 108 dilute (lean) phase 213 liquids, mixing 282, 293 -— dune flow 214 — — model, 106, 196 - formation 219 _ _ _ shear-thinning fluid 108, 187 — -electrostatic charging 221 relation for flocculated suspensions 121 horizontal 213 — — rheology, two-phase flow 191 — — -energy 217 — measurement, stirred vessels 283 - - .moving bed 213, 214 — number 283, 286 non-uniform suspended flow 214 — requirement, pumping liquids 371 plug flow 214 PRANDTL, L, 61, 667,692, 702,720, 725, 735 practical applications 224 Prandtl mixing length 702 pressure drop 218, 219, 220 — number 388,416, 523, 689,699 rotary feed valves 218 liquids, gases 390, 689 slip velocity 219 molten metals 689 slug flow 21.4 turbulent 717 stationary bed 214 — one-seventh power law 84,676, 683. 711 — — uniform suspended flow 214 — velocity distribution 683 —.— vertical transport 223 PRATT, H. R, C. 651,656 — transport, example 225 PRATT, N. H. 497,517,565 gases and solids 181 PRAUSNITZ, J. M. 599,655 Poise 9 PRESENT, R. D. 575, 655 POI.SEUI.LLE, J. 78, 139 Pressure 3 Poiseuilie's law 78 — absolute 237 Polar molecules, radiation 465 — and area for flow 156 Polymeric solutions, rheological properties 209 — at pump delivery 318 Porosity of bed 207 — cell, differential 239 Porous solid as pseudo-homogeneous medium 635 — converging/diverging nozzles 156 effective diffusivity 635 — difference 237 Portable mixers 306 — drop 58,67, 127, 158, 161, 181, 196 Positive displacement pumps 315 ——- Bingham plastic, air injection 194 - rotary 321 frictional and acceleration losses 187 — — rotary pumps 321 ._ _ _ gas-liquid flow 187, 188 type fans 344 gas-liquid system 185 Potential energy 44 hydraulic transport 200, 209 — head 43 hydrostatic component, hydraulic transport 223 Pound 3, 4, 7 in contacting devices 695 — force 3, 5, 6 heat exchangers, example 432, 433 — weight, 5 - pipes 58, 63 Poundai 3, 5 calculation 67 POWELL, R. W. 649, 650, 652, 653, 656 compressible fluids i 58, 160 Power 7 — consumption in mixing 282, 293 incompressible fluids 68 — — dimensional analysis 283 — -— measurements, hydraulic transport 211 high viscosity system 283 methods for its determination 187 — __ iow viscosity system 282 — — non-Newtonian fluids, in pipes 136 — stirred vessels 282 — — pipe fittings 524 thixotropic, time-dependent liquids 293 plate and fin heat exchangers 552 — curve, highly viscous liquids 288 shear-thinning fluid 136 mixers 283 static mixer 309 propeller mixer 284 tube side, heat exchanger 523 pseudoplastic fluids 292 __ two-phase 192, 193 impeller types 292 — effect on boiling 490 turbine mixer 289 heat transfer coefficient, boiling 488 — for compression 346 — energy 44 mixing, example 286 Pressure-enthalpy diagram for water and steam 813 pumping 367 Pressure, gauge 237 gases 374 Bourdon 237, 238, 239 liquids 367 — gradient, flow against 667 — law and Newtonian velocity profiles 125 — head 43
  4. INDEX Radiation, two-surface enclosure 459 Response time constant 403 Radiosity 458 RESTER, S. 643,655 Rarn or plunger pumps 318 Return bends, heat exchanger 505 RAMSHAW, C. 553, 566 Reversed flow 668 RANZ, W. E. 652, 653, 656 Reversibility, isothermal flow 143 RAO, M. A, 280,311 Reversible adiabatic, isentropic flow 148 Rapid flow 100 — change 28 -— to tranquil flow, hydraulic jump 102 — changes due to shear 114 Rate and time for mixing 298 REVILOCK, J. F. 479, 564 — of momentum transfer 670 Reynolds analogy 720 — -shear 105 between momentum heat and mass transfer 720 — - strain 104 concentration gradient 720 RAY, B B. 435,563 flow in pipe 731 Reaction vessels, heat transfer in 496 heat transfer across turbulent region 725 with jacket 499 — simple form, 720 Real surfaces, radiation 441, 443 Taylor-Prandtl modification 725 REAVELL, B. N. 274,302,311 — temperature gradient 720 Reboilers 494, 495, 496 universal velocity profile 720 Reciprocal rule 448 —- number 14, 64, 160, 167, 183, 188, 416, 425, 664 Reciprocating piston compressor 347 — .— ari£| shear stress 74 — pumps 316 critical 82 example 320 — — flow over plane surface 664. 726 — piston pump 316 for mixing 283 — plunger or ram pump 318 stable streamline to turbulent flow 64 Reciprocity relationship, radiation 448 hydraulic transport 196 Rectangular duct 87 _ m mixer 286 REDMAN, J. 550, 566 —- — Metzner and Reed 191 Reduced coordinates 35 non-Newtonian fluids 133 — pressure 35, 488 — pilot tube 245 — temperature 35 plane surface 664, 726 - volume 35 scale-up of stirred vessels 282 REED, C, E. 544, 566, 637, 655 —— shear-thinning suspensions 187 REED,!. C. 124, 137, 139 ——- time for mixing 299 References, flow and pressure measurement REYNOLDS, O. 59. 63, 720, 735 (Chapter 6) 272 Reynolds stresses 703 in pipes and channels (Chapter 3) 139 Reynolds' apparatus for tracing flow patterns 59 measurement (Chapter 6) 272 Rheogram 105, 197 of compressible fluids (Chapter 4) 179 Rheological equation (Cross) 110 fluids, energy and momentum relationships Rheology 105, 195 (Chapter 2) 56 — and fluid structure 120 multiphase mixtures (Chapter 5) 227 Rheopexy or negative thixotropy 114 — heat transfer (Chapter 9) 562 RHODES, F. H. 517,565 — humidification and water cooling (Chapter 13) 786 RICHARDSON,]. F. 119, 131, 138, 139, 185, 186, — liquid mixing (Chapter 7) 311 187, 191, 194, 197, 199, 200, 201, 202, 203, 207, — mass transfer (Chapter 10) 655 209, 210, 217, 218, 219, 220, 227, 228, 229. 362, — momentum heat and mass transfer (Chapter 32) 363, 376, 397, 562 735 RIEGER, F. 293.312 — pumping of fluids (Chapter 8) 376 ROCO, M. C. 205, 207, 228 — the boundary layer (Chapter 11) 692 ROHATGl, N. D. 214, 224, 229 — units and dimensions (Chapter 1) 22 ROHSENOW, W. M. 482, 491, 492. 564 Reflectivity 446 ROMERO, J. J. B. 555,566 REID.R, C. 599,655 ROMOS, H. L. 293,312 REIHER, M. 426, 563 Rootes blower 344 Relative humidity 739 Rotameter, example 260 Relief valves 143 Rotameters 257 Residence time distribution 311 — floats, different types 260 mean, C.S.T.R. 310 — standard type 260 Resistance, interfacial 599 Rotary blowers 344 — thermal 390,517,518 and compressors, sliding vane type 346 — to flow in pipes 65 — gear pumps 321 Resistances in series, conduction, example 391 — vacuum pumps, liquid ring 365
  5. INDEX 891 Single stage compression, with clearance 352 Stanton number and heat transfer coefficient 730 pumps, vacuum producing 365 _ _ point value 732 Single-acting pumps 316 for mass transfer 722 SKELLAND, A. H. P. Ill, 116,131,139, 280, 282, point value, flow over plane surface 730 288, 290, 293, 301, 311, 554, 566 STANTON,!. 63,65 Skin friction 651,695,716 Static mixers 307 effect on heat and mass transfer 651 — — laminar flow 307, 308 frictional drag at surface of smooth pipe 716 viscous materials 308 Sliding vane, rotary blowers and compressors 346 — pressure 233 - — vacuum pumps 365 measurement of 242 Slip velocity, measurement of 199 Steam and water, pressure-enthalpy diagram 813 pneumatic conveying 219 temperature-entropy diagram 814 Slug 3, 5 — jet ejectors 365, 366, 367, 368 — flow, gas-liquid 183, 185 — vacuum producing equipment 364 SLUSSER, R. P. 524,565, 566 — metering 252 SMALL, M. 203, 204, 228 — tables 806 SMITH, B. D. 244, 272 STEELE, K. 341,376 SMITH,!. C. 300,312 Stefan-Boltzmann constant 441 SMITH, J. M. 293, 294, 295, 297, 312 law 441 SMITH, W. Q. 477,564 STEFAN,!. 578,655 Solids, creep 115 Stefan's law of diffusion 578, 587 Solids-gas flow 211 STERBACER, Z. 288,311 mixing 275 STEW ART, I. W. 308,309,312 Solids-liquid flow 195 Stirred vessel, heat transfer rates, example 498 foodstuffs 210 time for heating, example 501 low density particles 210 — vessels, example 498, 501 Solids-liquid-gas mixing 275 power consumption 282 Solids-liquid mixing 275 Stirring action of bubbles, heat transfer 484 Solids-solids mixing 275 STODOLA, A. 172, 179 Sonic velocity 150, 156,158, 189 Strain 105 Soret effect, thermal diffusion 589 Stream velocity 61 SPAL.DING, D. B. 393, 562 Streamline see also Laminar SPARROW, E. M. 465, 564 — boundary layer 664, 670 Specific energy, open channel flow 98 — displacement thickness 673 — heat 7 rate of thickening 673 of gas at constant pressure 30, 33 ———- thickness 673 . _ volume 30, 33 — flow 39,59,64,75, 183,189 _ rati0 J 4K Bingham plastic, pipe 124 — heats of gases (table) 794 — — boundary layer 664 liquids (table) 793 heat transfer 420 — speed of pumps 334 over a plane surface 687 — volume of dry gas 749 in a pipe, non-Newtonian fluid 122 Spectral emissive power 439 boundary layer 664 black body 440 momentum transfer 694 — emissivity, non-conductors 442 — power-law fluid, pipe 122 SPEDDINO, P. L. 186,227 unstable 64 Sphere, centre temperature 407 — to turbulent transition point, in pipe 64 — temperature distribution 409 Streamlines 39 Spheres, heat, transfer 392 — straight tube, constriction, immersed object 39, 40 — mass transfer 617,652 Streamtubes 39,41 Spherical droplet in a liquid, mass transfer 617 STREAT, M. 198,210,227,229 Spiral heat exchangers 550 STREIFF, F. 307,312 Spray dryers 393 Stretching, flow of viscoelastic fluids 117 — ponds 762 STROUHAL, F. 266,273 Spreading of drop, example 19 Sub-cooled boiling 492 Stability parameter for flow 82 Subsonic velocity 155 maximum value 83 Sulzer static mixer 309 Stagewi.se mass transfer processes 622 Summation rule, radiation 454 Standard orifice meter 249 Superheated steam, enthalpy (SI units) 812 — venturi meter 255 entropy (SI units) 812 Stanton number 416, 418, 722 Supersaturation on mixing two humid gases 753
  6. INDEX 893 Triangular notch 264 Two-film theory, absorption 601 Trouton ratio 117 diffusion, Whitman 600 Tube banks, pressure drop in flow over 93,431 mass transfer 600 — bundle diameter, heat exchanger 509 steady state, molecular diffusion 600,601 — — heat exchanger 504, 507 Two-phase flow, critical velocity 187 — bundles 427,429 _ energy, pressure and momentum relations 187 heat transfer 427 -example 190 - pressure drop 93,431 —— holdup, liquid 188 — dimensions, heat exchanger 508 momentum, pressure and energy relations 187 steel 508 — Newtonian fluids, laminar or turbulent flow 187 — layout, heat exchanger 509, 510 non-Newtonian, turbulent flow 187 — length, heat exchanger 508 power-law model, shear-thinning fluid 187 — pitch, heat exchanger 509, 528 pressure drop, frictional 188 — sheet thickness, heat exchanger 507 _ — and acceleration losses 188 — side friction factor, heat exchanger 525 _ methods for its determination 187 pressure drop, heat exchanger 523 _ practical methods of evaluation 188 TUBULAR EXCHANGER MANUFACTURERS' _ __ momentum and energy relations 187 ASSOCIATION see TEMA ——_ term in vertical flow, hydrostatic 188 TUCKER, G. 229 — — Reynolds number 188 Turbine flowmeters, liquid meters 271 separated flow model 188 Turbines, flat-bladed 295 streamline 189 — radial flow type 295 turbulent 189 — Rushton type 293, 303 — velocity, streamline to turbulent transition 187 — shrouded 305 — •— viscous flow 189 Turboblowers 344 — mixtures, with gas or vapour 182 Turbocompressors 346, 347 — pressure drop 192,193 Turbulence, anisotropic 701 UHL, V. W. 288,311 — effect on condensation 476, 477 ULBRECHT, J. 282,293, 300, 311,312 — intensity 701 ULLRICH, H. 293,312 — isotropic 279,701 Ultrasonic flowmeters 266 — mass transfer across a phase boundary 600 Doppler 267 — onset of 82 time of flight 266, 267 — promoters 651 UNDERWOOD, A. J. V. 386,511, 514, 562,565 — scale of 702 Units 2,3 Turbulent boundary layer 664, 675 displacement thickness 677 — and dimensions 1 examples 9, 10, 17, 19 — rate of thickening 677 thickness 677 —— — further reading 22 _ nomenclature 22 — eddies 701 — conversion factors 10 boundary layer 667 Universal gas constant 31 — flow 39, 60, 63, 75, 160, 183, 187, 189, 207 boundary layer 664 — velocity profile 707, 727 approximate form 711 eddy transport 701 _ buffer layer 707 example 86 laminar sub-layer 707 — — flocculated suspensions 196 — turbulent core 706 — — in boundary layer 61, 664, 675 _ f j Reynolds analogy 727 pipe 83,681,701 use o n mixing 277 — velocity gradients 708 natural convection 435 Unsheared plug flow 112 Unsteady state conduction, example 398 nature of 701 _ of a plastic sheet, example 409 shear-thinning fluids 136 . _ Schmidt's method, example 400 tranquil, rapid and critical 95 _ through a plastic sheet, example 409 — mass transfer 7! 7 — —- various shapes, example 403 — mixing 279 heat transfer 394, 500 — Prandtl number 717 example 398 — region, eddy motion 675 mass transfer 590, 591 — Schmidt number 717 — thermal conduction 401 — zone, Reynolds analogy 729 Upper Newtonian viscosity 110 TURTLE, R. B. 200, 201, 203, 204, 228 TUTHILL, J. P. 293,312 V-notch 264 Two-film theory 600 Vacseal pumps 341
  7. INDEX 895 Vortex formation on aerofoil 664,665 Weir 244, 261 Vortex formation, toroidal type 297 — example 262,263 — free 54,55 WEISMAN, J. 183,184,185, 227 — shedding flowmeters 266 WEST, A. S. 498,499, 500,565 — single-celled 297 WESTWATER, J, W. 482,564 Votator 554 Wet bulb temperature 738, 742, 749 WADE, S. H. 649, 650, 656 _— compared with adiabatic saturation 745 Wake in flow over flat plates 666 effect of gas velocity 743 WA.LDIE, B. 410, 562 humidity determination 756 Wall shear stress, effect of curvature 712 — — thermometer 757 - slip 77,119 WEXLER, A. 759,786 WALLIS, G. B. 183, 184, 227 WHITE, C. M. 87,139 WALLIS, J. D. 483,564 WHITE, J.L. 120,139 WALTERS,K. Ill, 115,116,131,139 WHITE, R. R. 779,786 WARDLE, A. P. 197,227 WHITMAN, W. G, 600,655 WASHINGTON, L. 433,563 WHORLOW, R. H, 118,139 Water and steam, pressure-enthalpy diagram 813 Wien's displacement law 440 temperature-entropy diagram 814 WIGHTMAN, E. J, 233,272 — cooling 738, 762 WILDE, H. D. 363, 377 towers 738 WILKE, C. R. 597,619, 647, 655 approximate calculations 775 WILLIAMSON, G. J. 771,776,786 calculation of height 769 WILLS, M. J. N. 534,566 change in condition of air 772 WILSON, E. E. 517,565 commercial 775 WILSON, K.C. 205,228 construction for height 770 Wilson plot 517 - countercurrent 738 WlNKELMANN, A. 581, 655 design 738 WlNTERTON, R. H. S. 417, 563 forced draught 762 WOOD, B. 762,775,786 heat and mass transfer coefficients 774 induced draught 765 WOOLLATT, E. 170, 179 Work done by fluid 28,45 mechanical draught 762,764 natural draught 762, 765 WORSTER,R.C. 210,229 packing height 767 WURSTER, A. 433,563 — sensible heat and evaporation 694 WYPICH.P.W. 225,229 ___ shells 762 YAP,C. Y. 294,301,312 — spray distribution 763 Yield stress 104,111, 126, 196 —— — temperature and humidity gradients 773 Yoo, S. S, 137, 140 — film coefficient 520,521 YOUNGER, K. R. 517,565 — hammer 44- — vapour, emissivity 467 ZALTASH, A. 214, 224,229 — velocity, optimum, heat exchanger 505 ZANDI.I. 203,228 — viscosity 795 Zero wall slip 77 WATSON, K. M. 35 ZlELlNSKI. J. M. 596, 655 Watt 3, 7, 8 Zivi, S. M. 775,786 Waves, shock 174 ZUBER, N. 491.492,494,565