List of top Questions asked in GATE Agricultural Engineering- 2023

A copper ball and a steel ball having diameters \(d_1\) and \(d_2\), respectively, are initially at 200°C. Both are cooled to ambient 30°C. If both reach 120°C in equal duration, find ratio \(d_1/d_2\). Assume Biot < 0.1.

Two cylindrical reservoirs 'A' and 'B' are connected by a 30 m long pipe of 250 mm internal diameter as shown. Darcy friction factor for the pipe is 0.025. Initially reservoir 'A' was full and reservoir 'B' was empty. Neglecting entrance and exit losses, find the time required to empty reservoir 'A' in hours (rounded off to 3 decimal places). \begin{center} \includegraphics[width=0.5\textwidth]{03.jpeg} \end{center}

The carrot slices (water activity = 0.89) are to be preserved using osmo-dehydration. Addition of salt (NaCl) to 20% sucrose solution (water activity = 0.987) reduces the water activity to 0.85. Find the percentage of NaCl added to the solution. (Molecular mass of sucrose = 342, molecular mass of NaCl = 58.44).

A 10 m pipe carries peak discharge = 1 m\(^3\)/s, head = 4 m, entrance loss coefficient = 0.5, friction loss coefficient = 0.02. Find neutral slope of water level in %.

A homogenous anisotropic earthen dam of height 52 m with a free board of 2 m is constructed on an impermeable foundation. The horizontal and vertical hydraulic conductivities of soil are \(K_h = 4.5 \times 10^{-8} \, m/s\) and \(K_v = 2.0 \times 10^{-8} \, m/s\). There are 6 flow channels and 25 equipotential drops in a square flownet drawn in the transformed dam section. If the downstream dam side is dry, the quantity of seepage per unit length through the dam in m\(^3\)/day/m is \underline{\hspace{3cm}}.

The apparent wall shear stress in a 0.6 m long pipe line carrying refined oil is 12.5 Pa. If the pressure drop along the length is 300 Pa and flow rate is 0.25 m\(^3\)/s, the absolute viscosity of oil in \(10^{-3}\) Pa·s is \underline{\hspace{3cm}}.

Discharge from centrifugal pump at 1000 rpm with head = 30 m is 300 L/min. Efficiency = 65%. If speed increases to 1200 rpm, find power required.

A salt affected crop field is to be leached with irrigation water having salt concentration of 3.5 meq/L. Salt concentration in saturation extract of soil is 15.2 meq/L. Leaching efficiency of field = 55%. In March, ET\(_0\) = 150 mm, effective rainfall = 75 mm, crop coefficient = 1.05. Find leaching requirement for the month in mm.

A 0.30 m well penetrates an unconfined aquifer (saturated depth = 40 m). Pumping 0.03 m\(^3\)/s for 8 hours. Drawdowns in two observation wells: 3 m at 20 m, 2 m at 50 m. Find drawdown in pumping well in m.

A single disc clutch is used to transmit 10 kW power at 1400 rpm. The axial pressure = 0.07 N/mm\(^2\), coefficient of friction = 0.25, ratio of inner to outer radius = 0.8. If the uniform wear theory applies, the required face width of clutch lining is \underline{\hspace{3cm}}.

In a tractor seat system, the chassis frequency and seat suspension damping rate are 20 rad s\(^{-1}\) and 400 N m\(^{-1}\) s, respectively. The critical damping rate of the tractor seat system is 1600 N m\(^{-1}\) s. If the combined mass of the seat and operator is 80 kg, the transmissibility of vibration is \underline{\hspace{2cm}} (rounded off to 2 decimal places).

In a locality 'A', the probability of a convective storm event is 0.7 with a density function \[ f_{X_1}(x_1) = e^{-x_1}, \; x_1 > 0 \] The probability of a tropical cyclone-induced storm in the same location is given by the density function \[ f_{X_2}(x_2) = 2 e^{-2x_2}, \; x_2 > 0 \] The probability of occurring more than 1 unit of storm event is \underline{\hspace{3cm}} (rounded off to 2 decimal places).

Given that \[ \frac{dy}{dx} = 2x + y, y(0) = 1 \] Using Runge-Kutta fourth order method, the value of \(y\) at \(x = 0.2\) is \underline{\hspace{2cm}} (rounded off to 3 decimal places).

A power operated chaff cutter with a mean cutting radius of 0.25 m is fitted with two cutting knives and is rotating at 300 rpm. Thirty maize stalks with a mean diameter of 12 mm are fed through the throat at a time. The dynamic shear strength of the stalk is 0.05 N mm\(^{-2}\). The mass and radius of gyration of the flywheel (including knives) are 40 kg and 0.27 m, respectively. The total shaft power requirement in kW is \underline{\hspace{4cm}} (rounded off to 2 decimal places).

A two-wheel drive tractor with a total weight of 24 kN has a static weight distribution of 30% and 70% at the front and rear axles, respectively. When the tractor is operated on a level ground of pure sand, the maximum tractive force developed is 13 kN. If external weight of 1.5 kN is added to the rear axle, neglecting weight transfer, the change in maximum tractive force in kN is \underline{\hspace{4cm}}.

A 4-stroke diesel engine can be operated with either diesel (HV = 45 MJ/kg) or biodiesel B20 (HV = 42.1 MJ/kg). Brake specific fuel consumption: diesel = 260 g/kWh, B20 = 310 g/kWh. For brake power = 20 kW, the change in brake thermal efficiency of the engine when B20 is used is \underline{\hspace{3cm}}.

A solar photovoltaic system receives radiations between 400–750 W/m\(^2\). Efficiency = 14%. Cell parameters: \(V_{oc} = 21.6 \, V\), \(I_{sc} = 3.22 \, A\), fill factor = 0.72. Find minimum cell area required to generate 10 kW power.

In a juice filtration process, solid concentration per m\(^3\) of filtrate is 0.2 kg. During filtration of 12.49 m\(^3\) of juice, 0.02 m thick cake (porosity of 0.32) is deposited. If 2.5 kg of solid is collected in 180 s, the pressure drop across the cake in kPa is: \[ \text{Absolute viscosity of juice} = 2.12 \times 10^{-3} \, \text{kg m}^{-1}\text{s}^{-1}, \text{Specific cake resistance} = 1.2 \times 10^8 \, \text{m kg}^{-1} \]

Cheese is packed in a bilayer plastic package made of low density polyethylene (LDPE) and polyethylene terephthalate (PET). Thickness of LDPE and PET in the package are 1.5 mm and 1.3 mm, respectively. The surface area of the plastic package is 6.25 cm\(^2\). The partial pressure difference of oxygen across the package wall is 0.30 atm. The permeability coefficient of oxygen in LDPE and PET are \(4.18 \times 10^{-8} \, \text{cm}^3 \, \text{cm cm}^{-2} \text{s}^{-1}\text{atm}^{-1}\) and \(1.67 \times 10^{-10} \, \text{cm}^3 \, \text{cm cm}^{-2} \text{s}^{-1}\text{atm}^{-1}\), respectively. If the food gets spoiled when it absorbs 0.025 ml oxygen, then the shelf life of food in days is:

The rotor shaft of an ice cream freezer consists of 3 scraper blades. The temperature difference between the ice cream mix and the refrigerant during freezing of ice cream is \(30^\circ C\). Density and latent heat of fusion of ice are 917 kg m\(^{-3}\) and 335 kJ kg\(^{-1}\), respectively. The overall heat transfer coefficient is 2000 kJ m\(^{-2}\) h\(^{-1}\) \(^{\circ}C^{-1}\). If the maximum thickness of ice formed before being scraped off is 10 μm, the minimum speed of the scraper shaft in rpm is:

The percentage absolute humidity of air becomes equal to the percentage relative humidity, when:

Dimensionless numbers play an important role in correlating transfer coefficients during forced convection. In relation to the dimensionless numbers, the correct statement(s) is/are:

A vector \(\vec{F} = 5\hat{i} - 10\hat{j} + 8\hat{k}\) is passing through the origin of a 3-D frame. Considering the tendency of rotation in the counter clockwise direction as positive, the moment about a point \(A: (3, 4, 8)\) is:

A vertical disc plough with 5 discs is operated at a depth of 0.15 m. The disc angle and disc diameter are \(40^\circ\) and 0.6 m, respectively. If overlap between two consecutive discs is 0.12 m at 0.15 m depth of cut, the total width of cut at the specified depth in m is:

In a 9 × 20 cm fluted roller type seed drill, each fluted roller is discharging 4.25 g of seed per revolution of fluted roller shaft. The fluted roller shaft rotates once for two complete rotations of the ground drive wheel of the seed drill. The rolling diameter of the ground drive wheel is 0.35 m. Considering no skid of the ground drive wheel, the seed rate in kg/ha is (take \(\pi = 3.14\)):