Theory

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Frictional Head Drop in Screens

Reference Document :-

Chemical Engineers' Handbook by Perry & Chilton, Page 5-37

The flow through a screen can be considered as flow through a number of orifices or nozzles in parallel.Thus the pressure drop or head loss across a screen can be computed from an oricice type equation.The resulting equation for head loss is :-

where

head loss,m of fluidn = no.of screens in seriesC = screen discharge coefficient( is a function of screen's Renolds no, Re)

Book by Perry &Chilton)

fractional free projected area of screen

=

centre to centre spacing of square screen wiresd= diameter of screen wires

g = acceleration due to gravity ( 9.80665m/s)V = superficial velocity ahead of screen,m/s

Experimental data indicate that for a series of screens, the over-all head loss is directly proportionalto the number of screens in series, as given by the above equation, and is not affected by either thespacing between successive screens or by their orientation with respect to one another.

Screen discharge coefficient C is a function of screen Reynold's Number,1

Ds = aperture width, mC is given by the curve under fig. 5-44, approximated by the following tabular data :-

Re C

0.1 0.03100.12 0.03400.14 0.03680.16 0.03930.18 0.04180.2 0.0441

0.22 0.0463Re C

Head loss through the screen, Dh = (n/C2) x {(1-a2)/a2} x (V2/2g)

Dh =

(for Plain square mesh screen, C vs.Re is given in fig.5-44,page 5-37 of of Chem.eng.Hand

a =

{(l-d)/l}2

l=

.Re=Ds X V/(a X n) =

where, n=kinetic viscosity of fluid(=µ/density of fluid) in m2/s

Theory

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0.24 0.04830.26 0.05040.28 0.05230.3 0.0542

0.32 0.05600.34 0.05770.36 0.05940.38 0.06110.4 0.0627

0.42 0.06430.44 0.06580.46 0.06730.48 0.06880.5 0.0702

0.52 0.07170.54 0.07300.56 0.07440.58 0.07580.6 0.0771

0.62 0.07840.64 0.07960.66 0.08090.68 0.08210.7 0.0834

0.72 0.08460.74 0.08580.76 0.08690.78 0.08810.8 0.0892

0.82 0.09040.84 0.09150.86 0.09260.88 0.09370.9 0.0948

0.92 0.09580.94 0.09690.96 0.09790.98 0.0990

1 0.10001.2 0.10981.4 0.11871.6 0.12711.8 0.13502 0.1425

2.2 0.14962.4 0.15642.6 0.1629Re C

2.8 0.1692

Theory

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3 0.17533.2 0.18123.4 0.18693.6 0.19243.8 0.19784 0.2031

4.2 0.20824.4 0.21334.6 0.21824.8 0.22305 0.2277

5.2 0.23235.4 0.23695.6 0.24135.8 0.24576 0.2500

6.2 0.25426.4 0.25836.6 0.26236.8 0.26627 0.2701

7.2 0.27397.4 0.27767.6 0.28137.8 0.28498 0.2884

8.2 0.29198.4 0.29538.6 0.29878.8 0.30209 0.3053

9.2 0.30859.4 0.31179.6 0.31489.8 0.317910 0.321012 0.349514 0.374916 0.397918 0.418920 0.438422 0.456424 0.473326 0.489228 0.504230 0.5184Re C

32 0.531934 0.5447

Theory

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36 0.557038 0.568740 0.580042 0.590944 0.601346 0.611448 0.621150 0.630552 0.639654 0.648456 0.656958 0.665260 0.673362 0.681164 0.688866 0.696268 0.703570 0.710572 0.717474 0.724276 0.730878 0.737280 0.743582 0.749784 0.755786 0.761788 0.767590 0.773192 0.778794 0.784296 0.789698 0.7948

100 0.8000120 0.8370140 0.8697160 0.8989180 0.9255200 0.9500220 0.9726240 0.9937260 1.0135280 1.0322300 1.0499320 1.0707340 1.0901Re C

360 1.1081380 1.1249400 1.1407

Theory

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420 1.1555440 1.1693460 1.1824480 1.1947500 1.2063520 1.2174540 1.2278560 1.2377580 1.2470600 1.2560620 1.2644640 1.2725660 1.2802680 1.2875700 1.2945720 1.3012740 1.3076760 1.3137780 1.3196800 1.3252820 1.3305840 1.3356860 1.3406880 1.3453900 1.3498920 1.3518940 1.3536960 1.3554980 1.3571

1000 1.35871200 1.37241400 1.38241600 1.38991800 1.39562000 1.39992200 1.40322400 1.40572600 1.40762800 1.40893000 1.40993200 1.41163400 1.41333600 1.41503800 1.4169Re C

4000 1.41884200 1.42084400 1.42284600 1.4249

Theory

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4800 1.42695000 1.42905200 1.43115400 1.43325600 1.43535800 1.43746000 1.43956200 1.44166400 1.44376600 1.44586800 1.44797000 1.45007200 1.45217400 1.45417600 1.45627800 1.45828000 1.46038200 1.46238400 1.46438600 1.46638800 1.46839000 1.47039200 1.47239400 1.47429600 1.47629800 1.4781

10000 1.480012000 1.488414000 1.495216000 1.500718000 1.505220000 1.509122000 1.512424000 1.515326000 1.517828000 1.520030000 1.521932000 1.523734000 1.525236000 1.526738000 1.527940000 1.529142000 1.5301

Re C

44000 1.531146000 1.532048000 1.532850000 1.533552000 1.534254000 1.5348

Theory

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56000 1.535358000 1.535960000 1.536362000 1.536864000 1.537266000 1.537668000 1.537970000 1.538272000 1.538574000 1.538876000 1.539078000 1.539380000 1.539582000 1.539784000 1.539886000 1.540088000 1.540190000 1.540392000 1.540494000 1.540596000 1.540698000 1.5406

100000 1.5407

Calculation Sheet

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PRESSURE DROP CALCULATION FOR STRAINER

Flow rate of liquid through strainer= 25

6 cst 0.000006Strainer inlet size= 100 mm NB (ID=102.26mm)

Average Strainer Diameter 100 mm

Strainer effective length 405 mm

Straining area= 0.127235

Screen : 32 0.79375 mm 32 swgmesh 32 swg= 0.0108 inch 0.27432 mm

(see.table:I-25, ref:piping hand book by crocker & king)

0.51943 mm = 0.000519 m

size in inch.& swg=screen wire gauge

0.428239

Now,velocity of liquid through strainer ,V= 0.0545798845 m/s

11.033716201

Ds = aperture width, mScreen discharge coeficient,C= 0.3361483648

No. of screen in series= 1

0.0059854201 mlcor. 5.9854200873 mmlc

(Ref.eqn.5-100,page 5-37 of Chem.eng.Hand Book by Perry &Chilton)

where

head loss,m of fluidn = no.of screens in seriesC = screen discharge coefficient( is a function of screen's Renolds no, Re)

Book by Perry &Chilton)

fractional free projected area of screen

=

centre to centre spacing of square screen wiresd= diameter of screen wires

g = acceleration due to gravity ( 9.80665m/s)V = superficial velocity ahead of screen,m/s

m3/hr

Max. Kinematic viscosity of liquid (n)= m2/sec

m2

Hence size of opening (aperture width)Ds=

Note:mesh size=no.of wires per linear inch or. Spacing between two wires is the reciprocal of mesh

Approx. % open area, i.e. fractional free projected area of screen, a =

Renold's no.Re=Ds X V/(a X n) =

where, n=kinetic viscosity of fluid(=µ/density of fluid) in m2/s

Head loss through the screen, Dh = (n/C2) x {(1-a2)/a2} x (V2/2g)

Dh =

(for Plain square mesh screen, C vs.Re is given in fig.5-44,page 5-37 of of Chem.eng.Hand

a =

{(l-d)/l}2

l=

REYNOLD'S NUMBER INPUT=

S D Calc D Actl Re C Calc C Actl

-2.3026 -3.50656 -3.50656 0.099999 0.03 0.030 -2.3026 -2.3026 1 0.099999 0.099999

2.3026 -1.208128 -1.203973 10.00015 0.298756 0.3 trial4.6052 -0.223144 -0.223144 100.003 0.8 0.8

-2.302585 -3.473763 -3.473768 0.1 0.031 0.031-2.120264 -3.381289 0.12 0.034004-1.966113 -3.303068 0.14 0.03677-1.832581 -3.235284 0.16 0.039349-1.714798 -3.175475 0.18 0.041774-1.609438 -3.121957 -3.101093 0.2 0.044071 0.045-1.514128 -3.073532 0.22 0.046257-1.427116 -3.029313 0.24 0.048349-1.347074 -2.988626 0.26 0.050357-1.272966 -2.950948 0.28 0.05229-1.203973 -2.915864 -2.900422 0.3 0.054157 0.055-1.139434 -2.883039 0.32 0.055964

-1.07881 -2.8522 0.34 0.057717-1.021651 -2.82312 0.36 0.05942-0.967584 -2.795608 0.38 0.061078-0.916291 -2.769504 -2.780621 0.4 0.062693 0.062-0.867501 -2.74467 0.42 0.064269-0.820981 -2.720989 0.44 0.06581-0.776529 -2.698359 0.46 0.067316-0.733969 -2.676689 0.48 0.068791-0.693147 -2.655901 -2.65926 0.5 0.070236 0.07 zone - 1-0.653926 -2.635927 0.52 0.071653-0.616186 -2.616704 0.54 0.073043-0.579818 -2.59818 0.56 0.074409-0.544727 -2.580303 0.58 0.075751-0.510826 -2.563031 -2.551046 0.6 0.077071 0.078-0.478036 -2.546324 0.62 0.078369-0.446287 -2.530146 0.64 0.079647-0.415515 -2.514464 0.66 0.080906-0.385662 -2.49925 0.68 0.082147-0.356675 -2.484475 -2.501036 0.7 0.083369 0.082

-0.328504 -2.470116 0.72 0.084575-0.301105 -2.456149 0.74 0.085765-0.274437 -2.442554 0.76 0.086939-0.248461 -2.42931 0.78 0.088098-0.223144 -2.416402 -2.430418 0.8 0.089242 0.088-0.198451 -2.403811 0.82 0.090373-0.174353 -2.391522 0.84 0.09149-0.150823 -2.379523 0.86 0.092595-0.127833 -2.367798 0.88 0.093687-0.105361 -2.356336 -2.385967 0.9 0.094767 0.092-0.083382 -2.345126 0.92 0.095835-0.061875 -2.334156 0.94 0.096892-0.040822 -2.323416 0.96 0.097938-0.020203 -2.312897 0.98 0.098974

0 -2.30259 -2.302585 1 0.1 0.10.182322 -2.209549 1.2 0.109750.336472 -2.130849 1.4 0.1187360.470004 -2.062651 1.6 0.1271170.587787 -2.002475 1.8 0.1350010.693147 -1.94863 -1.89712 2 0.142469 0.150.788457 -1.899909 2.2 0.1495820.875469 -1.855419 2.4 0.1563870.955511 -1.814483 2.6 0.1629221.029619 -1.776575 2.8 0.1692171.098612 -1.741277 -1.742969 3 0.175296 0.1751.163151 -1.708251 3.2 0.1811821.223775 -1.677224 3.4 0.1868921.280934 -1.647965 3.6 0.1924411.335001 -1.620285 3.8 0.1978421.386294 -1.594022 -1.609438 4 0.203107 0.21.435085 -1.569037 4.2 0.2082461.481605 -1.545211 4.4 0.2132671.526056 -1.522442 4.6 0.2181781.568616 -1.50064 4.8 0.2229871.609438 -1.479726 -1.469676 5 0.2277 0.231.648659 -1.459629 5.2 0.2323221.686399 -1.44029 5.4 0.2368591.722767 -1.421652 5.6 0.2413151.757858 -1.403666 5.8 0.2456951.791759 -1.386289 -1.386294 6 0.250001 0.25

1.791759 -1.386285 -1.386294 6 0.250002 0.251.824549 -1.369726 6.2 0.2541771.856298 -1.35376 6.4 0.258267

1.88707 -1.338349 6.6 0.2622781.916923 -1.323458 6.8 0.266213

1.94591 -1.309054 -1.290984 7 0.270075 0.2751.974081 -1.29511 7.2 0.273868

2.00148 -1.281597 7.4 0.2775942.028148 -1.268493 7.6 0.2812552.054124 -1.255774 7.8 0.2848552.079442 -1.243419 -1.237874 8 0.288396 0.292.104134 -1.231411 8.2 0.291882.128232 -1.21973 8.4 0.29531

2.151762 -1.208362 8.6 0.2986862.174752 -1.19729 8.8 0.3020122.197225 -1.1865 -1.203973 9 0.305288 0.3 zone - 22.219203 -1.17598 9.2 0.308517

2.24071 -1.165716 9.4 0.3116992.261763 -1.155699 9.6 0.3148372.282382 -1.145916 9.8 0.3179332.302585 -1.136358 -1.139434 10 0.320986 0.322.484907 -1.051317 12 0.3494772.639057 -0.981124 14 0.374892.772589 -0.921585 16 0.3978882.890372 -0.870042 18 0.4189342.995732 -0.82471 -0.84397 20 0.438362 0.433.091042 -0.784332 22 0.4564253.178054 -0.747992 24 0.4733163.258097 -0.715003 26 0.4891913.332205 -0.684836 28 0.5041733.401197 -0.657076 -0.653926 30 0.518365 0.523.465736 -0.631392 32 0.5318513.526361 -0.607516 34 0.5447023.583519 -0.585227 36 0.556983.637586 -0.564341 38 0.5687353.688879 -0.544704 -0.544727 40 0.580013 0.58

3.73767 -0.526187 42 0.5908543.78419 -0.508677 44 0.601291

3.828641 -0.492079 46 0.6113543.871201 -0.476309 48 0.6210713.912023 -0.461296 -0.462035 50 0.630466 0.633.951244 -0.446974 52 0.639563.988984 -0.433289 54 0.6483734.025352 -0.42019 56 0.6569224.060443 -0.407634 58 0.6652224.094345 -0.39558 -0.385662 60 0.673289 0.684.127134 -0.383994 62 0.6811364.158883 -0.372843 64 0.6887744.189655 -0.362098 66 0.6962144.219508 -0.351734 68 0.7034674.248495 -0.341726 -0.34249 70 0.710543 0.714.276666 -0.332054 72 0.7174494.304065 -0.322696 74 0.7241944.330733 -0.313636 76 0.7307854.356709 -0.304856 78 0.7372294.382027 -0.296341 -0.287682 80 0.743534 0.754.406719 -0.288077 82 0.7497044.430817 -0.280051 84 0.7557454.454347 -0.272251 86 0.7616634.477337 -0.264665 88 0.767463

4.49981 -0.257283 -0.248461 90 0.773149 0.784.521789 -0.250096 92 0.7787264.543295 -0.243094 94 0.7841984.564348 -0.236269 96 0.7895684.584967 -0.229613 98 0.794841

4.60517 -0.223119 -0.223144 100 0.80002 0.8

4.60517 -0.223173 -0.223144 100 0.799976 0.84.787492 -0.177882 120 0.8370414.941642 -0.13964 140 0.8696715.075174 -0.106552 160 0.8989295.192957 -0.077395 180 0.9255255.298317 -0.051336 -0.051293 200 0.949959 0.95 zone - 35.393628 -0.027782 220 0.97265.480639 -0.006295 240 0.9937255.560682 0.013458 260 1.013549

5.63479 0.031735 280 1.0322445.703782 0.048741 0.04879 300 1.049948 1.05

5.703782 0.048661 0.04879 300 1.049865 1.055.768321 0.068333 320 1.0707225.828946 0.086254 340 1.0900835.886104 0.102655 360 1.1081095.940171 0.117727 380 1.1249375.991465 0.131628 0.139762 400 1.140684 1.156.040255 0.144492 420 1.1554526.086775 0.156431 440 1.169336.131226 0.167542 460 1.1823946.173786 0.177907 480 1.1947146.214608 0.187599 0.182322 500 1.206349 1.2 zone - 46.253829 0.19668 520 1.2173546.291569 0.205204 540 1.2277766.327937 0.21322 560 1.2376576.363028 0.220771 580 1.247037

6.39693 0.227893 0.223144 600 1.255951 1.256.429719 0.234621 620 1.2644296.461468 0.240984 640 1.272501

6.49224 0.247011 660 1.2801936.522093 0.252724 680 1.287528

6.55108 0.258146 0.239017 700 1.294528 1.276.579251 0.263297 720 1.301213

6.60665 0.268195 740 1.3076026.633318 0.272856 760 1.3137116.659294 0.277296 780 1.3195576.684612 0.281527 0.262364 800 1.325152 1.36.709304 0.285564 820 1.3305126.733402 0.289416 840 1.3356486.756932 0.293096 860 1.3405716.779922 0.296612 880 1.3452936.802395 0.299974 0.300105 900 1.349824 1.35

6.802395 0.30004 0.300105 900 1.349913 1.356.824374 0.301438 920 1.351801

6.84588 0.302783 940 1.3536216.866933 0.30408 960 1.3553776.887553 0.30533 980 1.3570726.907755 0.306535 0.322083 1000 1.358709 1.387.090077 0.316554 1200 1.372397.244228 0.323819 1400 1.3823967.377759 0.329219 1600 1.3898827.495542 0.333293 1800 1.395557

7.600902 0.336392 0.336472 2000 1.399888 1.4 zone -57.696213 0.33875 2200 1.4031937.783224 0.340534 2400 1.4056987.863267 0.341865 2600 1.407577.937375 0.342831 2800 1.408938.006368 0.343501 0.34359 3000 1.409874 1.41

8.006368 0.343592 0.34359 3000 1.410003 1.418.070906 0.344699 3200 1.4115658.131531 0.345893 3400 1.4132518.188689 0.347154 3600 1.4150358.242756 0.34847 3800 1.416898

8.29405 0.349827 0.350657 4000 1.418823 1.428.34284 0.351218 4200 1.4207968.38936 0.352633 4400 1.422809

8.433812 0.354067 4600 1.4248518.476371 0.355516 4800 1.4269168.517193 0.356974 0.357674 5000 1.428999 1.43 zone -68.556414 0.358439 5200 1.4310938.594154 0.359907 5400 1.4331968.630522 0.361376 5600 1.4353038.665613 0.362845 5800 1.4374138.699515 0.364311 0.364643 6000 1.439522 1.448.732305 0.365774 6200 1.4416298.764053 0.367231 6400 1.4437328.794825 0.368683 6600 1.4458298.824678 0.370128 6800 1.447928.853665 0.371566 0.371564 7000 1.450003 1.458.881836 0.372996 7200 1.4520788.909235 0.374417 7400 1.4541448.935904 0.37583 7600 1.45628.961879 0.377234 7800 1.4582468.987197 0.378629 0.378436 8000 1.460281 1.469.011889 0.380014 8200 1.4623059.035987 0.38139 8400 1.4643189.059517 0.382756 8600 1.466329.082507 0.384112 8800 1.46831

9.10498 0.385459 0.385262 9000 1.470288 1.479.126959 0.386795 9200 1.4722559.148465 0.388122 9400 1.474219.169518 0.389439 9600 1.4761539.190138 0.390747 9800 1.478084

9.21034 0.392045 0.392042 10000 1.480004 1.48

9.21034 0.391939 0.392042 10000 1.479847 1.489.392662 0.397705 12000 1.4884059.546813 0.402235 14000 1.4951639.680344 0.405903 16000 1.5006589.798127 0.408942 18000 1.5052249.903488 0.411503 0.398776 20000 1.509085 1.499.998798 0.413693 22000 1.51239310.08581 0.415587 24000 1.51525910.16585 0.417239 26000 1.51776610.23996 0.418693 28000 1.519974

10.30895 0.419981 0.405465 30000 1.521933 1.5 zone -710.37349 0.421129 32000 1.5236810.43412 0.422156 34000 1.52524710.49127 0.42308 36000 1.52665610.54534 0.423914 38000 1.52792910.59663 0.424668 0.408793 40000 1.529083 1.50510.64542 0.425354 42000 1.53013210.69194 0.425978 44000 1.531087

10.7364 0.426548 46000 1.5319610.77896 0.427068 48000 1.53275710.81978 0.427545 0.41211 50000 1.533488 1.51

10.859 0.427982 52000 1.53415810.89674 0.428383 54000 1.53477410.93311 0.428752 56000 1.53534

10.9682 0.429091 58000 1.53586111.0021 0.429403 0.415415 60000 1.53634 1.515

11.03489 0.42969 62000 1.53678111.06664 0.429954 64000 1.53718711.09741 0.430198 66000 1.53756211.12726 0.430422 68000 1.53790611.15625 0.430628 0.41871 70000 1.538224 1.5211.18442 0.430818 72000 1.53851611.21182 0.430992 74000 1.53878411.23849 0.431153 76000 1.5390311.26446 0.431299 78000 1.53925611.28978 0.431434 0.421994 80000 1.539463 1.52511.31447 0.431557 82000 1.53965311.33857 0.431669 84000 1.539825

11.3621 0.431771 86000 1.53998311.38509 0.431864 88000 1.54012511.40756 0.431947 0.425268 90000 1.540254 1.5311.42954 0.432023 92000 1.5403711.45105 0.43209 94000 1.540474

11.4721 0.43215 96000 1.54056711.49272 0.432204 98000 1.54064911.51293 0.43225 0.431782 100000 1.540721 1.54

Re0.1

110

1001000

10000100000

RE S P Q R D C11.0337162011 2.400956 -2.39878 0.624087 -0.03293 -1.090203 0.336148 =FRICTIONAL COEFFICIENT OUTPUT

D1 D2 D3 S1 S2 S3 R Q P

-3.47377 -2.30259 -1.38629 -2.3026 0 1.791759 0.000675 0.510188 -2.30259

-3.47377 -2.30259 -1.38629 -2.3026 0 1.791759 0.000675 0.510188 -2.30259

-1.38629 -0.54473 -0.22316 1.791759 3.688879 4.60517 -0.032932 0.624087 -2.398779

-0.22314 -0.051293 0.04879 4.60517 5.298317 5.703782 -0.000989 0.257713 -1.388987

0.04879016417 0.187753 0.300159 5.703782 6.214608 6.802395 -0.073546 1.148584 -4.109802

0.30010459245 0.336472 0.34359 6.802395 7.600902 8.006368 -0.023249 0.380401 -1.21176

0.34358970439 0.371564 0.392042 8.006368 8.853665 9.21034 0.020266 -0.30867 1.515828

0.39204451109 0.427692 0.432417 9.21034 10.81978 11.51293 -0.006659 0.155524 -0.475521

C0.03

0.10.30.81.41.51.6

1

10

Discharge coefficient,C

Column K

Reynolds numberFig. 5-44

C

1

10

Discharge coefficient,C

Column K

Reynolds numberFig. 5-44

C

=FRICTIONAL COEFFICIENT OUTPUT

INPUT SWG = 32 32

20 0.036 32 0.0108 0.0108 0.0108 021 0.03222 0.028 0.0108 =OUTPUT WIRE SIZE, INCH23 0.02424 0.02225 0.02026 0.01827 0.016428 0.014829 0.013630 0.012431 0.011632 0.010833 0.010034 0.009235 0.008436 0.007637 0.006838 0.006039 0.005240 0.004841 0.004442 0.004043 0.003644 0.003245 0.002846 0.002447 0.002048 0.0016

Table:I-25 (ref:piping hand book by crocker & king)Wire and sheet metal gauges(dimension and thickness in decimal parts of an inch)

ga

ug

e n

o.

ga

ug

e n

o.

ga

ug

e n

o.

0000000 0.500 13 0.092 32 0.0108000000 0.464 14 0.080 33 0.0100

00000 0.432 15 0.072 34 0.00920000 0.400 16 0.064 35 0.0084

000 0.372 17 0.056 36 0.007600 0.348 18 0.048 37 0.0068

0 0.324 19 0.040 38 0.00601 0.300 20 0.036 39 0.00522 0.276 21 0.032 40 0.00483 0.252 22 0.028 41 0.00444 0.232 23 0.024 42 0.0040

Brit

ish

Im

pe

rial

Sta

nd

ard

w

ire

ga

ug

e(s

wg

):

Brit

ish

Im

pe

rial

Sta

nd

ard

w

ire

ga

ug

e(s

wg

):

Brit

ish

Im

pe

rial

Sta

nd

ard

w

ire

ga

ug

e(s

wg

):

5 0.212 24 0.022 43 0.00366 0.192 25 0.020 44 0.00327 0.176 26 0.018 45 0.00288 0.160 27 0.0164 46 0.00249 0.144 28 0.0148 47 0.0020

10 0.128 29 0.0136 48 0.001611 0.116 30 0.0124 49 0.001212 0.104 31 0.0116 50 0.0010

0