Mechanical Engineering Gate 2022 Set-1 Questions with Answer

Ques 14 GATE 2022 SET-1

The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the inlet pressure (P0) is increased while keeping the back pressure (Pback) unchanged, which of the following statements is/are true?

Ques 15 GATE 2022 SET-1

A solid spherical bead of lead (uniform density = 11000 kg/m³) of diameter d = 0.1 mm sinks with a constant velocity V in a large stagnant pool of a liquid (dynamic viscosity = 1.1 × 10^-3 kg⋅m^-1⋅s^-1). The coefficient of drag is given by C_D = 24/Re, where the Reynolds number (Re) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as D = (C_D)(0.5ρV²)(π D²/4), where ρ is the density of the liquid. 1 Neglect the buoyancy force. Using g = 10 m/s², the velocity V is __________ m/s.

Ques 16 GATE 2022 SET-1

Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location, the density and velocity are 1 kg/m³ and 100 m/s, respectively. At a downstream location, velocity is 170 m/s. If the pressure drop between these locations is 10 kPa, the force exerted by the gas on the pipe is _________ N.

Ques 17 GATE 2022 SET-1

A steady two-dimensional flow field is specified by the stream function
ψ = kx³y,
where x and y are in meters and k = 1 m⁻²·s⁻¹. The magnitude of acceleration at a point (x, y) = (1 m, 1 m) is ________ m/s² (round off to 2 decimal places).

Ques 18 GATE 2022 SET-1

A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is v⃗=(2𝑥)î +(𝑦+3𝑡)ĵ , given and the temperature field is T=2𝑥² +𝑥𝑦+4𝑡, where x and y are the spatial coordinates, and t is the time. The time rate of change of temperature recorded by the probe at (x=1, y=1, t=1) is?

Ques 19 GATE 2022 SET-1

A flat plate made of cast iron is exposed to a solar flux of 600 W/m² at an ambient temperature of 25 °C. Assume that the entire solar flux is absorbed by the plate.
Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 × 10^-8 W/m²-K⁴. Neglect all other modes of heat transfer except radiation.
Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ °C (round off to the nearest integer).

Ques 20 GATE 2022 SET-1

Consider a rod of uniform thermal conductivity whose one end (x=0) is insulated and the other end (x=L) is exposed to air at T∞ with heat transfer coefficient h. The rate of internal heat generation per unit volume is given as

Ques 21 GATE 2022 SET-1

Consider a one-dimensional steady heat conduction process through a solid slab of thickness 0.1 m. The higher temperature side A has a surface temperature of 80°C, and the heat transfer rate per unit area to the low temperature side B is 4.5 kW/m². The thermal conductivity of the slab is 15 W/m·K. The rate of entropy generation per unit area during the heat transfer process is ________ W/m²·K (round off to 2 decimal places).

Ques 22 GATE 2022 SET-1

Consider a solid slab (thermal conductivity, k = 10 W·m⁻¹·K⁻¹) with thickness 0.2 m and of infinite extent in the other two directions as shown in the figure. Surface 2, at 300 K, is exposed to a fluid flow at free stream temperature (T_∞) of 293 K, with a convective heat transfer coefficient (h) of 100 W·m⁻²·K⁻¹. Surface 2 exchanges heat by radiation with very large surroundings at 0 K. Radiative heat transfer inside the solid slab is neglected. The Stefan-Boltzmann constant is 5.67×10^-8 W·m⁻²·K⁻¹. The temperature T1 of Surface 1 of the slab, under steady-state conditions, is _________ K (round off to the nearest integer).

Ques 23 GATE 2022 SET-1

During open-heart surgery, a patient’s blood is cooled down to 25 °C from 37 °C using a concentric tube counter-flow heat exchanger. Water enters the heat exchanger at 4 °C and leaves at 18 °C. Blood flow rate during the surgery is 5 L/minute.
Use the following fluid properties:

Ques 24 GATE 2022 SET-1

Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity G is ____________ hours.

Ques 25 GATE 2022 SET-1

An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).

Ques 26 GATE 2022 SET-1

The product structure diagram shows the number of different components required at each level to produce one unit of the final product P. If there are 50 units of on-hand inventory of component A, the number of additional units of component A needed to produce 10 units of product P is _________ (in integer).