GATE question papers: Agricultural Engineering 2007 (AG)

Q. 1 – Q. 20 carry one mark each.

1. An ellipsoidal object has three axes measuring 40 cm, 20 cm and 20 cm respectively. The volume of the object is

(A) 4.23 liters (B) 8.38 liters (C) 12.63 liters (D) 17.05 liters

2. is the Laplace Transform of

(A) exp (-at) sin wt (B) exp (-at) sinh wt

3. For station X, the maximum one day rainfall with 25 years return period is 100 mm. The probability of a on day rainfall equal to or greater than 100 mm at station X occurring at least once in 15 successive years is
(A) 0.458 (B) 0.500 (C) 0.637 (D) 0.990

4. Taking y (0) = 0 and using Euler's method with size h = 0.1 solution of the differential equation

= 2 x y + 1 gives the value of y(0.3) as

(A) 0.3101 (B) 0.3142 (C) 0.6202 (D) 4.080

5. Integrating the function f (x) = 1 + e^-x sin (4x) over the interval [0, 1] using Simpson's 1/3rd rule gives

(A) 1.021 (B) 0.091 (C) 1.321 (D) 2.642

6. A lubricating oil with high viscosity index is desirable for tractor engine due to

(A) More variation of viscosity with temperature

(B) Less variation of viscosity with temperature

(D) High cloud point

7. In a tractor cab, the temperature comfort zone for the tractor operator is between

(A) 287 and 291 K (B) 288 and 293 K

8. As per ASABE standards, the three-point hitch of a two-wheel drive tractor with a maximum drawbar power of 45 kW comes under the category

(A) I (B) II (C) III (D) IV

9. As compared to diesel, the heating value and exhaust emissions such as CO, CO₂ and smoke density of biodiesel when used in compression ignition engine are

(A) Lower and higher respectively (B) Higher and Lower respectively

10. The theoretical percentage variation in speed of a chain as it leaves an 8 teeth sprocket rotating at a uniform velocity is

(A) 0.0 (B) 7.9 (C) 29.3 (D) 34.3

11. The angle between the lines AB and BC whose respective bearings are 35° and 140° is

(A) 75° (B) 115° (C) 175° (D) 185°

12. A fluid in which shear stress is more than the yield value and proportional to the rate of shear strain is called

(A) Newtonian fluid (B) Non- Newtonian fluid

13. When the water level in a well is at a depth of 7 m from the surface, the most suitable pump to lift water for irrigation is

(A) Submersible pump (B) Horizontal centrifugal pump

14. The specific gravity and void ratio of a soil sample are G and e respectively. The hydraulic gradient is

(A) (B) (C) (D)

15. A soil 0.8 m deep has volumetric water content of 0.12. The quantity of water needed to bring the volumetric water content to 0.30 is

(A) 0.144 m of water (B) 0.180 m of water

16. A heater is placed in front of a continuous countercurrent dryer. Air at 40 °C and 70% RH is fed into the heater from which the air exits at 65 °C. If saturation vapour pressure at 40 °C and 65 °C are 0.074 bar and 0.250 bar respectively, then relative humidity of the air coming out of the heater and entering the dryer is

(A) 21% (B) 27% (C) 32% (D) 38%

17. Crushing efficiency of any grinder rarely exceeds

(A) 1% (B) 5% (C) 10% (D) 20%

18. Bacterial population in milk increases 200 times in 18 hours of storage at 20 °C. The increase in population in 3 hours of storage at the same temperature is

(A) 1.34 times (B) 2.42 times (C) 7.02 times (D) 14.14 times

19. A vegetable oil is flowing through a vertical wall as a film. The density and viscosity of the oil are 920 kg m^-3 and 0.28 Pa s respectively. If the average velocity of the film is 0.05 m s^-1, the thickness of the film is

(A) 0.14 mm (B) 0.36 mm (C) 1.76 mm (D) 2.16 mm

20. Air at 101.325 kPa pressure is used to dry a vegetable material at 52 °C. Saturation pressure of water at 52 °C is 13.51 kPa. If the mass transfer coefficient for the case of equimolar counter diffusion is 4.79 ´ 10^-4 kg mole m^-2 s^-1 mole fraction^-1, then, the mass transfer coefficient for the case of diffusion through non diffusing gas (k_Y) in kg mole m^-2 s^-1 mole fraction^-1 is

(A) 4.96 ´ 10^-4 (B) 5.14 ´ 10^-4 (C) 7.83 ´ 10^-4(D) 1.02 ´ 10^-4

Q. 21 – Q. 75 carry two mark each.

21. An oil engine works on the ideal diesel cycle with a compression ration of 18:1. The constant pressure energy addition ceases at 10% of the stroke. The intake pressure and temperature are100 kpa and 300 K respectively. The hourly air consumption is 100 m³. If the ratio of specific heats is 1.4, the maximum temperature in the cycle is

(A) 953.3 K (B) 1334.6 K (C) 2154.5 K (D) 2573.9 K

22. While testing a tractor, the airborne sound intensity is increased so that the root mean square sound pressure is doubled. The corresponding increase in sound pressure level to the reference sound pressure of 2 ´ 10^-5 Pa is

(A) 2 dB (B) 4 dB (C) 6 dB (D) 8 dB

23. A piston with 50 mm diameter and length 50 mm is to be moved at a velocity of 0.25 m s^-1 in a hydraulic cylinder with 50.2 mm diameter. The cylinder is full of oil with a kinematic viscosity of

9 ´ 10^-4 m² s^-1 and a density of 880 kg m^-3. Assuming pressure difference between inside and out side of the cylinder as zero, the force required to move the piston is

(A) 7.772 N (B) 15.543 N (C) 76.243 N (D) 152.476 N

24. A single phase 230 V electric motor while running at 1400 rpm develops a torque of 3.1 Nm. If the phase angle between the voltage and current is 38° and the power efficiency of the motor is 80%, the amount of electric current drawn by the electric motor is

(A) 2.470 A (B) 3.135 A (C) 4.810 A (D) 5.512 A

25. The mechanical efficiency of a power tiller engine developing 7.5 kW is 80%. The calorific value of diesel is 45 MJ kg^-1. If the indicated thermal efficiency is 35%, the brake specific fuel consumption of the engine is

(A) 0.135 kg kW^-¹ h^-¹ (B) 0.228 kg kW^-¹ h^-¹

26. A tractor engine developing 30 KW rejects heat at the rate of 0.58 kW per kW of engine output. A water cooling system is to be installed in the tractor. The expected temperature rise as air moves through the radiator is 20 K. the frontal area of the radiator is limited to 0.16 m². If density of air is 1.29 kg m^-³ and specific heat of air is 1.0 kJ kg^-¹ K^-¹, the amount of air to be blown per unit time through the radiator frontal area is

(A) 0.674 m³s^-¹ (B) 0.870 m³s^-¹ (C) 1.162 m³s^-¹ (D) 1.502 m³s^-¹

27. A two-wheel drive tractor weighing 20 kN has a wheel base of 2.1 m with a static weight distribution of 35% and 65% at the front and rear axles respectively. On a level ground, the tractor moves at a speed of 4 km h^-¹. Considering small steer angle, the cornering force acting on each of the front tyre for a tuning radius of 1.8 m is

(A) 0.244 kN (B) 0.454 kN (C) 0.489 kN (D) 0.907 kN

28. A tractor drawn rotary cultivator is concurrent revolution mode is to be operated at a depth of 150 mm and at a forward speed of 3.6 km h^-¹. The radius of working set is 280 mm. the number of blades, which would cut identical path is 3. The working width of the cultivator is 1.8 m. the cultivator is to be powered from the tractor PTO running at 540 rpm through a suitable gearbox. For getting a tilling pitch of 74.1 mm, the suitable gear ratio is

(A) 1:2 (B) 1:1.5 (C) 1.5:1 (D) 2:1

29. A solar photovoltaic system comprising solar photovoltaic array, inverter and a motor-pump unit is installed for supplying drinking water in a village. There are 24 modules in the array and each module contains 36 number of cells of size 104 ´ 104 mm with a conversion efficiency of 12.8%. the global solar radiation incident normally on the cells is 945 W m^-². The power consumed in lifting the water is found to be 435 W. If the pump-motor unit efficiency is 45%, the efficiency of the inverter is

(A) 56.21% (B) 69.42% (C) 80.25% (D) 85.52%

30. A farmer has a choice of buying a 4 bottom ´ 41 cm mould board plough for Rs 8570 or a 5 bottom ´ 45 cm mould board plough for Rs 12000. Each plough has a life of 15 years. Neglect salvage value, interest charges and other costs on the ploughs. With either plough the operating speed is 6.5 km h^-¹ and field efficiency is 82%. Assume that the cost per heactare for tractor energy to be same for both the ploughs. If the labor cost is Rs. 10 per hour, the minimum number of hectares that would justify the purchase of the larger plough (i.e., break even point) is

(A) 73.7 (B) 89.9 (C) 737.3 (D) 899.4

31. A flange mounted shear pin is used on a shaft as a safety device. The steel shear pin has a diameter of 2.38 mm and is to be mounted on the flange of a shaft rotating at 650 rpm. The maximum power transmitted by the shaft is 4.5 k W. If the shear strength of the material of pin is 310 Mpa, The radial distance of its mounting is

(A) 5.02 mm (B) 11.98 mm (C) 47.94 mm (D) 301.20 mm

32. A right hand offset disk harrow is operating with front and rear gang angles of 15° and 21° respectively. The centers of the two gangs are 2.45 m and 4.25 m behind a transverse line through the hitch point on the tractor drawbar. The horizontal soil force components are: L_f = 3.1 kN, S_F = 2.65 kN, L_T = 3.35 kN, S_T = 2.65 kN. The amount of offset of the center of cut with respect of the hitch point is

(A) 0.740 m (B) 0.795 m (C) 0.968 m (D) 1.006 m

33. A gravity feed type liquid fertilizer distributor has fixed orifices for metering. Liquid is supplied from a top vented tank with a height of 460 mm. The bottom of the tank is 610 mm above the ground and the ends of the delivery tube are 75 mm below the ground level. The metering heads (including orifices) are just below the tank, but the delivery tubes are small enough so that each one remains full of liquid between the orifice and the outlet end (thereby producing a negative pressure head on the orifice). The ratio between flow rates when the tank is full and when it filled to a height of only 25 mm is

(A) 1.27 (B) 1.61 (C) 2.31 (D) 4.28

34. A 6 bladed forage blower operates at 540 rpm. For a feed rate of 6.5 ´ 10⁴ kg h^-1, the mass of corn silage carried on each impeller blade is

(A) 0.334 kg (B) 2.006 kg (C) 12.037 kg (D) 20.060 kg

35. A flat leather belt with 9 ´ 250 mm cross section is used to drive a cast iron pulley of diameter 0.90 m running at 336 rpm. The active are of contact on the smaller pulley is 120°. The belt weighs 980 kg m^-3. Coefficient of friction between the leather and cast iron is 0.35. Centrifugal tension experienced by the belt is

(A) 5.5 N (B) 56.4 N (C) 552.8 N (D) 2211.2 N

36. A strain gauge of 120 W nominal resistance and 2.1 gauge factor is mounted on a tensile steel member. The longitudinal axis of the strain gauge is along the length of the member, Young's modulus of steel is 2.1 ´ 10¹¹ Pa. The change in resistance of the gauge is 0.08064 W. The stress experienced by the steel member is

(A) 67.2 ´ 10⁶ Pa (B) 141.1 ´ 10⁶ Pa (C) 268.8 ´ 10⁶ Pa (D) 296.4 ´ 10⁶ Pa

37. In a four bar linkage, the fixed link is horizontal and has a length of 60 mm. The crank marks an angle of 30° with the fixed link and is attached to one end of the fixed link. The lengths of crank, coupler, and follower links are 20, 70 and 50 mm respectively. For the open chain configuration, the angle of coupler with respect to the horizontal is

(A) 2 degrees (B) 32 degrees (C) 122 degrees (D) 152 degrees

38. The left limb of a U-tube manometer is connected to a pipe in which water flows and the right limb containing mercury is open to the atmosphere. The center of the pipe is 200 mm below the level of mercury in the right limb and difference of mercury levels in the two limbs is 300 mm. The pressure in the pipe line is

(A) 19 kPa (B) 29 kPa (C) 39 kPa (D) 49 kPa

39. A hydraulically efficient trapezoidal drainage channel has to be designed for draining 400 ha of land with a drainage coefficient of 20 mm. If the recommended side slope and depth are 2:1 and 1.06 m respectively, the bottom width is

(A) 0.25 m (B) 0.50 m (C) 0.75 m (D) 1.00 m

40. An unconfined aquifer is pumped at a constant rate of 10 1 s^-1. Steady state draw downs measured at radial distances of 30 m and 60 m are 0.80 m and 0.70 m, respectively. Original Thickness of aquifer is 30 m. Transmissibility of the aquifer is

(A) 19 m² d^-¹ (B) 760 m² d^-¹ (C) 952 m² d^-¹ (D) 982 m² d^-¹

41. A centrifugal pump delivers 30 1 s^-1 of water against static suction and delivery heads o 6 m and 10 m respectively. The length and diameter of delivery pipe are 100 m and 100 mm respectively. The outlet of delivery pipe is submerged. Friction factor for the pipe is 0.03. If the minor losses in the delivery pipe amount to 1.0 m, pressure at delivery end of the pump is

(A) 327 kPa (B) 385 kPa (C) 680 kPa (D) 984 kPa

42. The areas within the contour lines at the site of a proposed reservoir and dam are as follows:

Contour, m	20		24	26	28	30	32
Area, m²	100	220	600	1800	4500	10000	25000

If 20 m R.L. represents the bottom of the reservoir and 32 m R.L. represents the water surface, the volume of water in the reservoir obtained by the trapezoidal formula is

(A) 21110 m³(B) 32220 m³ (C) 42220m³ (D) 59340 m³

43. In a sub-surface drainage system, tile drains are laid with a slope of 0.28% to carry a peak discharge of 3 liter s^-1 per drain. If the Manning's n is 0.011, the practical diameter of tile required is

(A) 50 mm (B) 75 mm (C) 100 mm (D) 150 mm

44. A recharge well of 300 mm diameter is constructed in a confined aquifer of 1000 m² d^-2 transmissibility. From the top of impermeable bed, the water level in the well is 50 m and the height of constant water level is 40 m. The constant water level occurs at a distance of 150 m from the center of the well. The possible maximum recharge rate is

(A) 3.16 m³ min^-¹ (B) 6.32 m³ min^-¹(C) 9.48 m³ min^-¹(D) 12.64 m³ min^-¹

45. The discharge through a 90° V- notch for a head of 0.5 m and coefficient of discharge of 0.6 is

(A) 0.25 m³ s^-¹ (B) 0.50 m³ s^-¹ (C) 0.65 m³ s^-¹ (D) 0.75 m³ s^-¹

46. A cohesive soil has an angle of shearing of 15° and a cohesion of 35 kpa. The value of lateral pressure in the cell for failure to occur at a total stress of 300 kPa during the triaxial test is

(A) 59.58 kPa (B) 122.92 kPa (C) 140.41 kPa (D) 230.34 kPa

47. The normal annual rainfall at stations I, II, III and IV in a basin are 155, 150, 120 and 105 cm respectively. In the year 2000, stations I, II and III received annual rainfalls of 156, 140 cm respectively. Estimated value of rainfall at station IV during the year 2000 is

(A) 98.2 cm (B) 105.0 cm (C) 133.3 cm (D) 141.7 cm

48. The maximum rainfall with a return period of 25 years is given below for a watershed having a time of concentration of 47.65 minutes:

Time (min)	10	20 000	30	40	60
Rainfall depth(mm)	52.5	55.00	57.50	60.00	65.00

In this watershed, 2.0 km² area has cultivated sandy soil (C = 0.2) and the remaining 3.0 km² has cultivated clay soil (C = 0.7). The peak rate of runoff from the watershed is

(A) 4.29 m³ s^-¹(B) 5.41 m³ s^-¹ (C) 42.99 m³ s^-¹ (D) 54.13 m³ s^-¹

49. A drop spillway is subjected to horizontal and vertical forces of 40.8 kN and 36.5 kN respectively. The area of plane of sliding is 10 m². Angle of internal friction and cohesive resistance of foundation material are 25° and 4.9 kPa respectively. The factor of safety against sliding is

(A) 0.53 (B) 0.61 (C) 1.62 (D) 1.86

50. The soil loss from a field with 5% slope and for crop management factor of 0.25 is 44.80 Mg ha^-1. Contouring along with crop management factor of 0.15 is adopted as the soil conservation measure in the field. The changed soil loss from the field is

(A) 1.61 Mg ha^-¹ (B) 2.68 Mg ha^-¹ (C) 16.12 Mg ha^-¹ (D) 26.87 Mg ha^-¹

51. A field is irrigated by constructing 100 m long furrows spaced at 0.75 m apart. The advance time to the end of furrow was 30 mm with an inflow rate of 2 litre s^-1. After that the inflow rate was cutback to 0.5 litre s^-1 and continued for one hour. The average depth of irrigation is

(A) 2.4 cm (B) 7.2 cm (C) 9.0 cm (D) 18.0 cm

52. A sprinkler system consists of two 192 m long laterals. On each lateral, sixteen sprinklers are located at an interval of 12 m. The spacing between the laterals is 10 m. The required capacity (in litre s^-1) of sprinkler system for application rate of 1.0 cm h^-1 is

(A) 5.33 (B) 10.66 (C) 14.22 (D) 17.06

53. A 50 km long canal with an average width of 25 m is used for irrigation. Mean daily evaporation as measured from a Class A evaporation pan is 5 mm d^-1. Considering the pan coefficient as 0.80, the mean daily evaporation loss from this canal is

(A) 5.00 ´ 10³ m³ d^-¹ (B) 6.25 ´ 10³ m³ d^-¹

54. To deliver 1.3 litre min^-1 discharge, the operating pressure of a 3 m long, 3 mm diameter bubbler tube is

(A) 1.64 kPa (B) 16.46 kPa (C) 164.61 kPa (D) 1646.20 kPa

55. Dry bulb and wet bulb temperatures of air fed into a dryer are found to be 60 °C and 35 °C respectively. Saturation humidity at wet bulb temperature is 0.0365 kg H₂O kg dry air^-1. If specific heat capacities of dry air and water vapour are 1.008 and 1.915 kJ kg^-1 K^-1 respectively and latent heat of vaporization at wet bulb temperature is 2.42 MJ kg^-1 then humidity ratio of air is

(A) 0.0193 kg H₂O kg dry air^-¹ (B) 0.0225 kg H₂O kg dry air^-¹

56. A refrigerator with a COP of 3.2 uses 2.4 kg min^-1 refrigerant extracting 150 kJ kg^-1 heat in the evaporator. Assuming compressor efficiency of 85% the minimum size of the motor is

(A) 0.5 hp (B) 1.5 hp (C) 2.0 hp (D) 3.0 hp

57. If thermal conductivity, mass diffusivity, equimolar mass transfer coefficient based on concentration gradient, density and specific heat capacity of air are 0.03 W m^-1 K^-1, 2.4 ´ 10⁵ m² s^-1, 0.3 m s^-1, 1.0 kg m^-3 and 1.0 kJ kg^-1 K^-1 respectively, then convective heat transfer coefficient of air is

(A) 7.43 W m^-² K^-¹ (B) 74.27 W m^-² K^-¹

58. At 65 °C, Henderson constant C and n are 7.4 ´ 10^-4 K^-1 and 0.56 respectively. The equilibrium moisture content corresponding to 40% relative humidity is

(A) 38% (wet basis) (B) 78% (dry basis)

59. Effectiveness of countercurrent heat exchanger is given by

If same liquid at the same flow rate is used as heating and cooling media through a countercurrent double tube heat exchanger then effectiveness is given by.

(A) (B) (C) (D)

60. A pulse mill grinds Bengal gram of 2 mm volume- surface mean diameter to powder of 100 m m volume-surface mean diameter. The ration of Rittinger's to Kick's constant in the grinding operation is

(A) 0.317 kWh kg^-¹ (B) 3.15 mm

61. Angle of internal friction for rice grain is 27 °, bulk density of rice at 14% moisture content is 833 kg m^—3 and coefficient of friction between rice and concrete wall is 0.5. For a silo of 5 m diameter and 20 m height, the ratio between the lateral pressures at the bottom of the silo obtained by Rankine and Janssen formulae is

(A) 1.63 (B) 3.16 (C) 6.13 (D) 9.47

62. Assuming psychrometric ratio to be unity, milk of 50% total solids is spray dried to powder of 5% moisture content on dry basis. Dry bulb and wet bulb temperatures of the inlet air to the spray dryer are 200 °C and 50 °C respectively. Latent heat of vaporization at the wet bulb temperature is 2393 kJ kg^-1. Assuming no sensible heating of powder the outlet air temperature is 80 °C. If inlet air absolute humidity was 0.015 kg H₂O kg dry air^-1, then kg of dry air required per kg feed is

(A) 4.7 (B) 5.9 (C) 7.4 (D) 9.5

63. Peas of 1.1 cm diameter are dried by air at 65.8 °C in a packed bed drier. The void fraction of the bed is 0.35 and the bed has a diameter of 0.5 m and a height of 0.8 m. The flow rater and the viscosity of air are 0.12 kg s^-1 and 2.03 ´ 10^-5 Pa s respectively. Reynolds number for the packed bed is

(A) 13 (B) 340 (C) 908 (D) 1359

64. A rectangular fin of length 12 cm, width 22 cm and thickness 1.5 cm is connected to a tube at a temperature of 0 °C. The thermal conductivity of the fin material is 150 W m^-1 K^-1. The tip of the fin is not insulated. Air at a temperature of 5 °C is in contact with the fin. The heat transfer coefficient between the fin and the air is 25 W m^-2 K^-1. The rate of heat transfer is

(A) 3.33W (B) 6.63 W (C) 9.13 W (D) 15.23 W

65. In order to reduce heat loss, a steam line with a tube diameter of 1.0 cm is insulated with a material having thermal conductivity of 0.108 W m^-1 K^-1. Heat is dissipated from the outer surface of the insulating material by natural convection with a heat transfer coefficient of 12 W m^-2 K^-1 into the ambient at a constant temperature. The heat loss becomes maximum when the thickness of insulation is

(A) 0.5 mm (B) 2 mm (C) 4 mm (D) 6.5 mm

66. Air carrying particles of density of 700 kg m^-3 and average diameter of 25 mm enters a cyclone of 0.7 m diameter at a tangential velocity of 30 m s^-1at 0.35 m. The density and viscosity of air are 1.1614 kg m^-3 and 1.85 ´ 10^-5 Pa s respectively. The terminal radial velocity of the particle is

(A) 0.17 m s^-¹(B) 1.69 m s^-¹ (C) 3.37 m s^-¹ (D) 16.52 m s^-¹

67. A long cylindrical piece of meat having a diameter of 0.02 m containing 80% moisture is being frozen with air at -30 °C. Initial temperature of the meat is -2.5 °C (freezing point). The heat transfer coefficient of the freezer unit is 20 W m^-2 K^-1. If density of the unfrozen meat is 1050 kg m^-3 and the thermal conductivity of the frozen meat is 1.025 W m^-1 K^-1, the latent heat of fusion for water is 335 kJ kg^-1, shape factors P and R are (1/4) and (1/16) respectively, the freezing time is

(A) 0.158 h (B) 0.373 h (C) 0.464 h (D) 2.12 h

68. A single effect evaporator is used to concentrate 5000 kg h^-1 of a 1.5 wt% sugar solution entering at 50 °C to a concentration of 2 wt% at 101.325 kPa. Steam supplied is saturated at 169.06 kPa

(115 °C). The overall heat transfer coefficient is 1550 W m^-2 K^-1. The boiling point os solution is the same as that of water. The specific heat of the feed is 4021 kJ kg^-1 K^-1. The latent heat of water at 100 °C is 2257.06 kJ kg^-1 and the latent heat of steam at 115 °C is 2216.52 kJ kg^-1. The required surface area for heat transfer is

(A) 6.9 m² (B) 10.7 m² (C) 13.9 m² (D) 46.3 m²

69. In a cold store of 30 m ´ 150 m ´ 15 m size, 4000 tonnes of potato having the specific heat of 3.62 kJ kg^-1 K^-1 and heat of respiration of 20 W m^-3 is kept at 30 °C. Potato is required to be cooled to
2 °C in 30 days. Neglecting other sources of heat, the capacity of the refrigeration plant required is

(A) 6 TR (B) 38 TR (C) 44 TR (D) 83 TR

70. A diatomic, adiabatically compressible fluid having the molecular mass of 16 is flowing through a nozzle at a temperature of 20 °C. If the velocity of the fluid is 430 m s^-1, the Mach Number is

(A) 0.93 (B) 0.97 (C) 1.03 (D) 1.07

Common Data for Questions 71, 72, 73:

A 35 K W two-wheel drive tractor weighing 20 kN is fitted with6-16 8PR tyre at the front axle and 13.6-28

12PR tyre at the rear axle. The ratio of section height and section width for all tyres is 0.75. The tractor has

a wheel base of 2.1 m and the center of gravity is located 0.7 m ahead of the rear axle center on a horizontal

plane. The tractor is to be towed on a level ground having sandy clay loam soil at 10% moisture content with

a come index o f1200 kPa.

71. The wheel numeric for each of the rear wheels is

(A) 39.50 (B) 58.17 (C) 79.01 (D) 116.37

72. Rolling resistance of each of the front wheels is

(A) 0.244 kN (B) 0.354 kN (C) 0.575 kN (D) 0.707 kN

73. If the same tractor is to be towed on a level ground with compacted dry clay soil, the force required for towing is

(A) 0.27 kN (B) 0.40 kN (C) 0.53 kN (D) 0.80 kN

Common Data for Questions 74, 75:

74. The specific energy of flowing water is

(A) 1.25 m (B) 1.45 m (C) 2.25 m (D) 3.25 m

75. The depth for minimum specific energy is

(A) 0.56 m (B) 0.66 m (C) 0.86 m (D) 1.06 m

Statement for Linked Answer Questions 76 & 77:

A flat plate solar collector with an absorber area for 1.0 ´ 1.5 m receives a solar flux of 850 W m^-2 on the top

cover. The indicated solar flux absorbed in the absorber plate is 600 W m^-2. The ambient temperature is 297

K. The heat loss coefficient of the collector at the side, bottom and top are 0.35, 0.65 and 3.50 W m^-2 K^-1

respectively with a collector heat-removal factor of 0.85. The collector fluid temperature is 333 K.

76. Useful heat gain rate for the collector is

(A) 558.45 W (B) 604.35 W (C) 657.01 W (D) 711.02 W

77. Instantaneous collector efficiency is

(A) 43.80% (B) 47.40% (C) 51.53% (D) 55.76%

Statement for Linked Answer Questions 78& 79:

A field sprayer having a boom with 20 nozzles spaced 0.46 m apart is to be designed for a maximum

application rate of750 liter ha^-1 at 520 kPa pressure. The forward speed of travel is 6.5 km h^-1. Neglect field

losses and assume that 10% of the pump output is bypassed.

78. The required pump capacity is

(A) 67.95 litre min^-¹ (B) 74.75 litre min^-¹

79. If mechanical agitation requires 375 W input power and the pump efficiency is 70 %, the maximum power input required is

(A) 720 W (B) 879 W (C) 1095 W (D) 1403 W

Statement for Linked Answer Questions 80 & 83:

A 4-h unit hydrograph (UH) is used to derive S- hydrograph. The ordinates of 4-h UH are given below:

Tim e (h)	0	4	8	12	16	20	24	28	32	36	40	44
4-h UH ordinates (m³s^-1)	0	20	80	130	150	130	90	52	27	15	5	0

80. Equilibrium discharge and its time of occurrence for the derived S-hydrograph are

(A) 150 m³ s^-¹ and 16 h (B) 380 m³ s^-¹ and 16 h

81. Area of watershed is

(A) 215.98 km² (B) 251.61 km² (C) 547.15 km² (D) 1006.47 km²

Statement for Linked Answer Questions 82 & 83:

Bacillus stearothermophilus has a z value of 10.20 °C at a reference temperature of 121 °C

82. The activation energy for the destruction of Bacillus stearothermophilus is

(A) 327.56 MJ kg mole^-1 (B) 298.95 MJ kg mole^-1

83. The z value of the same organism at a reference temperature of 135 °C is

(A) 9.73 °C (B) 10.20 °C (C) 10.95 °C (D) 11.15 °C

Statement for Linked Answer Questions 84 & 85:

Ice cream at a temperature of -18 °C is being transported through a refrigerated truck having outside

dimensions of 6 m length, 3 m width and 2 m height. The truck is traveling at a speed of 90 km h^-1 on a

highway where the air temperature is 45 °C. The truck is insulated in a way such that the outside

surface temperature of the truck is maintained at 15 °C. Assume that there is no heat transfer from the front

and back of the truck.

Properties of air at 30 °C are: p – 1.1514 kg m^-3, m = 1.86 ´ 10^-5 Pa s, C_p = 1.007 kJ kg^-1 K^-1, k = 0.0265 W

m^-1 K^-1. Use the relation: Nu = 0.036 Re^0.8 Pr^0.33

84. The average heat transfer coefficient of the system is

(A) 22.06 W m^-2 K^-1 (B) 30.52 W m^-2 K^-1

85. The rate of heat transfer at the four surfaces is

(A) 47.8 k W (B) 86.1 k W (C) 95.7 k W (D) 114.7 k W

GATE question papers: Agricultural Engineering 2007 (AG)

End of Question Papers