GATE ME purpose:exam-prep PYQs & Answers — Page 39

Questions 381–390 of 1040. Imported answers require independent review unless marked reviewed.

Topic practice 1040 questionsPage 39 of 104

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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Saturated vapor at 200 °C condenses to saturated liquid at the rate of 150 kg/s on the shell side of a heat exchanger (enthalpy of condensation h_fg = 2400 kJ/kg). A fluid with c_p = 4 kJ·kg⁻¹·K⁻¹ enters at 100 °C on the tube side. If the effectiveness of the heat exchanger is 0.9, then the mass flow rate of the fluid in the tube side is ________ kg/s (in integer).

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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/min.

Use the following fluid properties:

Fluid	Density (kg/m )	Specific heat (J/kg-K)
Blood	1050	3740
Water	1000	4200

Effectiveness of the heat exchanger is ________ (round off to 2 decimal places).

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Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 1500 W/m² is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200 °C. The Reynolds number (Re) of the flow is 8500, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 W·m⁻¹·K⁻¹ and 2600 J·kg⁻¹·K⁻¹, respectively. The correlation Nu = 0.023 Re⁰·⁸ Pr⁰·⁴ is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ °C (round off to the nearest integer).

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GATE ME purpose:exam-prep PYQs

Question 61

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Question 65

Question 65