Mathematical Models and the Soil Hydraulic Properties

Transcription

1 Bullei UASVM Hoiculue 66/9 Pi ISSN ; Elecoic ISSN Maeaical Model ad e Soil Hydaulic Popeie Floica MATEI Macel IRJA Ioaa POP Vioel BUIU Maia MICULA Faculy of Hoiculue Uiveiy of Agiculual Sciece ad Veeiay Medicie Cluj- Napoca Calea Maau Roaia; faldea@uavcluj.o Abac: Soil ydaulic popeie decibe e wae ad e ceical apo pocee i e oil. May aeaical odel ave bee exeively ued o decibe ee pocee Gade 958 va Geuce 98 Wag e al. 4. I i oe we aalye oil ydaulic popeie uig diffee aeaical odel. Baed o eauee ad uig fiig ecique we deeie e expeio of e ydaulic coduciviy ad wae diffuiviy uiable fo ou daa. Te oil wae diffuiviy i ipoa i ode o obai e aalyical oluio of e Ricad equaio wic ow e oil wae coe diibuio i pace. Alo we deeie e oil wae coe fo e Ricad equaio i diffuiviy fo fo e coa coefficie. ey wod: diffuio equaio ydaulic coduciviy wae diffuiviy Guplo INTROUCTION Maeaical odel ave bee ued i cieific eeac o pedic ad odel diffee peoea. We focu o e wae flow i uauaed oil. acy ad lae Buckiga ad obaied epiically equaio a odel e wae flow i oil. Te liiaio of e acy-buckiga equaio i due o e aupio a wae coe doe o cagig i ie. ue o i liiaio ee odel i o ofe applicable. To cage i iuaio ave bee ued e acy-buckiga equaio o decibe e flux deiy ad e coiuiy equaio o decibe e ae of fillig o epyig wi wae of e oil poe. Cobie ee equaio Ricad ad obaied a equaio applicable i uauaed oil: δ δ δ δ wee epee ydaulic coduciviy e peue ead ad e oil wae coe. Equaio i oliea ad o eay o olve. I ad bee ade effo i ode o wie equaio i a fo of diffuio equaio fo wic e oluio ae kow i oe cae ivolvig bouday ad iiial codiio applicable o oil wae flow poce. Equaio afoed o equaio 7 i applicable oly o uauaed flow. I e oe cae equaio ca be wie i capaciy fo a i applicable o auaed ad uauaed flow bu i oe difficul o olve. MATERIALS AN METHOS Te fi ai i o udy e oil ydaulic coduciviy ad wae diffuiviy baed o wae flow expeie i uauaed oil. Tee ae ay aalyical fucio exeively udied i ode o obai e eioed popeie of oil Gade 958 Hiellel 76

2 77 acaoki e al I wa i follow we coide e va Geuce aalyical fucio popoed i i udy fo elaio bewee oil wae coe ad peue ead. wee ae udeeied paaee > ad ad deoe eidual ad auaed oil wae coe. I e pape of va Geuce va Geuce 98 baed o Muale elaio fo pedicig e elaive ydaulic coduciviy e obaied [ ].5 3 wee i e ydaulic coduciviy a auaio. Fo ad 3 e obaied ydaulic coduciviy a a fucio of peue ead [ ] ] [ ] [ 4 Te elaio fo e oil wae diffuiviy i d d 5 eplacig ad 4 i 5 eul. 6 Te ecod ai of ou udy i o olve e Ricad equaio i diffuiviy fo 7 we ad ae coa. To fid ee coa we coide e aupio of Sivaava Sivaava e al. 99. Replacig e e i elaio 5 equaio 7 becoe k 8 wee S S k 9 We coide e followig bouday ad iiial codiio: > i Uig e eoy of e paial diffeeial equaio Cak 976 we bouday codiio a ad e iiial codiio e oluio of equaio 7 a e fo: k efc k k efc exp wee. d e x efc x π

3 RESULTS AN ISCUTIONS Uig e eoeical coideaio fo peviou ecio ad eauee obaied i field uig a iaaeou pofile eod we fid e be fi paaee fo e fucio popoed i peviou ecio. We ue a oliea fiig pocedue baed o Leveveg-Maquad algoi ipleeed i Guplo ofwae. Te elaio bewee oil wae coe ad ydaulic coduciviy baed o aalyical fucio ad 4 ae illuaed i e ex figue; alo e be fiig paaee ae give. Fig.. Volueic wae coe veu peue ead Tea fucio i give by va Geuce ad Tea i give by fucio 3 Aalyig e eul fo Guplo ofwae we ca obeve a e be fiig fucio i give by e fucio A γ C A 3 π γ C a iead of va Geuce fucio Tea i above figue. Te pyical eaig of paaee ivolved i e above elaio ae: A e offe value fo A aea of Caucy diibuio ad a abcia of e cee of a. We coclude a Caucy diibuio i oe appopiae fo daa baed o e aalyi of e fial u of quae of eidual a i.6758 fo Caucy diibuio ad.459 fo Va va Geuce fucio. Te be value fo fiig paaee ae Tab. Be fiig paaee fo oil wae coe veu peue ead Va Geuce Caucy diibuio Fial e of paaee Aypoic Sd Eo Fial e of paaee Aypoic Sd Eo A ± % A.987 ± % A.9897 ± % A ± % c.838 ± % a ± %.47 ± % γ C ±.4 4.8% ± % Uig e be fiig paaee ad elaio 3 we ave: 78

4 Fig.. Hydaulic coduciviy veu Nex figue ow e elaio bewee ydaulic coduciviy ad peue ead uig eaued value ad fucio gave by 3 wi be fiig paaee obaied uig Guplo fiig faciliie. Fig. 3. Hydaulic coduciviy veu peue ead uig fucio 4 Be fiig paaee fo ydaulic coduciviy veu peue ead Tab. Va Geuce aalyical fucio Fial e of paaee Aypoic Sd. Eo.9/ % 3.759/ % Uig e elaio 5 ad e above paaee eiaio we obai e ex figue Fig. 4. Vaiaio of wae diffuiviy veu 79

5 Nex we give e oluio fo poble defied by 7 ad we podig o e uface. Te calculaed value fo 6 5 ad k ae k Te oluio of e poble i i k k k efc efc i exp 4 Figue 5 ow e vaiaio of wae coe wi a fou diffee oe of ie. Fig. 5 Gapical epeeaio of e oluio of 7 ad a diffee oe of ie CONCLUSION Tee ae ay aaliycal expeio fo udy e oil ydological paaee. Evey ie we oeoe udy e wae flow i oil u cooe e o uiable aalyical expeio fo ivolved eauee. A we ca obeve fo Figue we ade oe cage fo fucio i ode o obai e be fiig paaee fo ou daa. If we aiai e bouday codiio e oluio of iiial bouday poble goe o effecive oil wae coe Figue 5. Ackowledge. Ti udy a bee fiaced by e UEFISCSU pojec ype PNII- IEI pojec. 43/7. REFERENCES. Cak J Te aeaic of iffuio Oxfod Uiv. Pe.. Gade W. R Soe eady ae oluio of e uauaed oiue flow equaio wi applicaio o evapoapiaio fo a wae able Soil Sci. vol. 85 pp Hiellel.. Ioducio o evioeal oil pyic Acadeic Pe. 4. Si B. R.G. acaoki Z.F. Zag G.W. Paki ad.e. Elick 999. Meauee of ydaulic popeie duig coa flux ifilaio: Field aveage. Soil Sci. Soc. A. J. 63: uilek M.. Niele 994. Soil Hydology Caea Velag. 6. Sivaava R. T. C. Ji Ye 99. Wae Reou. Re. Vol 7 pp Geuce Va M. T 98 A cloed fo equaio fo pedicig coduciviy of uauaed oil Soil Sciece Soc. Of Aeica Joual vol Wag Q. M. Sao R. Hoo 4. A iple eod fo eiaig wae diffuuviy of uauaed oil Soil Sciece Soc. of Aeica Joual vol. 68 pp