Edulean. Bacelona, Spain. June n Expeiment in flow of fluids in unsteady state, with contol Lucila Méndez Chávez, ntonio Valiente Badeas Facultad de Química, UNM. C.U. México.F. bstact he authos ae pofessos of Chemical Engineeing in the Faculty of Chemisty at the Univesidad Nacional utónoma de México (UNM) and they wok in the so called Laboatoy of Unit Opeations. In this laboatoy the students of the Chemical Engineeing take pactical couses in which they apply what they have lean in the theoetical couses. he expeimental teaching is vey impotant in the significant leaning of the students of engineeing. It foments the inteactivity and the paticipation of the students, popitiating that they acquie knowledge, dexteities, habits and attitudes. In this wok an expeiment of flow of fluids is pesented by means of which the students could acquie the significant leaning when facing a classic expeiment. mong the pactical execises with appaatus and equipments, the authos ae inteested in the field of unsteady state in fluid flow. his kind of flow is pesent, fo example in the dischage of tanks. In this aticle they pesent expeiments that the students pefom and which can be contolled automatically and elated to the theoetical models. Passwod: Expeimentation., Unsteady state, Flow of fluids. Contol
Flow of fluids in tansient state. he flow of fluid at the tansient state can be found in the phenomenon of the unloading of tanks. We can take fo example, a tank like the one that appeas next, which has an oifice in its pat infeio by which the wate escapes. nothe expeiment moe complicated is the unloading of a tank that has a pipe in its base. Unloading of a tank that has a pipe in its base. he system that is analyzed is the following one: he tank unloads the liquid to the atmosphee. Fo this case the matte balance would give: u d Equation (6) d o Being u the speed of the wate coming out of the pipe, the coss-sectional aea of the tank and o the coss-sectional aea of the unloading pipe. he enegy balance would be fo this case the following one, consideing that thee is potential enegy, kinetic, of pesent pessue and fiction: u g P M F Making the simplifications petinent we have left that: u u Le g f (5) Whee u is the aveage speed in the unloading pipe, Le is the equivalent length of the unloading, is the diamete of the unloading pipe and f is acy facto. Making adjustments we will have: u f Le g (6)
Of whee: u g (7) Being Le f (8) Uniting (6) with (7) u o d d g (9) Of whee: d d () o g d d () g o hat upon integation gives us: f d d g () i o o i f (3) g In a system simila to the following one, expeiments of unloading of tanks took place. In a laboatoy expeiment it was let the wate escape of a tank connected to a pipe obtaining the following data: able eight total Z in ime θ in seconds otal height Z in ime θ in seconds cm. cm. 73 35 46.7 7 7 33 54. 69 4.57 3 6.3 67 9 7.8 65 9.7 7 8 63 36.9 5 88.8 6 44.7 3 97.4 59 5 8
altua total en m 57 6 9 7. 55 67.7 7 7.6 53 75.3 5 37.7 5 83 49 9.8 47 99.3 45 6.6 43 4 4.3 39 3.5 37 38.6 3.5.5.5 descaga del tanque y =.739e -.x R =.9998 5 5 5 tiempo en segundos In the shown case, the length of staight tube is of 3, 7 m; the equivalent length of the accessoies is of 4, 6 L m. he diamete of the pipe is of,93 cm. eason why = = f =.7. he aea of the tank is of,55 m and the coss-sectional aea of the pipe is of 3,439 xs -4 m. heefoe the equation is fo ou equal case a: 4( Z Z ) (8) pplying the pevious equation to the height data it is obtained that: Real time in sec. Z m able Incement of time otal Calculated time in sec..73 7.7 7.58678 7.58678 4.57.69 7.54646 5.6597.67 7.5745873.6395484 9.7.65 7.6944 3.44897 36.7.63 7.636863 37.874758 44.7.6 7.6675953 45.5349353 5.59 7.696776 53.53 6.57 7.79973 6.9454 67.7.55 7.75478 68.69535 75.3.53 7.784676 76.4755
83.5 7.885 84.867834 9.8.49 7.844648 9.9477 99.3.47 7.874388.37 6.6.45 7.9596757 7.9939 4.43 7.93833 5.84754.3.4 7.97389 3.8858 3.5.39 8.4895 3.8764 38.6.37 8.377439 39.8658 46.7.35 8.7736 47.9339 54..33 8.659 56.3839 6.3.3 8.4774 64.7949 7.8.9 8.763379 7.355746 8.7 8.36 8.567866 88.8.5 8.4837749 88.8644 97.4.3 8.8594 97.363 8. 8.33569 5.4379 7..9 8.369989 3.78389 7.6.7 8.398368.88 Which agees athe well with the expeimental data. he discepancy in the last data must be due to the eddy appeaance that altes the flow of fluid. But what would happen if we use a cylindical tank, in a hoizontal position as the one pesented in the following figue? l L=3m =m 79 cm. 7 cm. =.5 B Figua 3 Pefoming an expeiment in the above tank we found the following data: able 3 Lites ime in seconds eight in cm. 64 38 58.5
3 75 53.5 4 6 49. 5 58 45 6 95 4.3 7 34 37.7 8 7 34.5 9 39 3. 347 7.9 389 4.5 47. 3 468 7.4 4 56 3.6 5 556 6 596 6.3 7 64.7 8 685 98.8 9 77 94.6 77 9. 86 84.3 he above data wee teated to give the following table: θ / θ ime in seconds / θ 38 5.5.447 38.447 37 5.35 75.35 4 4.3.48 6.48 4 4.. 58. 37 3.7. 95. 39 3.6.93 34.93 37 3..864 7.864 38 3.3.868 39.868
38 3.3.868 347.868 4 3.4.89 389.89 38 3.4.894 47.894 4 3.7.9 468.9 48 3.8.79 56.79 4 3.6.9 556.9 4 3.7.95 596.95 44 3.6.88 64.88 45 3.9.866 685.866 4 4.. 77. 44 4.5. 77. 45 5.8.8 86.8 nd also to give the following table: able 5 Flow /time ime in seconds Flowl /time.63 38.63.7 75.7.43 6.43.38 58.38.7 95.7.54 34.54.7 7.7.63 39.63.63 347.63.38 389.38.63 47.63.43 468.43
incementos caudal.8 56.8.5 556.5.5 596.5.7 64.7. 685..38 77.38.7 77.7. 86. Fom the above tables we constucted the following gaphics: Gáfico 3. caudal /tiempo 3.5.5.5 4 6 8 tiempo caudal /tiempo Gafico 5 / θ.6.4...8.6.4. 4 6 8 tiempo en segundos / θ
altua en cm. Gáfico 4 descaga del tanque 5 altua en cm 5 4 6 8 tiempo en segundos ow to intepet these data? L l B In this case the enegy balance would give an equation like numbe 4 u B g f Le nd the mateial balance would give: C = d Bu B d (9), if we make equal to 4 we would obtain:
Le f g d d B () But in this case the aea vaies with the height.since: L l l is the cod and L is the length of the cylinde. Figue 5 d l () d = height of liquid above the tank diamete (7) hus uniting with 5 6 and 7 then: Le f g d d L B () nd : d B d g Le f L (3) Which is not easy to integate. oweve, equation (3) can be set as: (4) l d
L (5) B f Le g = Note that to find the download time we must integate fom + wich is the oiginal a until the a final wich is just. heefoe to obtain patial dischage times we have to integate (numeically) fom the factions of the oiginal height ( +). In the case at hand: System equivalent length Le = 9.6 m iamete of dischage pipe.5 inches, Cd 4 =.489 m. he pipe oughness.5 Fiction facto at full tubulence f.3 ank length L = 3m ischage pipe aea B =.35 m. heefoe = 57 nd the equation () fo ou system is: 57 (6) With the above equation can be calculated the incements of time, depending on the height. abla 6 eight in cm. Real time Incement of Incement of time 64 Calculated time 58.5 38 -.55 4.56483 4.56 53.5 75 -.5 43.39963 85.8947583 49. 6 -.43 4.838 6.996 45 58 -.4 4.58754 67.6587 4.3 95 -.37 38.434457 5.75937 37.7 34 -.36 38.33733 44.859 34.5 7 -.3 34.9733 78.99974 3. 39 -.33 36.798687 35.79593 7.9 347 -.33 37.894 35.9953
iempo en segundos 4.5 389 -.34 38.86483 39.85993. 47 -.34 39.5766 43.57 7.4 468 -.37 4.736497 473.743 3.6 56 -.38 43.7877 57.53447 556 -.36 4.53 558.63597 6.3 596 -.37 4.5864 6..7 64 -.36 39.4787639 639.7876 98.8 685 -.39 4.7956 68.987 94.6 77 -.4 4.969788 7.8555 9. 77 -.45 4.9689 763.87979 84.3 86 -.58 43.897489 87.64778 escaga del tanque 8 6 4 tiempo eal tiempo calculado 7 9 3 5 7 ltua en cm. hose expeiments could be contolled and monitoed by means of new contol devises povided by the company Emeson. Conclusions o esults he expeiments wee pefomed with simple equipment that could be monitoed by means of contol devises as level and flow contol, povided by a company. he data wee plotted in a compute. fte these, the students had to pedict the behavio obseved in the expeiments by means of thei knowledge in flow of fluids. hey developed the appopiated equations fo each case, and late compaed the pedicted with the expeimental data. hey found a vey good ageement. Between the theoy and the expeiments.
Bibliogaphy. - Bid, Stewat y Lightfoot- anspot Phenomena- second edition, Wiley -7 Chapte 7 Peg. 97.. - M. enn "Pocess Fluid Mechanics"- Pentice all 98, Chapte 5 page 79. 3.- Valiente Badeas ntonio- Poblemas de flujo de fluidos- Limusa- México -998.