GATE ME format:nat PYQs & Answers — Page 14

Questions 131–140 of 418. Imported answers require independent review unless marked reviewed.

Topic practice 418 questionsPage 14 of 42

A project consists of five activities (A, B, C, D and E). The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor(s) are listed in the table. The expected time of the project completion is __________ weeks (in integer).

Activity	Optimistic time	Most likely time	Pessimistic time	Immediate predecessor(s)
A	4	5	6	None
B	1	3	5	A
C	1	2	3	A
D	2	4	6	C
E	3	4	5	B, D

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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 low temperature side B is 4.5 kW/m

. 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/m

.K (round off to 2 decimal places).

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A rigid tank of volume of 8 m

is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacuated. The air pressure and temperature inside the pipeline are maintained at 600 kPa and 306 K, respectively. The filling of the tank begins by opening the valve and the process ends when the tank pressure is equal to the pipeline pressure. During the filling process, heat loss to the surrounding is 1000 kJ. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kg.K and 0.718 kJ/kg.K, respectively. Neglect changes in kinetic energy and potential energy.

The final temperature of the tank after the completion of the filling process is __________ K (round off to the nearest integer).

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In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressure turbine. The expansion work in the high-pressure turbine is 400 kJ/kg and in the low-pressure turbine is 850 kJ/kg, whereas the pump work is 15 kJ/kg. If the cycle efficiency is 32%, the heat rejected in the condenser is ________ kJ/kg (round off to 2 decimal places).

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At steady state, 500 kg/s of steam enters a turbine with specific enthalpy equal to 3500 kJ/kg and specific entropy equal to 6.5 kJ·kg⁻¹·K⁻¹. It expands reversibly in the turbine to the condenser pressure. Heat loss occurs reversibly in the turbine at a temperature of 500 K. If the exit specific enthalpy and specific entropy are 2500 kJ/kg and 6.3 kJ·kg⁻¹·K⁻¹, respectively, the work output from the turbine is ________ MW (in integer).

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An engine running on an air standard Otto cycle has a displacement volume 250 cm

and a clearance volume 35.7 cm

. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).

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A uniform wooden rod (specific gravity = 0.6, diameter = 4 cm and length = 8 m) is immersed in the water and is hinged without friction at point A on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = 11.4) is attached to the free end of the rod to keep the assembly in static equilibrium inside the water. For simplicity, assume that the radius of the ball is much smaller than the length of the rod.

Assume density of water = 10³ kg/m³ and π = 3.14.

Radius of the ball is ______ cm (round off to 2 decimal places).

Diagram for Mechanical Engineering question 62

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A steady two-dimensional flow field is specified by the stream function

where

and

are in meter and the constant

. The magnitude of acceleration at a point

is ________ m/s

(round off to 2 decimal places).

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Consider steady state, one-dimensional heat conduction in an infinite slab of thickness 2L (L = 1 m) as shown in the figure. The conductivity (k) of the material varies with temperature as k = CT, where T is the temperature in K, and C is a constant equal to 2 W·m⁻¹·K⁻². There is a uniform heat generation of 1280 kW/m³ in the slab. If both faces of the slab are maintained at 600 K, then the temperature at x = 0 is _______ K (in integer).

Diagram for Mechanical Engineering question 63

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Consider a solid slab (thermal conductivity,

W·m

·K

) 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 a free stream temperature (

) of 293 K, with a convective heat transfer coefficient (

) of 100 W·m

·K

. Surface 2 is opaque, diffuse and gray with an emissivity (

) of 0.5 and exchanges heat by radiation with very large surroundings at 0 K. The radiation heat transfer inside the solid slab is neglected. The Stefan-Boltzmann constant is

W·m

·K

. The temperature

of Surface 1 of the slab, under steady-state conditions, is ________ K (round off to the nearest integer).

Diagram for Mechanical Engineering question 64

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GATE ME format:nat PYQs

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Question 64