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WATER RISE MATHEMATICAL MODEL IN SIMPLE CURVILINEAR CAPILLARIES

https://doi.org/10.12737/1288

Abstract

Side shoots and plant branches unlike trunks are often not rectilinear — they can be compared with various mathematical curves. Xylem of such branches copies their curvilinearity. It motivates the spatial curvature of the chains of its tracheids and vessels. A mathematical model of water lifting and distribution caused by the surface tension forces in the symmetrical curved capillary branches of various configurations is considered. The process analysis shows that with the expansion in number of branches, water advancing in the curvilinear capillary system increases. Water volume rising in the side curvilinear capillary branches, other factors being equal, is greater than in rectilinear ones. It is found that the total water rise height in the vertical (rectilinear) capillary — if there are side curvilinear capillaries — increases, and it does not depend on the type of the function that describes the curvature of the lateral curvilinear capillaries.

About the Authors

Iosif Anshelevich Kipnis
“KASIOR” Research and Production Company (“NPF KASIOR” LLC). Russia
Russian Federation


Yury Mikhailovich Vernigorov
Don State Technical University. Russia
Russian Federation


References

1. Vernigorov, Y. M., Kipnis, I. A. Matematicheskoye modelirovaniye raspredeleniya zhidkosti v vetvyashchikhsya kapillyarnykh sistemakh. [Mathematical modeling of liquid distribution in branch capillary systems.] Vestnik of Don State Technical University, 2010, vol. 10, no. 8 (51), pp. 1195–1206 (in Russian).

2. Vernigorov, Y. M., Kipnis, I. A. Kapillyarnaya model drevesnykh stvolov. [Capillary model of tree trunks.] Vestnik of Don State Technical University, 2012, no. 6 (67), pp. 24–40 (in Russian).

3. Lotova, L. I. Botanika. Morfologiya i anatomiya vysshikh rasteniy. [Botany. Morphology and anatomy of higher plants.] Moscow : Librokom, 2010, 512 p. (in Russian).

4. Timonin, A. K. Botanika. Vysshiye rasteniya. [Botany. Higher plants.] Moscow : Akademiya, 2007, vol. 3, 349 p. (in Russian).


Review

For citations:


Kipnis I.A., Vernigorov Yu.M. WATER RISE MATHEMATICAL MODEL IN SIMPLE CURVILINEAR CAPILLARIES. Vestnik of Don State Technical University. 2013;13(5-6):110-119. (In Russ.) https://doi.org/10.12737/1288

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