# Fluid Mechanics and Thermal Sciences (Test 4)

## Gate Exam : Me Mechanical Engineering

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Fluid Mechanics and Thermal Sciences
| Fluid Mechanics and Thermal Sciences |
Q.1
Figure shows the schematic for the measurement of velocity of air (density = 1.2kg /m3 ) through a constant–area duct using a pitot tube and a water-tube manometer. The differential head of water (density = 1000 kg /m3) in the two columns of the manometer is 10mm. Take acceleration due to gravity as 9.8m / s2. The velocity of air in m/s is

A. 6.4
B. 9.0
C. 12.8
D. 25.6
Explaination / Solution:

From Bernoulli’s equation

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Q.2
An ideal Brayton cycle, operating between the pressure limits of 1 bar and 6 bar, has minimum and maximum temperatures of 300K and 1500K. The ratio of specific heats of the working fluid is 1.4. The approximate final temperatures in Kelvin at the end of the compression and expansion processes are respectively
A. 500 and 900
B. 900 and 500
C. 500 and 500
D. 900 and 900
Explaination / Solution:

Ideal Brayton cycle
At the end of compression, temperature.

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Q.3
A mass m of a perfect gas at pressure p1 and volume V1 undergoes an isothermal process. The final pressure is p2 and volume is V2. The work done on the system is considered positive. If R is the gas constant and T is the temperature, then the work done in the process is
A. p1V1 In V2/V1
B. -p1V1 In p1/p2
C. RT In V2/V1
D. -mRT In p2/p1
Explaination / Solution:

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Q.4
Consider steady-state heat conduction across the thickness in a plane composite wall (as shown in the figure) exposed to convection conditions on both sides.

Assuming negligible contact resistance between the wall surfaces, the interface temperature, T (in oC), of the two walls will be
A. -0.05
B. 2.75
C. 3.75
D. 4.50
Explaination / Solution:
No Explaination.

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Q.5
Radiative heat transfer is intended between the inner surfaces of two very large isothermal parallel metal plates. While the upper plate (designated as plate 1) is a black surface and the warmer one being maintained at 727oC, the lower plate ( plate 2) is a diffuse and gray surface with an emissivity of 0.7 and is kept at 227oC. Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady state conditions to exist. Stefan Boltzmann constant is given as 5.67 × 10-8 W/m2K4
The irradiation (in kW/m2) for the upper plate (plate 1) is

A. 2.5
B. 3.6
C. 17.0
D. 19.5
Explaination / Solution:
No Explaination.

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Q.6
The demand and forecast for February are 12000 and 10275, respectively. Using single exponential smoothening method (smoothening coefficient = 0.25), forecast for the month of March is
A. 431
B. 9587
C. 10706
D. 11000
Explaination / Solution:
No Explaination.

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Q.7
A cylinder contains  5m3  of ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is
A. 804.7
B. 953.2
C. 981.7
D. 1012.2
Explaination / Solution:

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Q.8
Water has a critical specific volume of 0.003155 / m3 kg. A closed and rigid steel tank of volume 0.025 m3 contains a mixture of water and steam at 0.1MPa. The mass of the mixture is 10 kg. The tank is now slowly heated. The liquid level inside the tank
A. will rise
B. will fall
C. will remain constant
D. may rise or fall depending on the amount of heat transferred
Explaination / Solution:
No Explaination.

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Q.9
The temperature distribution within the thermal boundary layer over a heated isothermal flat plate is given by  where Tw and T are the temperature of plate and free stream respectively, and y is the normal distance measured from the plate. The local Nusselt number based on the thermal boundary layer thickness δt is given by
A. 1.33
B. 1.50
C. 2.0
D. 4.64
Explaination / Solution:
No Explaination.

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Q.10
Which combination of the following statements about steady incompressible forced vortex flow is correct ?
P: Shear stress is zero at all points in the flow.
Q: Vorticity is zero at all points in the flow.
R: Velocity is directly proportional to the radius from the center of the vortex.
S: Total mechanical energy per unit mass is constant in the entire flow field.
A. P and Q
B. R and S
C. P and R
D. P and S