Mathematical Method for Droplet Size Distribution of Agricultural Nozzles

Kurt Tomantschger, Dragan V. Petrović, Rade L. Radojević, Vjekoslav Tadić*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


One of the technical factors from agricultural nozzles and overall plant protection is droplet diameter, which exclusively depends on working pressure, ISO number and nozzle type. Therefore, this paper was aimed to describe mathematical model for droplet size distribution. Through field exploitation experiment, data was used from three ISO numbers of nozzles (hollow cone 80 015; 02 and 03), two air-assisted sprayers (axial and radial fan) and two permanent crops (vineyard and an apple orchard). Water sensitive papers were used for evaluation of droplet diameters, and digital image analysis with Image J software was used for data processing. Mathematical model through homogenous diffusion equation and simplified differential equation shows that droplet size distribution had exponential function of modelling. Theoretical mathematical model was confirmed in experimental results, where coefficient of determination of exponential regression model for 80 015 nozzles was 0.93 with 5.15 of RMSE. The same coefficient for 80 02 nozzles was 0.96 with 2.88 of RMSE and for 80 03 nozzle R 2 was 0.93 with 3.25 of RMSE. In addition, it is proved that droplet diameter depends on operating pressure with very high negative correlation (80 03 nozzles: r = −0.98; 80 02 nozzles: r = −0.97; 80 015 nozzles: r = −0.95). This data will help future researchers in their papers to facilitate and describe similar models for plat protection processes, and all agricultural producers to determine optimal operating pressure which is immensely important in economic, biologic, technical and ecologic aspect.

Original languageEnglish
Pages (from-to)1749-1754
Number of pages6
JournalTehnicki Vjesnik - Technical Gazette
Issue number5
Publication statusPublished - 2021


  • Agricultural nozzles
  • Diffusion equations, droplet size distribution
  • Partial differential equation
  • Plant protection

ASJC Scopus subject areas

  • Engineering(all)

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