Clulting Tnk Wetted Are ving time, inresing ur B n Jones, P.., P.E. C lulting wetted re in rtillfilled orizontl or vertil lindril or ellitil tnk n e omlited, deending on fluid eigt nd te se of te eds (ends) of orizontl tnk or te ed (ottom) of vertil tnk. Et equtions re now ville for severl ommonlenountered tnk ses. Tese equtions n e used to mke rid nd urte wettedre lultions. All equtions re rigorous. All re equtions give wetted res in squre units from tnk dimensions in onsistent liner units. All vriles defining tnk ses required for tnk wettedre lultions re defined in te Vriles nd efinitions sider. Grill, Figs. nd sow orizontl lindril tnk rmeters, Figs. 3 nd sow vertil lindril tnk rmeters, nd Fig. 5 sows some orizontl ellitil tnk rmeters. Ellitil orizontl tnks wit emiellisoidl eds nd vertil tnks wit emiellisoidl ottoms re te onl tes of ellitil tnks onsidered. Horizontl Clindril Tnks Wetted re s funtion of fluid eigt n e lulted for orizontl lindril tnk wit eiter onil, emiseroidl, gu, seril, or toriseril eds were te fluid eigt,, is mesured from te tnk ottom to te fluid surfe, see Figs. nd. A gu ed is onil ed of orizontl tnk were te e of te onil ed is level wit te to of te lindril setion of te tnk s sown in Fig.. A toriseril ed is n AMEte (dised) ed defined knuklerdius rmeter, k, nd disrdius rmeter, f, s sown in Fig.. A seroidl ed must e emiseroid; onl emiseroid is vlid no segment of n seroid will work s it will in te se of seril ed were te ed m e seril segment. For seril ed,, were is te rdius of te lindril tnk od. Were onve onil, emiseroidl, gu, seril, or toriseril eds re onsidered, ten L/. Bot eds of orizontl lindril tnk must e identil for te equtions to work; i.e., if one ed is onil, te oter must e onil wit te sme dimensions. However, te equtions n e omined to del wit wettedre lultions of orizontl tnks wit eds of different ses. For instne, if orizontl lindril tnk s onil ed on one end nd seril ed on te oter end, lulte fluid wetted res of two tnks, one wit onil eds nd te oter wit seril eds, nd verge te results to get te desired wetted re. Te eds of orizontl tnk m e flt ( ), onve ( ), or onve ( ). Wetted ed res re te sme for onve or onve eds wit te sme dimensions, so te sme formuls n e used for eiter onve or onve eds. Te following vriles must e witin te rnges stted: for seril eds L/ for onve ends for ll tnks f.5 for toriseril eds k.5 for toriseril eds L ³ Pge of 7
Vriles nd efinitions ider (ee Figs. 5) is te distne orizontl tnk's eds etend eond ( ) or into ( ) its lindril or ellitil od setion or te det te ottom etends elow te lindril or ellitil od setion of vertil tnk. For orizontl tnk wit flt eds or vertil tnk wit flt ottom. is te orizontl semiis of te ellitil ross setion of orizontl ellitil tnk or te mjor semiis of te ellitil ross setion of vertil ellitil tnk. is te vertil semiis of te ellitil ross setion of orizontl ellitil tnk or te minor semiis of te ellitil ross setion of vertil ellitil tnk. C is te wetted rosssetionl lengt of te fluid in orizontl tnk's lindril setion. is te dimeter of te lindril setion of orizontl or vertil tnk. f is te disrdius rmeter for tnks wit toriseril (dised) eds (ends or ottoms); f is te dis rdius. is te eigt of fluid in tnk mesured from te lowest rt of te tnk to te fluid surfe. k is te knuklerdius rmeter for tnks wit toriseril eds (ends or ottoms); k is te knukle rdius. L is te lengt of te lindril setion of orizontl tnk. r is te rdius of seril ed of orizontl tnk or seril ottom of vertil tnk. is te rdius of te lindril setion of orizontl or vertil tnk. is te wetted re, of fluid det, in orizontl or vertil lindril tnk. Pge of 7
Pge 3 of 7 Horizontl Clindril Tnk Equtions Here re te seifi equtions for wetted surfe res of orizontl lindril tnks wit onil, emiseroidl, gu, seril, nd toriseril eds (use rdin ngulr mesure for ll trigonometri funtions, nd / for ll equtions): Conil eds. ) ( os.. ll Hemiseroidl eds. ( ) ( ) ò ò dd. ll seil ses of emiseroidl eds: ) ( os. ln L... ( ) L... os L.... ln L... ( ) L.... os L...
Pge of 7 Gu eds. ò ò ) ( dd.. ll eril eds..... seil ses for seril eds: ) ( os.......... ( ).. ( )... ( ) ( ) ò sin d
Toriseril eds. k G f(s,t) dd ò ò G f(s,t) dd f ò ò L f k... fsin ò os ( k) sin fos f k d...... k( sin) k( sin) seil ses for toriseril eds: L f k ( k) sin k.. L f k ( k) sin k.. were in ll ove equtions: f(s,t) º (t (s )(s t t ) (t s t ) ) G º s t s t ( ) s º k t º k ( ) f os kos f dis ftor f dis rdius k knukle ftor k knukle rdius Pge 5 of 7 k sin (f k) In ll orizontl tnk equtions ove, is te wetted re of fluid in te tnk in squre units onsistent wit te liner units of tnk dimension rmeters, nd C is te rosssetionl wetted lengt of fluid on te lindril od of te tnk in liner units onsistent wit te liner units used for nd. Te eqution for C is given : C os...
Figure. Prmeters for Horizontl Clindril Tnks wit Conil, Hemiseroidl, Gu, or eril Heds. eril ed Clindril Tue Hemiseroidl ed r(sere) Gu ed Conil ed (sere) (emiseroid) (one; gu) L C Wetted rosssetionl lengt CO ECTION OF CYLINICAL TUBE. Bot eds of tnk must e identil. Aove digrm is for definition of rmeters onl.. Clindril tue of dimeter ( ), rdius ( ), nd lengt L (L ³ ). 3. For seril ed of rdius r, r ³ nd.. For onve ed oter tn seril,, for onve ed. 5. L ³ for ³, L ³ for. 6. eroidl ed must e emiseroid. 7.. Pge 6 of 7
Figure. Prmeters for Horizontl Clindril Tnks wit Toriseril Heds. k f kd(sin α) L Horizontl Clindril Tnk Emles Te following emles n e used to verif orret lition of ll equtions. For ll orizontl tnk emles te tnk dimeter is 7 nd te lindril tnk od is long. In ll ses find te wetted surfe,, in ft,given te stted ed te nd dimensions nd te fluid eigt,, in te tnk: Conil ed: 8,.3586 ft 8, 36.3767 ft 8, 8 8.3858 ft Hemiseroidl ed:,.5995 ft, 36 38.785 ft, 8 7.8975 ft 36,.55668 ft 36, 36 5.7965 ft 36, 8 9.36 ft 8,.969 ft 8, 36 63.786 ft 8, 8 6.3379 ft Pge 7 of 7
Gu ed: 8, 9.5 ft 8, 36 9.9833 ft 8, 8 67.67 ft eril ed:, 99.9977 ft, 36 35.888 ft, 8 7.677 ft 36,.55668 ft 36, 36 5.7965 ft 36, 8 9.36 ft Toriseril ed: f, k.6,.8.79 ft f, k.6, 9.99 ft f, k.6, 36 7.7876 ft f, k.6, 8 6.66 ft f, k.6, 69.7 3.788 ft For tis toriseril ed,.93. Wen.8, te ed wetted re is onl in te toroidl setion of e ed, i.e., k(sin α). f.9, k., 3 6.8339 ft f.9, k., 96.857 ft f.9, k., 36 3.8 ft f.9, k., 8 6.737 ft f.9, k., 69 33.6365 ft For tis toriseril ed,.969. Wen 3, te ed wetted re is onl in te toroidl setion of e ed, i.e., k(sin α). Pge 8 of 7
Vertil Clindril Tnks Wetted surfe re in vertil lindril tnk wit eiter onil, emiseroidl, seril, or toriseril ottom n e lulted, were te fluid eigt,, is mesured from te enter of te ottom of te tnk to te surfe of te fluid in te tnk. ee Figs. 3 nd for tnk onfigurtions nd dimension rmeters, wi re lso defined in te Vriles nd efinitions sider. A toriseril ottom is n AMEte ottom defined knuklerdius ftor nd disrdius ftor s sown grill in Fig.. Te knukle rdius will ten e k nd te dis rdius will e f. A seroidl ottom must e emiseroid. To find te wetted re of onve ottom vertil tnk, te equtions for onve ottom vertil tnk n e used wit te following formul: (onve) totl ottom re totl ottom re ottom re for...... ³ Te following rmeter rnges must e oserved: ³ for ll vertil tnks, for seril ottom f.5 for toriseril ottom k.5 for toriseril ottom Vertil Clindril Tnk Equtions Here re te seifi equtions for wetted surfe res in vertil lindril tnks wit onil, seroidl, seril, nd toriseril ottoms. Use rdin ngulr mesure for ll trigonometri funtions; nd for ll equtions: Conil ottom.... ( )... Pge 9 of 7
Pge of 7 Hemiseroidl ottom......... ( )... sin os ) ( ) ( ) (...... ( ) ( ) ( )... ln ) ( ) ( ) ( ( ) os... ³ ) (...... ³... ) ( ln
eril ottom. ( ) ( )...... Toriseril ottom. f... f k ( k) sin sin... k k f k ( k)sin ³ k ( f k) ( )... k sin f ( os ) k os f dis ftor f dis rdius k knukle ftor k knukle rdius Pge of 7
Figure 3. Prmeters for Vertil Clindril Tnks wit Conil, Hemiseroidl, or eril Bottoms. seril ottom emiseroidl ottom Conil ottom Figure. Prmeters for Vertil Clindril Tnks wit Toriseril Bottoms. f k Pge of 7
Vertil Clindril Tnk Emles Te following emles n e used to verif orret lition of ll equtions. For ll emles, te tnk dimeter is 7 nd te ottoms re onve or onve, s noted. In ll ses find te wetted surfe,, in ft, given te stted ed te nd dimensions nd te fluid eigt,, in te tnk: Conve Bottom (ft ) Conve Bottom (ft ) Conil ed: 36, 36 39.98595 96.536 8,.7897 73.3 8, 36 6.579.773 8, 8 7.389.5 8, 6 65.9735.3767 8, 7 8.83 6.3 Hemiseroidl ed:,.76 38.6393,.537 8.998, 8 8.998 9.89859 36, 8 8.733 56.5867 36, 36 56.5867 3.973 36, 6 9.778 5.7965 8, 3.6693 7.6996 8, 8 69.678.8653 8, 7 7.669 8.56 eril ed:,.35 39.699,.87 78.5398, 8 78.5398 6.3893 36, 8 8.733 56.5867 36, 36 56.5867 3.973 36, 6 9.778 5.7965 Toriseril ed: f, k.6, 6.839 6.399 f, k.6, 6 8.8956 3.75 f, k.6, 33.988 5.7638 f, k.6,.93 33.598 5.656 f, k.6, 36.93 7. 9.3573 For tis toriseril ed,.93, nd wen, te ed wetted re is onl in te seril rt of te onve ed nd onl in te torioidl rt of te onve ed. f.9, k., 6 6.966.8 f.9, k., 8.697 8.9893 f.9, k., 3.8983 6.5835 f.9, k.,.969 35.98 59.7 f.9, k., 38.969 73.67936 97.83 For tis toriseril ed,.969, nd wen 6, te ed wetted re is onl in te seril rt of te onve ed nd onl in te toroidl rt of te onve ed. Pge 3 of 7
Horizontl Ellitil Tnks wit Hemiellisoidl Heds A orizontl ellitil tnk is tnk wit orizontl od wi s n ellitil rosssetion. Te onl se onsidered is one wit emiellisoidl eds (wi inludes flt eds if ). Figure 5 sows te onl onfigurtions onsidered for orizontl ellitil tnks te ellitil es re rllel or erendiulr to level ground. Te orizontl is s lengt nd te vertil is s lengt. For onve ed L/. Te wetted surfe res of onve nd onve orizontl ellitil tnks re identil, oter rmeters eing te sme. Figure 5. Prmeters for Horizontl Ellitil Tnks. Pge of 7
Pge 5 of 7 Horizontl Ellitil Tnk Equtions Te wetted surfe re of orizontl ellitil tnk wit emiellisoidl eds wit nd is given :...... H B H B were: ( ) ( )... ) ( os... L L H H B B B ³ º º º º ò ò ò ò... dd d... d Horizontl Ellitil Tnk Emles Te following emles will verif orret lition of te equtions for wetted surfe res,, of orizontl ellitil tnks wit emiellisoidl eds. All tnk dimensions re in ines, te wetted surfe res re in ft, nd te ellitil od lengt for e emle is ines. ft ft (flt ed) 36 68.6583 6.6698 3.7687 98.7675 36 38.97 3.6837 36 3.8538.6956 36 3.7687 98.7675 6 63.687 5.65787 36 85.636 6.6698 9.93 98.7675 36 73.89 3.6837 36 53.5.6956 36 9.93 98.7675 6 5.6 5.65787
Pge 6 of 7 Vertil Ellitil Tnks wit Hemiellisoidl Bottoms A vertil ellitil tnk is tnk wit vertil od wi s n ellitil rosssetion. Te onl se onsidered is one wit emiellisoidl ottom (wi inludes flt ottom if ). If te mjor semiis of te ellitil rosssetion is, ten te minor semiis is nd vie vers. Onl onve ottoms n e lulted wit te equtions, onve ottoms n e ndled using te sme tenique desried in te setion on vertil lindril tnks. For ll vertil tnks. Vertil Ellitil Tnk Equtions Te wetted surfe re of vertil ellitil tnk wit emiellisoidl ottom is given : ( ) ò ò,,...,,...,,... d d were: ( ) ( ) ( ) ( ) dd dd ò ò ò ò º º Vertil Ellitil Tnk Emles Te following emles of vertil ellitil tnks wit emiellisoidl ottoms will serve to verif orret lition of te equtions. Liner dimensions in ines, res in ft : ft ft (flt ottom) ft (onve ottom) 8 3 7.68779 9.8888 9.567 8.9388 36.979 6.33 6 7.568 86.63 95.8365
n Jones is retired senior roess emist from tokusen Louisin, LLC, Grville, LA. Contt im t rjones@ellsout.net or (5)76565. EJ //7 File: TANKAEA.OC Pge 7 of 7