GATE 2024 AG – Question 54
A boom sprayer has 12 nozzles at 50 cm spacing, speed 3.5 km/hour, initial nozzle pressure250 kPa and application rate 1.5 m³/ha. Pump flow bypasses12% to tank;line pressure loss is 10% of pump pressure. Pump efficiency is 60%. Raise nozzle pressure10% with the same nozzles. Find pump power in kW, to three decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.520 to 0.540
Explanation
Effective width is 6 m and area rate is $6(3.5)/10=2.1$ ha/hour. Initial nozzle flow is 3.15 m³/hour. Fixed-nozzle flow scales as square root of pressure, so new nozzle flow is $3.15\sqrt{1.1}$ m³/hour. Pump flow is this divided by .88. New nozzle pressure is 275 kPa and pump pressure $275/.9=305.5556$ kPa. Input power is $$P=\frac{(3.15\sqrt{1.1}/.88/3600)(305555.6)}{.60}=531.0809\ \mathrm W.$$ Answer **0.531 kW**.