Skip to main content
Log in

Quantum mechanics applied to the dynamic assessment of a cluster of water particles in sprinkler irrigation

  • Published:
Journal of Engineering Thermophysics Aims and scope

Abstract

The problem of liquid droplets crossing a gas is common to many scientific and technical issues and, in particular, also to sprinkler irrigation; thus, when designing a sprinkler irrigation system, it is essential to fully understand how droplets mechanically behave during their flight and how a mathematical modeling can cope with all the variables affecting one another during such a complicate thermal fluid dynamic process. In the thematic scientific literature, the classic approach has been recently challenged by an alternative quantum one, provided in two different formulations referring to a single droplet dynamics: one focusing on a full description of the process (time-dependent Schrödinger equation); the other focusing on the discovery of an easier-to-use method (scale relativity theory); both allowing for a broader microscopical insight of the actual mechanics of single water droplets in sprinkler irrigation. The present contribution is aimed at developing the quantum procedure extending it to a cluster of water particles, as one droplet during its aerial flight conditions the others, which are in its vicinity and vice versa.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Al-Rashid, S.N., Habeeb, M.A., and Amed, K.A., Application of the Scale Relativity (ScR) Theory to the Problem of a Particle in a Finite One-Dimensional Square Well (FODSW) Potential, J. Quantum Inf. Sci., 2011, vol. 1, pp. 7–17.

    Article  Google Scholar 

  2. Bird, R.B., Steward, W.E., and Lighfoot, E.N., Transport Phenomena, New York: Wiley, 1960.

    Google Scholar 

  3. Bird, S.L., Perry, S.G., Ray, S.L., and Teske, M.E., Evaluation of the AGDISP Aerial Spray Algorithms in the AgDRIFT Model, Env. Tox. Chem., 2002, vol. 21, no. 3, pp. 672–681.

    Article  Google Scholar 

  4. Bohm, D., A Suggested Interpretation of the Quantum Theory in Terms of “Hidden Variables,” pt. 1, Phys. Rev., 1952A, vol. 85, no. 2, pp. 166–179.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Bohm, D., A Suggested Interpretation of the Quantum Theory in Terms of “Hidden Variables,” pt. 2, Phys. Rev., 1952b, vol. 85, no. 2, pp. 180–193.

    Article  MathSciNet  ADS  Google Scholar 

  6. De Wrachien, D. and Lorenzini, G., Modelling Jet Flow and Losses in Sprinkler Irrigation: Overview and Perspective of a New Approach, Biosyst. Eng., 2006, vol. 94, no. 2, pp. 297–309.

    Article  Google Scholar 

  7. De Wrachien, D., Lorenzini, G., and Mambretti, S., Water Droplet Trajectories in an Irrigation Spray: The Classical and Quantum Mechanical Pictures, 40th Int. Symp. on Agricultural Engineering, Opatija, Croatia, 2012, pp. 85–96.

  8. Dirac, P.A., Quantized Singularities in the Electromagnetic Field, Proc. Royal Soc., 1931, vol. A133, pp. 1–60.

    Google Scholar 

  9. Edling, R.J., Kinetic Energy, Evaporation and Wind Drift of Droplets from Low Pressure Irrigation Nozzles, Trans. ASAE, 1985, vol. 28, no. 5, pp. 1543–1550.

    Google Scholar 

  10. Hermann, R.P., Numerical Simulation of a Quantum Particle in a Box, J. Phys., 1: Math. General, 1997, vol. 30, no. 11, pp. 3967–3975.

    Article  MathSciNet  MATH  Google Scholar 

  11. Hewitt, A.J., Johnson, D.A., Fish, J.D., Hermansky, C.G., and Valcore, D.L., Development of Spray Drift Task Force Database for Aerial Applications, Env. Tox. Chem., 2002, vol. 21, no. 3, pp. 648–658.

    Article  Google Scholar 

  12. Holland, P., Quantum Field Dynamics from Trajectories, in Quantum Trajectories, Chattaraj, Ed., CRC Press, 2011, pp. 73–86.

  13. Ghosh, S.K., Quantum Fluid Dynamics within the Framework of Density Functional Theory, in Quantum Trajectories, Chattaraj, Ed., CRC Press, 2011, pp. 183–195.

  14. Goldstein, S., Tumulka, R., and Zanghi, N., Bohmian Trajectories as the Foundation of Quantum Mechanics, in Quantum Trajectories, Chattaraj, Ed., CRC Press, 2011, pp. 1–15.

  15. Keller, J. and Bliesner, R.D., Sprinkler and Trickle Irrigation, New York: Van Nostrand Reinhold, 1990.

    Google Scholar 

  16. Kendrick, B.K., Direct Numerical Solution of the Quantum Hydrodynamic Equation of Motion, in Quantum Trajectories, Chattaraj, Ed., CRC Press, 2011, pp. 325–344.

  17. Kincaid, D.C. and Longley, T.S., A Water Droplet Evaporation and Temperature Model, Trans. ASAE, 1989, vol. 32, no. 2, pp. 457–463.

    Google Scholar 

  18. Kinzer, G.D. and Gunn, R., The Evaporation, Temperature and Thermal Relaxation Time of Freely Falling Water Drops, J. Meteor., 1951, vol. 8, no. 2, pp. 71–83.

    Article  Google Scholar 

  19. Lopreore, C.L. and Wyatt, R.E., Quantum Wave Packet Dynamics with Trajectories, Phys. Rev. Lett., 1999, vol. 82, pp. 5190–5193.

    Article  ADS  Google Scholar 

  20. Lorenzini, G., Air Temperature Effect on Spray Evaporation in Sprinkler Irrigation, Irrig. Drai., 2002, vol. 51, no. 4, pp. 301–309.

    Article  Google Scholar 

  21. Lorenzini, G., Simplified Modelling of Sprinkler Droplet Dynamics, Biosyst. Eng., 2004, vol. 87, no. 1, pp. 1–11.

    Article  Google Scholar 

  22. Lorenzini, G.,Water Droplet Dynamics and Evaporation in an Irrigation Spray, Trans. Asabe, 2006, vol. 49, no. 2, pp. 545–549.

  23. Lorenzini, G., Conti, A., and De Wrachien, D., Computational Fluid Dynamics (CFD) Picture of Water Droplet Evaporation in Air, Irrig. Drai. Syst. Eng., 2012, vol. 1, no. 1, pp. 1–12.

    Google Scholar 

  24. Madelung, E., Eine Anschauliche Deutung der Gleichung von Schrödinger, Naturwissenschaften, 1926, vol. 14, no. 45, pp. 1004–1004.

    Article  ADS  Google Scholar 

  25. Nottale, L., The Theory of Scale Relativity, Int. J. Modern Phys., 1992, vol. 7, no. 20, pp. 4899–4935.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Teske, M.E., Hermansky, C.G., and Riley, C.M., Evaporation Rates of Agricultural Spray Material at Low Relative Wind Speeds, Atomizat. Spray, 1998a, vol. 8, pp. 471–478.

    Google Scholar 

  27. Teske, M.E., Thistle, H.W., and Eav, B., New Ways to Predict Aerial Spray Deposition and Drift, J. Forestry, 1998b, vol. 96, no. 6, pp. 25–31.

    Google Scholar 

  28. Teske, M.E. and Ice, G.G., A One-Dimensional Model for Aerial Spray Assessment in Forest Streams, J. Forestry, 2002, vol. 100, no. 3, pp. 40–45.

    Google Scholar 

  29. Thompson. A.L., Gilley, J.R, and Norman, J.M., A Sprinkler Water Droplet Evaporation and Plant Canopy Model, pt. 2, Model Applications, Trans. ASAE, vol. 36, no. 3, pp. 743–750.

  30. Wyatt, R.E., Quantum Dynamics with Trajectories, Introduction to Quantum Dynamics, Springer, 2005.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Lorenzini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Wrachien, D., Lorenzini, G. Quantum mechanics applied to the dynamic assessment of a cluster of water particles in sprinkler irrigation. J. Engin. Thermophys. 21, 193–197 (2012). https://doi.org/10.1134/S1810232812030046

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1810232812030046

Keywords

Navigation