gravity force buoyancy force drag force where p density of particle density of fluid A cross section perpendicular to the direction of motion

Transcription

1 orce acting on the ettling article SEDIMENTATION gravity force boyancy force drag force In cae of floating: their i zero. f k V g Vg f A where denity of article denity of flid A cro ection erendiclar to the direction of otion Rearrangeent of the eqation Aing herical article of diaeter d, rearrange the eqation, and define (d) and () a: d f Re Re f g d d Generalized ettling lot Y=() againt X=(d) Stoke: lainar region Newton: trblent region, rarely ed becae of the very high ile Aroxiation of the Newton region: X Y 0. Exact forla for the Stoke region: X Y

2 Proble Sandy ldge i ettled in a chanel of bae area 5. Sand denity i 800 /, denity i 00 /, it vicoity i 0 - Pa. a) What i it caacity if the diaeter of allet article to be ettled i 0 -? b) 0 /in of the ae ldge i to be treated in another ettler of bae area 0. What diaeter article will be ettled? c) In the cae of b), i.e. 0 /in of the ae ldge, how any tray are to be alied to ettle ot article with diaeter 50? Soltion: A = 5 = 5 = 800 / k = 00 / k = 0 - Pa d = 0 - = 0-5 V =? a) What i it caacity if the diaeter of allet article to be ettled i 0 -? Caacity of the ettler ean the axi flow rate accetable. irt cote g Pa Then, ince velocity i to be calclated fro known diaeter, calclate (d): 5 X d d Thi fall to Stoke regie (according to the lot), th Y can be calclated with a forla: X 0.58 Y Pa Settling caacity deend on the bae area and the ettling velocity only. V A h b) 0 /in of the ae ldge i to be treated in another ettler of bae area 0. What diaeter article will be ettled? A = 0 V ' = 0 /in

3 Settling velocity (it ini) can be calclated fro the given caacity. V' A' ' 0 V' in ' A' in 0 60 h Now nknown diaeter i to coted fro know velocity. i the ae a earlier becae the aterial i the ae ' Y' ' Pa Thi vale fall to the tranient region, th X' i read fro the lot. X' d' d' d' Th, article with diaeter at leat a large a 0.8 will be ettled. c) In the cae of b), i.e. 0 /in of the ae ldge, how any tray are to be alied to ettle ot article with diaeter 50? A = 0 ' = 0 /in d = 50 = n =? Velocity i to be coted fro known diaeter. X'' d'' d'' Thi vale fall to the tranient region, th Y'' i read fro the lot. Y'' v'' 0. 6 ' ' v'' Pa '' '' How any tray? V V' n A' '' 0 V' n in. A' '' in Th, at leat 5 tray are needed. 5 i ore than. bt no roble if even aller article are alo ettled ot.

4 Proble After grinding of and llock, a fraction of article cale. to.5 have been earated by claifying the article with ieve. a) What velocity t be aintained in a ihon earator in order to earate the two aterial? b) De to an oeration failre, aller article of both kind ha got to the yte. What i the ini article ize at which the earation can be erfored? = 0.95 Pa = 00 / = 00 / llock = 500 / Soltion igre: ótvíz: leent, zén:, eddő: llock a) What velocity t be aintained in a ihon earator in order to earate the two aterial? Soltion ath Velocity relation If d < d and A < then Condition of earation egengedett ebeégtartoány: accetable (feaible) range of velocity Coal i lighter, teherfore it goe throgh wherea the heavier llock ettle ot. Or target i to ettle ot even the allet article of the heavy llock and, in the ae tie, to revent even the larget article of the lighter fro ettling ot.,aller,larg er d,l arg er d,aller in ax in ax

5 Coal Calclate g Pa diaeter velocity: X d d Tranient region, lot: Y. in in Mllock Calclate llock. llock llock g.80 llock diaeter velocity X llock d,larg er Pa Pa d llock tranient region, lot. Y 6. llock ax llock 5 llock ax llock llock llock llock,aller Pa 0.70 Th, velocity of the leent t be ket in the range of 0.05 / < < 0.70 /. 5

6 b) De to an oeration failre, aller article of both kind ha got to the yte. What i the ini article ize at which the earation can be erfored? If rather all article with diaeter d 0 are reent then the following extree itation ay haen: Mini velocity wa deterined in roble a) by the ettling velocity of the larger article of the lighter aterial (). At a velocity aller than thi ini, article of the lighter aterial are alo ettled ot. Now the qetion i what diaeter article of the heavier aterial (llock) will be ettled ot at the earlier ini velocity. in 0.05 d,llock =? Diaeter i to be coted to known velocity. llock i the ae a earlier Y' llock v ' llock. 07 llock Pa tranient region, lot. X' llock d' llock 0. 5 d' llock 0.5 d,llock llock Th, ettling velocity of llock article of diaeter 0.75 eqal the ettling velocity of the larget article. If ch or aller llock article get in the ihon earator then the earation becoe infeaible. 6

7 Proble Maxi tea velociy, deterined exerientally, i N = 0.5 / at an evaoration roce at noral boiling oint. Cro ection of the vaor channel i, and the rere in the evaorator i 666 Pa. What i the a flow rate of the tea ( vaor) leaving the evaorator? Material data at the given and noral rere: 666 Pa 05 Pa t b [ C] [/ ] [Pa] Water: = = 000 /. Note: Solvent i reoved fro a oltion in an evaoration roce. Solvent vaor i reoved and ore concentrated oltion reain in the veel. Dring the boiling and the eergence of vaor, however, liqid drolet are alo dragged by the vaor flow and carried away. or anwering the qetion given in the roble, we ae that the ratio of drolet of different cale are the ae in the two cae if the drolet ize are eqal. Soltion Data: v N = 0,5 / A = Soltion ath Accetable drolet ize carried over by the vaor are the ae at the two rere. N Plot ' Plot ' d d d' ' ' ' Atoheric (noral) rere Calclate. g Pa 7

8 velocity diaeter Y v N Pa tranient region, lot. X d. 5 d.5 d Th, axi accetable drolet ize i Lower rere irt calclate ' ' ' g 9.8 ' diaeter velocity X' d' ' d tranient region, lot. Y' ' ' ' ' Pa ' ' ' ' ' 0.7 Voletric flow rate V' ' A Ma flow rate ' V' ' h Pa 0.6 Th, the vaor velocity t not exceed 779 /h. At a higher velocity larger drolet wold be carried on. Note: Ma flow rate at atoheric rere i V vn A h 8

9 Proble Sandy ldg i to be ettled in a channel of bae area.5 and deth. = 800 / = 000 / = 0 - Pa a) In cae of flow rate 6 /in, how any tray are to be intalled to ettle ot and article larger than 50? In what region i the ettling roce erfored? b) If the tray are intalled a deterined in roble a/ and then the flow rate i dobled then what will be ini diaeter of the ettled artice? In what region i the ettling roce erfored? Data: A =.5 = 9 H = = 800 / = 000 / = 0 - Pa a) In cae of flow rate 6 /in, how any tray are to be intalled to ettle ot and article larger than 50? In what region i the ettling roce erfored? V = 6 /in = 0. / d = 50 = g 9.8 diaeter velocity: 5 X d d Stoke region, forla. X. Y Pa The needed nber of tray, inclding the botto of the channel: V n A 0. V n.5 5 A 9.50 over the botto of the channel.) Pa (Only tray are needed to be intalled 9

10 b) If the tray are intalled a deterined in roble a/ and then the flow rate i dobled then what will be ini diaeter of the ettled artice? In what region i the ettling roce erfored? The total area i changed: A' na 59 5 The new flow rate: V' V 0. Settling velocity deterined fro the flow rate: V' A' ' 0. V' ' A' 5.0 velocity diaeter, doe not change, it deend on the aterial only ' Y' ' Pa Stoke region, forla. X d' Y' d ' Y' ' d d', Th, and article larger than 67. will be ettled ot. 0