1st unit test paper & solution.pdf

Meghnad Saha Institute Of Technology

Paper: Engineering Thermodynamics & Fluid Mechanics (ME201) Btech (M.E.)-1st _{year 2}nd _semester

1st _{Unit Test} Date: 07/03/2013

Time:1.5hr Total marks:30

You can use the property charts to get the standard data of fluids which are not provided.

Group A

1. Choose the correct option only (Need not to write the full question): [1+1+1+1+1=5]

a) A well insulated cylinder has perfect vacuum in one half and an ideal gas at pressure P1 in the other half. The partition is broken and the gas occupies the entire volume V. If H1 and H2 are initial and final enthalpies of the ideal gas then i) H1=H2 ii)H2=H1/2 iii)H2=H1-(P1V1)/2 iv) H2=H1-P1(V1/V2)γ_V2

b) An ideal gas in a piston-cylinder arrangement is well insulated (ie. adiabatic wall). It is stirred slowly, so that the temperature increases to twice its value while the gas expands at constant pressure. The net work done by the gas is (considering stationary system & neglecting change of PE)

i) P(V2-V1) ii) -mCv(T2-T1) iii) –mCp (T2-T1) iv) (P1V1-P2V2)/(γ-1)

c) Which of the following statement is true

i) in an ideal gas (Cp/Cv) is a function of temperature

ii) internal energy is function of temperature only in simple compressible substance iii) expansion work done in an adiabatic process of a simple compressible system is

(P1V1-P2V2)/(γ-1)

iv) pressure & temperature can identify the state of a simple compressible substance

d) An ideal gas in a closed system goes through an quasi-static expansion process in which volume doubles. Which process will lead to the larges work output?

i) isothermal process ii) polytropic process with index 1.25 iii) with polytropic index 2 iii) with polytropic index 0.8

e) If the pressure is smaller than saturated pressure (Psat) at a given temperature T, then the

phase may be

i) sub cooled liquid ii) saturated liquid iii) saturated vapor iv) superheated vapor

Group B

2. Answer any two of the following [ 5+5=10]

a) Derive steady state energy equation for one inlet port and one exit port.

b) Consider an Adiabatic Cylinder -Piston arrangement as shown in the figure. The cylinder is filled with 1 kg of dry saturated water-vapour at 8.8 bar. The piston is compressed such that the pressure inside the chamber increases and the volume is reduced to half the initial volume. At the end of the process, the state of steam is still that of dry saturated vapour. What is the final pressure of the system (in bar)?

c) How kinematic & dynamic viscosity changes with temperature & pressure? Draw the

Group C

3. Answer any two from first four (a,b,c,d) & one from last two(e,f) [5+5+5=15]

a) A closed system contains 10 kg of an ideal gas. The initial state is 10 bar, 300 K, and the final state is 5 bar and process is isothermal. The process is not necessarily quasi-static. During the process, electric work of 50 kJ is absorbed, and the heat loss is 30 kJ. Sketch the process on a p–V diagram. Determine (a) change in energy, (b) expansion work, (c) total work.

b) A rigid metallic container is separated into two equal parts by a thin partition. One part contains 1 kg of saturated liquid water at 1000_{C. The other part is evacuated. The partition is}

broken, and equilibrium reestablished after some time. During the process, the temperature of the system is maintained by immersing it in an oil bath maintained at 1000_{C. Determine (a)}

final state of steam, (b) work done, and (c) heat transferred.

c) A centrifugal air compressor compresses 5 m3_{/min of gas from 10 N/cm}2 _{to 70 N/cm}2_{. The}

inlet and exit specific volumes are 0.8 m3_{/kg and 0.4 m}3_{/kg respectively. The duct diameter is}

10 cm at the inlet and 5 cm at the exit. Determine (a) rate of flow work, (b) mass flow rate, and (c) change in velocity.

d) A cylinder fitted with a piston has a volume of 0.1 m3 _{and contains 0.5 kg of steam at 0.4 MPa.}

Heat is transferred to the steam until the temperature is 300◦_{C, while the pressure remains}

constant. Determine the heat transfer and the work transfer for this process.

e) When a viscous fluid flows past a thin sharp-edged plate, a thin layer adjacent to the plate surface develops in which the velocity, changes rapidly from zero to the approach velocity, U, in a small distance, δ.

This layer is called a boundary layer. The thickness of this layer increases with the distance x along the plate as shown in figure. Assume that u=Uy/ δ and

U x 5 . 3 ν =

δ where ν

is the kinematic viscosity of the fluid. Determine an expression for the force (drag) that would be developed on one side of the plate of length l and width b. Express your answer in terms of l,b, ν & ρ;where ρ is fluid density.

f) The viscosity of liquids can be measured through the use of a rotating cylinder viscometer of the type illustrated in Fig. In this device the outer cylinder is fixed and the inner cylinder is rotated with an angular velocity ω, the torque

_T

o i,R

R , l , ,ω