List of top Farm Power Questions asked in GATE AG

A tractor PTO shaft, through a spur-gear reduction, drives a small grain auger, the PTO running at the standard 540 rpm. The driving gear on the PTO shaft has a 0.18 m pitch circle diameter.
The auger requires 3.5 kW, transmitted through this gear. The normal force along the line of action between the meshing teeth is 760 N. Assume involute spur gears, single tooth contact, and neglect friction.
The pressure angle (in degrees) is ________. (Rounded off to two decimal places)
(Take \(\pi = 3.14\))

A stationary Ackerman-steer tractor on a dry, clean concrete surface carries 12 kN vertical load on each front steered wheel of 0.28 m nominal tyre width (b). Assume uniform pressure distribution on the circular tyre-print area having diameter b. Effective friction coefficient between tyre and surface is 0.30.
The steering is individually power-assisted by a single-rod hydraulic cylinder, acting through a pitman arm resulting in 60 mm effective moment arm. The hydraulic relief valve is set to 8 MPa, and the cylinder bore is 32 mm (ignore rod area). Neglect other losses.
The maximum kingpin offset (in mm), which does not cause the maximum allowable kingpin torque to be exceeded, is ________. (Rounded off to the nearest integer)
(Take \(\pi = 3.14\))

A 2WD tractor has to develop 30 kN gross tractive force at the ground. Rolling radius of the rear-wheels is 0.73 m.
Each rear-wheel is driven by a simple planetary final-drive in which sun gear (26 teeth) is input, ring gear (78 teeth) is fixed, and the carrier is bolted to the rear-wheel hub.
The sun-planet external mesh efficiency is 98.5%, while the planet-ring internal mesh efficiency is 99%. Losses upstream of the final-drive are neglected.
The required sun-shaft input torque per rear-wheel (in kN.m) is ________. (Rounded off to two decimal places)

A four-cylinder four-stroke engine (100 mm bore and 120 mm stroke) runs at 1800 rpm mean speed with 0.9 MPa indicated mean effective pressure (IMEP).
The flywheel constant (ratio of the energy fluctuation to the indicated work per crankshaft revolution) is 0.30. All other losses are neglected.
For an allowable speed fluctuation of \(\pm 1\%\) about the mean, the required flywheel mass moment of inertia (in \(kg.m^2\)) is ________. (Rounded off to two decimal places)
(Take \(\pi = 3.14\))

A small horizontal axis wind turbine (HAWT) is designed to deliver 2 kW shaft power at a steady wind speed of \(7\ \text{m.s}^{-1}\). The HAWT operates with an aerodynamic power coefficient of 0.36, a drivetrain efficiency of 0.90, and an air density of \(1.225\ \text{kg.m}^{-3}\). Neglecting other losses, the required rotor diameter is \(X\) m. When the wind speed drops to \(6\ \text{m.s}^{-1}\), the shaft power is \(Y\) kW. Identify the nearest correct option for the \(X\) and \(Y\) combination (take \(\pi = 3.14\))

A tractor PTO runs at a constant speed of 540 rpm to drive a rotary tiller through a flange coupling having a shear pin parallel to the shaft. The shear pin axis is located 60 mm from the PTO shaft axis. The allowable shear stress of the pin material is 200 MPa. For overload safety, the pin must fail at 150% of the rated torque to protect the gearbox. The tiller requires 40 kW under normal load at the rated PTO speed. Neglecting bending, stress concentration effects, and other losses, the pin diameter, in mm, is nearest to (take \(\pi = 3.14\))

A flat belt of negligible mass and thickness drives an output pulley of 0.6 m diameter, rotating at 500 rpm without slip. The arc of contact is \(190^{\circ}\) for this pulley, while it is \(170^{\circ}\) for the smaller input pulley. The coefficient of friction between the belt and the pulleys is 0.30. The measured slack side tension is 250 N. Neglecting other losses, the power transmitted by the belt drive, in kW, is nearest to (take \(\pi = 3.14\))

The impeller speed of a centrifugal pump is increased by 30%. The power requirement of the pump increases by \(n\) times. The value of \(n\) is ________. (Rounded off to two decimal places)

At an initial pressure of 100 kPa, 1 kg air is compressed reversibly from 15 litres to 1 litre at final pressure of 2000 kPa. Neglecting other losses, the Polytropic Exponent (n) is ________. (Rounded off to three decimal places)

A 2WD tractor's driving axle experiences total dynamic normal load of 28 kN. The driving wheels have 0.60 m rolling radius. The total driving axle torque measured is 10.7 kN.m. At 18% wheel slip, the coefficient of net traction is 0.35. Tractive efficiency of the driving wheels, in %, is nearest to

The RMS sound pressure is increased by 50%. This increases the sound pressure level, in dB, nearly by

A tractor engine delivers 382 N.m brake torque at a rated speed of 2000 rpm. The radiator cooling fan draws 5% of the engine brake power. The fan pushes \(2.8\ \text{m}^3\text{s}^{-1}\) of air against 0.9 kPa static pressure rise. Assuming air as incompressible, and ignoring other losses, the fan efficiency, in %, is nearest to (Take \(\pi = 3.14\))

Fuel property that predominantly governs 'hard / cold starting' in SI engine is P; and the property that predominantly governs 'ignition delay' in CI engine is Q. Identify the correct option for P and Q combination.