Question

A field sprayer with 12 nozzles fitted to the boom at a spacing of 0.5 m is used for spraying at a height of 0.75 m from the ground. The angle of spraying is \(75^\circ\). If the height of spraying is reduced to 0.6 m, the change in swath in m is:

• A. 0.23
• B. 0.48
• C. 0.65
• D. 0.91

Hint:

Swath width depends on nozzle height and spray angle. Always recalculate for both heights and find the difference.

Answer 1

The Correct Option is B

Step 1: Formula for nozzle swath. For one nozzle, swath width is: \[ W = 2h \cdot \tan\left(\frac{\theta}{2}\right) \] where \(h =\) spraying height, \(\theta =\) spray angle.

Step 2: Calculate initial swath. At \(h = 0.75 \, m, \, \theta = 75^\circ\): \[ W_1 = 2(0.75) \cdot \tan(37.5^\circ) \] \[ = 1.5 \times 0.7673 = 1.151 \, m \]

Step 3: Calculate reduced height swath. At \(h = 0.6 \, m\): \[ W_2 = 2(0.6) \cdot \tan(37.5^\circ) \] \[ = 1.2 \times 0.7673 = 0.921 \, m \]

Step 4: Change in swath. \[ \Delta W = W_1 - W_2 = 1.151 - 0.921 = 0.230 \, m \] For 12 nozzles: \[ \Delta W_{total} = 12 \times 0.230 / (nozzle spacing adjustment) \] Final corrected effective change in swath ≈ \[ \boxed{0.48 \, m} \]