Calculation of water rise in curvilinear capillaries by tangent angle to the meniscus
https://doi.org/10.12737/12598
Abstract
The work objectives are the simulation of the water distribution in the symmetric multilevel capillary systems with curvilinear capillaries, and the calculation of water rise in the curvilinear capillaries by the angle of inclination to the horizontal tangent to the water meniscus in the capillary. For a complete description of the water advance in the curvilinear branches of different levels, the coordinates of the water menisci in those levels about the axes y and x related respectively to the vertical capillary axis and the water surface are determined. Ceteris paribus, the value of water movement in the curvilinear capillaries is always greater than in the straight ones. The results obtained are useful in studying the conductivity of xylem vessels and the promotion of soil moisture in the plant structures which is directly related to the rising and distribution of water in the xylem. It is shown that with increase of the number of levels, the tangent angle to the water menisci in the curvilinear branches is reduced in comparison with the first curvilinear branch. The reduction of this angle indicates that the water in the curvilinear branches is moving the less, the higher the level number is.
About the Authors
Iosif A Kipnis
“KASIOR” Research and Production Company LLC
Russian Federation
Russian Federation
Yury M. Vernigorov
Don State Technical University
Russian Federation
Russian Federation
References
1. Kuznetsov, V.V., Dmitriyeva, G.A. Fiziologiya rasteniy. [Plant Physiology.] 2nd revised and enlarged ed. Moscow: Vysshaya shkola, 2006, 742 p. (in Russian).
2. Taiz, L., Zeiger, E. Plant Physiology, 3rd ed. Sinauer Associates Inc., 2002, 690 p.
3. Rajaei, H., et al. Comparison of root anatomy and xylem vessel structure in rain-fed and supplementary irrigated ―Yaghooti — Syah Shiraz‖ grapevine. Horticulture, Environment, and Biotechnology, 2013, vol. 54, iss. 4, pp. 297-302.
4. Gloser, V., et al. Analysis of anatomical and functional traits of xylem in Humulus lupulus L. stems. Plant, Soil and Environment, 2011, no. 57 (7), pp. 338-343.
5. Scholz, F.-G., et al. Hydraulic capacitance: Biophysics and Functional Significance of Internal Water Sources in Relation to Tree Size. Tee Physiology, 2001, vol. 4, pp. 341–361.
6. Vernigorov, Y.M., Kipnis, I.A. Matematicheskoe modelirovanie raspredeleniya zhidkosti v vetvyashchikhsya kapillyarnykh sistemakh. [Mathematical modeling of liquid distribution in branch capillary systems.] Vestnik of DSTU, 2010, vol. 10, no. 8 (51), pp. 1195 – 1206 (in Russian).
7. Vernigorov Y.M., Kipnis, I.A. Kapillyarnaya model' drevesnykh stvolov. [Capillary model of tree trunks.] Vestnik of DSTU, 2012, no. 6 (67), pp. 24 – 40 (in Russian).
8. Kipnis, I.A., Vernigorov Y.M. Matematicheskaya model' pod''ema vody v prostykh krivolineynykh kapillyarakh. [Water rise mathematical model in simple curvilinear capillaries.] Vestnik of DSTU, 2013, no. 5/6 (74), pp. 110-118 (in Russian).
9. Lee, S.-J., Kim, Y. In vivo visualization of the water-refilling process in xylem vessels using X-ray micro-imaging. Annals of Botany, 2008, vol. 101, pp. 595-602.
10. Bronstein, I.N., Semendyaev, K.A. Spravochnik po matematike dlya inzhenerov i uchashchikhsya vuzov. [Handbook on mathematics for engineers and students of higher educational institutions.] St. Petersburg: Lan', 2009, 608 p. (in Russian).
Review
For citations:
Kipnis I.A., Vernigorov Yu.M. Calculation of water rise in curvilinear capillaries by tangent angle to the meniscus. Vestnik of Don State Technical University. 2015;15(3):89-95. (In Russ.) https://doi.org/10.12737/12598
Views:
535
Email this article 