Abstract
The velocity of air that crosses the canopy of tree crops when using orchard sprayers is a variable that affects pesticide dispersion in the environment. Therefore, having an equation to describe air velocity decay through the canopy is of interest. It was necessary to start from a more general non-linear ordinary differential equation (ODE) obtained from the momentum theorem. After approximating the non-linearity with some piecewise linear terms, analytic solutions were found. Subsequently, to obtain a single equation for velocity decay, a combination of these solutions was proposed by using rectangle functions formed through the hyperbolic tangent function. This single equation was assessed in comparison to the experimental value obtained on a vineyard row by measuring the air velocity at exit of canopy. The results have shown good correspondence, with a mean relative error of 6.6%; moreover, there was no significant difference. To simplify, a combination of only two linearized solutions was also proposed. Again, there was no significant difference between the experimental value and the predicted one, but the mean relative error between the two equations was 3.6%.
Highlights
In agrochemical applications on orchards and vineyards, the idea of producing droplets by using nozzles and transporting them to vegetation, by using an air jet generated by a fan, is the generally accepted method
Where vx is the maximum air jet velocity at the centerline (m/s); x is the distance travelled by the air jet from the output (m); xo is the distance, which is normally negative, between the vertex of the diffusion triangle and the output section (m); ro is the radius of the edge of the air outlet from the sprayer; cr (vx ) is an adimensional drag coefficient of the canopy that is dependent on vx ; and ρl (m–1 ) is coincident with the LAD
To compare the maximum velocities of the air jet within the canopy that was predicted by combination (10) (- - -- - -) with the one that was predicted by Equation (6) (- - - - - - -), Figure 4 shows the respective curves of the air velocity decay, vx, vs. the horizontal distance, x, from the outlet of the sprayer
Summary
In agrochemical applications on orchards and vineyards, the idea of producing droplets by using nozzles and transporting them to vegetation, by using an air jet generated by a fan, is the generally accepted method. If the speed is too high, the leaves align with the air stream, and much of the spray is not captured by the vegetation. Spray drift increases with velocity until approximately 50% of the spray does not land on the vegetation [3,4] and, causes both economic loss and environmental pollution. To help understand the experimental results, it is useful to find an equation that relates the air jet velocity vs the distance from the output of the sprayer fan when air passes through the
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