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ExlCh.Eff/21411l1201l1SPL

BACHELOR OF CHEMICAL ENGINEERING EXAMINATION,2011

( 2nd Year, 1st Semester)

MECHANICS OF FLUIDS

Time: Three hours Full Marks: 100

( 50 marks for each Part )

Use separate answer scripts for each Part

RT

-

I

Answer Question No 1 and any two from the rest

Assume any missing data

1. a) A velocity field is defined as

V=

3yi

- 6x]

8/10/2019 2nd-1st sem-2011Q

2/23

. J ::

[2J

2.

a)

-.

Patm

Fig 1

The Lid) ratio for both the branch o-a) and o-b) refer to

Fig 1) are 100. The Leq/d) ratio for a globe valve is 340 and

that of a gate valve is 8. The diameters of two branches are

same. Find the ratio offlow rates through line -a) and line

o-b) considering the Fanning friction factor to be invariant

of Reynolds. number fuUy rough zone). 5

b) Consider expansion of

multiple

n number of tubes each of

diameter do) into a header of diameter D Refer to Fig 2

or

turbulent

flow

0 Derive an expressionror pressure differentialP,-P2

i

h) Derivetheexpressionor mClionalloss,h

I

Consider that at section I the pressure is uniform across the

ross section

[ 3 ]

3.

a) You are an engineer for a company and are to select an

appropriate fluid meter from your waterhouse stock to

measure the water flow rate in a 6 inch nominal diameter)

schedule 40, horizontal commercial steel pipe. The fluid

meter is needed immediately, so no time is available for

machining or modification. The flow rate is estimated to be

3 3

between 0.0065 m /s and 0.-025m Is. A mercury manometer

is to be used to measure the appropriate pressure difference

to determine the flow rate.

Your instructions are to choose a fluid meter to determine

the flow rate with a maximum uncertainity of 10

percentage error) because of errors in reading in

manometer. You estimate that the manometer can be read

with an uncertainity absoluteerror) of 0.15 cm.

Net pressure drop across the meter must not exceed 7 kPa.

The following meters are available

Type of flow meter

Venturi

Throat / orifice diameter

4.5 in

Thin-plate orifice

2.5 in

Consider that the dischargecoefficient of venturimeterand

orificemeter are 0.94 and 0.61, respectively. The inside

diameter for a 6 inch Schedule40 commercialsteel pipe is

6.065 i:lch.

u ;

lL

i

f

A

do

f

1

1

ID

,

f

]I

I

Y

Fig

2

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[4J

4.

b) Explain the working principle of a rotameter. Why is itcalled

as an area meter ? 12+4

Water (at 25C, p =1000 kg/m3, /l = Icp) flows from a large

reservoir (zl = SSm) to a storage tank (z2 = 5m), as shown in

Fig.2. The pipe entrance at B is well rounded. The pipeline from

B to C contains 4 gate valves, three standard 90 elbows and

one tee with flow through the main run. The pipe line

trom

D to

E contains four gate valves, six 90 standard elbows, two 45

standard elbows, one tee with flow through the main run and a

venturi meter. The venturimeter is installed to measure the flow

rate. The reading of the manometer (manometric fluid mercury,

p

=

13600 kg/m ) connected between the upstream and the

throat of the venturimeteris 75cm. The pipe line is 300 m long

I

and is a 2 inch Schedule 40 (inside diameter 2.067 inch) steel

pipe. The loss coefficient (k) data for commercial(2 inch) pipe

fittingaregiven below:

Gatevalve

90 standardElbow

0.16

0.95

Tee, line flow

0.90

The discharge coefficient of venturimeter, Cv = 0.98.

Calculate (i) the

ow

rate through the pipeline, (ii) the power

input to thepumpfor theoverallefficiencyof 85 .(iii)pressure

[ 5 ]

~

~~7~ y]

Fig.

5. A catalyst having spherical particles of Dp= 50 microns and

Ps=1.65g/cm3is to be usedto contact a hydrocarbonvapor in a

fluidized reactor at 480C and I atm pressure. At rest the bed

has a porosity of 0.35 and a height of 1m. At operating

conditions, the fluid viscosity is 0.02 cp and its density is 3.4

kg/m3.The porosityat minimumfluidizationvelocity is 0.42.

a) Determine

i) the superficialgas velocitynecessaryto fluidize the bed

ii) the velocityat which the bed would begin to flowwith

the gas

ill) the extent of bed expansion when the gas velocity is

averageof velocitiespreviouslydetermined.

b) Does aggregative/ particulatefluidizationoccur?

The ErgunEquationfor flow through packedbed is as follows:

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[6 ]

RT

-

II

Answer

any three

questions.

All questions carry equal marks.

2 marks reserved for neat and well organized answer script.

Assume any missing data.

6. a) Find the dimensionality and diu:ctionality

for

the velocity

field given by V =axi + bX2j::..~xtlc (a, b, c are constants).

2

b) Consider a flow field given by V = Ai + btj, A = 2m/s,

B=0.3m/s2.Find the equation of pathline followed by the

particle located at (x, y = (1, 1) at the instant t = O. 4

c) A steady, incompressible flow is given byV =Axi

-Ayj; with

A = 2s-I. Determine the stream function that will yield this

velocityfield. 4

d) The velocity profile for an incompressible fluid at the

entranceto a pipe is flatas shown inFig.6.At section2 it is

parabolic and is given byV = Vm(1-r21R2).

Obtain the drag

force

F acting on the fluid in terms of the

pressure PI' P2' density p, Voand R. 6

[ 7 ]

7. Heavy oil having a specific gravity of 0.85 and an absolute

viscosity of 4x 10-2N.s/m2 is pumped through 20m ofO.052m

inside diameterPVCpipe(zerorelative roughness).Thepipeline

is shown in Fig.7and containsonecheckvalve,two gate valves,

four 45 standard elbowsand a nozzlewith a throat diameter of

0.026m. A manometer connecting the inlet and throat of the

nozzle reads 2.0m of mercury (specific gravity of 13.6). Find

the pressure loss between points 2 and 3. Neglect loss in the

nozzle.

Draw the nature of the Energy grade line and hydraulic grade

line.

Fitting

Checkvalve

Gatevalve

45 standard elbow

Loss coefficient

2.1

0.16

0.30

13+3

q.(j. ~L

~

- --

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[ 8 ]

8.

a) Petroleum oil of specific gravity 0.9 flows through a

horizontalpipe. A pitot tube is inserted at the center of the

pipe and its leads are filledwith the sameoil and attachedto

a U tube containingwater.Thereading of the manometeris

90 cm. Find the velocity at the center o f the pipe. 4

b) In fully rough zone friction factor is invariant of Reynold s

number justify with reasons. 3

c) Water is in turbulent flow through at 50 mm J.D. tube. The

pressure drop is 1.57 kN/mo per meter of tube. Calculate the

thickness oflaminar sublayer and buffer layer. Find the eddy

viscosity. Assume water viscosity as IO-3kglm.s.

The universal velocity distribution is given as follows

u+ =y+; O;s;y+;s; 5;u+ =-3.05+5Iny+; 5;s;y+ ;S;30

u+

=

5.5 + 2.5In y+; y+ ~30

d) Cd vs. N Re,pcurve for flow around a sphere shows an

abrupt decrease in drag coefficientat Re=3x 105. 2

9.

a) Draw the shear stress vs. deformation rate curve for

Binghamplasticandpseudoplasticfluid. 2

b) A water jet pump has jet area 0.01m2 and jet speed 20m/s.

The jet is within a secondary stream of water having speed

Vs=2m/s. The total area of the duct (the sum of the jet anl1

2 .

[ 9 ]

stream. The pressures of the jet and the secondary stream

are the same at the pump inlet. Determine the speed at the

pump exit and the pressure rise P2- Pl IO

V

2 W\1 s

= ~Js

--Q,) V)

O

cl.. :.o

t:W

- V) .Q

- :::

0

cv -

cJ ) Co.>

QJ (1) f O

-- 0. 0

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c: CLJ

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0.2 04 0.6 0.8

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103

2(1o } 3 4 5 6 S 10.

2(104} 3 4 5 6 8 105

0.00001

-.- -- 6-e1oe

7 -21107} 3-4_5 ,-,--

10

~

- Qonn,,-

E D - VU()5

--..

f)

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Reynolds number

R

=v

Figure 7.9

The Moody chart for friction factor from [3] .

0,1

0.09

0.08

0.07

0.06

0.05

0.04

....

....

0

0.03

U

2

c

0

....

0.025

;::;

ro

Q)

0::

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F Pipe diameter in feet D

0.5

8

1

.2 0.3 0.4

I

0.6 O.

,.,

0.01

0.008

0.006

0.005

0.004

0.003

,..,.

0.06

0.03

0.02 I.~

0.05

0.04

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0.03

0.025

0.002

VI

Q)

0.

0.

s

0.02 g

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Q)

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+=I

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0.0006

0.0005

0.0004

0.0003

0.018 ~

c:

~

;:,

0.016 -e

;:,

....

Q)

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Q)

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r

5 ?l

.

9. ~ 0

a

2. ...

C Q.

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., c '

3

-g g

...

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..

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N

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~ 8IINTEftNALINCOMPRESSIBlEViSCOuS FlDN

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FIg.8.15

50 80 150 300 500 800 1500 3000 SOOO

40 60 100 200 400 600 1000. 2QOO 400Ci'

Pipe diameter.p (millimeters)

Relative roughness for pipes of common engineering . mater ials . (Data

from~ usedPx..p .mILSJion

.

30

.

0 0

is

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[ 2 ]

.

6. a)A bracketis fixed to the wall by means of 4 identicalbolts and loadedby a vertical load as shown in.-

Fig. 6a. Material of bolts is C30 C.S (Gy=340

N mm2

and factor of safety is 3. Determine the nominal

diameterof the bolts. 10

b) A bracketis supported by means of 4 rivets of samesize, as shown in Fig. 6b. Determinethe diameterof

the rivet if the maximumpermissible shear stress.is 140MPa. 10

1~

i

SQO

f~

7S

T

~..

Fig. 6a

600

~

40kN

20kN

80

~

4-

t

~

f -

I

1

,;

/

Fig. 6b

7. a) Why is the cross-sectionof the flat belt pulley armelliptical? The major axis of an ellipticalpulley arm

placed inthe pl~e of rotation -Justify the statement. 2+6

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BACHELOROF CHEMICALENGINEERINGEXAMINATION,011

2nd Year, 1st Semester

MAmEMATICS

-

Time: Three hours

Full Marks: 100

Answer any six questions.

[ Four marks reserved for general proficiency]

I. a Find the necessary and sufficient condition for the ordinary

differential equation M x,y dx +N x,y dy =0 to be exact.

8

b Solvethe differentialequation

8/10/2019 2nd-1st sem-2011Q

13/23

[ 2 ]

b) Show that d~[ x-oJo (x)J ==-X-oJo+I(X).

c) Show that J _1 (x)

==

cosx .

2

4.

a) DefineLegandredifferentialequation. Provethat

Po(x)==~~

(

2-

1)

0

ill

20 dx x

b) Prove that xP~(x) ==

P~-I

(x) + nPo(x) .

c) Prove that Po(I)

== I.

ao 2

5.

a) Show that fe-x Hm(x)Ho(x)dx==O, m:;t:n

-ao

==2ill~, m ==n

{

xt

}

exp --

ao

b) Prove that

. ~-t == LLn(x)to.

0=0

c) Show that L2 (x) ==

~ (

x2

- 4x+2).

fl [;2

6. a) Solve ~

==X2

-t

using method of separation {)f

at

variables.Given that y(x,O)==f(x),

Zl o

==g(x).

[ 3 ]

4

b) If a string of length I is released from rest in the position

y

== 4A.x (~

- x) . Show that the motion is described by the

I

4

equation

y(

x t

)

- 321..~ 1 . (2n+1)1tX (2n+1

)

1tat

, - 3.J 3sm cos

7r 0=0

(2n+I) I I 8

2+6

6

~ 2 U

.

7.

a) Solve at

==

a 2 for 0 0 gIven that

2

Ux(0, t) ==Ux(1t,t ) ==0 and u (x,0) ==sin x .

8

b) Solve a2~ + a2~ ==0, which also satisfies the following

Ox Oy

boundary conditions u(O,y) ==

u l,y

==u(x,O) ==0 and

8

u( x,a) ==sin n1tX

I

.

8

()

8. a) A periodicfunctionof period 4 isdefined as

f(x)=lxl

-2

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[ 4 ]

9. a) State D Alambert s ratio test for convergence of infinite

series. 2

b) Test the following series for convergence

1 x3 1.3 x5 1.3.5x7

x+--+--+--+...

2 3 2.4 5 2.4.6 7

6

c) Test for the convergence of the series

i)

1 1 I

-+-+-+...

1.22 2.32 3.42

co

ii)

. .

n=lnn

8

8/10/2019 2nd-1st sem-2011Q

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D

0r.t L

C.w- ~)

ExlCh.E/Chem.lT /212/10/20 1

~SP\..

BACHEWR OF CHEMICALENGINEERINGEXAMINATION,011

( 2nd Year, 1st Semester)

PHYSICAL CHEMISTRY

Time: Three hours

Full Marks: 100

Use a separate Answer-Script for each part.

( 50 marks for each part )

PART

-

I

1. a) Define an ideal black body and give an example that

approximatelyrepresents it.Describe Stefan-Boltzmannlaw

of black body radiation. Show how it is consistent with the

Planck s distribution of frequency (v) dependent energy

8/10/2019 2nd-1st sem-2011Q

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[ 2 ]

2.

a) Describe a Hermitian operator and show that the eigen

functions of a hermitian operator having different eigen

values are orthogonal.

b) Evaluatethecommutator,[H,x], whereH isthe Hamiltonian

operator for a free particle.

c) State the Heisenberg s uncertainty principle. Find the

uncertainty in speed of an electron located within an atom

with positionaluncertaintyof 50 pm.

d) What is the probability of the I-s electron of a hydrogen

atom to be found in a spherical shell of radius r and r +dr

around the nucleus? Also find the most probable radial

distance of the I-s electron fromthe nucleus.Given, the I-s

orbital wavefunction of the hydrogen atom,

(

1 r

112--

l l-s (r) = J;c aJ .e ao ; (ao- Bohr radius).

3+3+5+6

3.

a) Define absorbance. Provide suitable justification for the

Lambert-Beer s law and state the reasons for the

photochemicalsystemsshowing deviations from it.

b) An electron is confined to a molecule of length 1.0 nm.

Consideringtheparticlein a boxmodel,find(a) itsminimum

energy and (b) the minimum excitation energy for the

electron from its lowest energy state.

c) Using rigid rotor model for studyingrctational motion of a

diatomic molecule, explain the equally spaced microwave

[ 3 ]

spectral lines observed experimentally and mention its

usefulness.

d) The force constant of the bromine molecule C~r 79Br)is

240Nm-l. Calculate the fundamentalvibrational frequency

and the zero point energy of the molecule. 5+5+4+3

P RT II

4.

a) How does viscosity of a liquid change with change of

temperature? 3

b) How can you determine the molecular weightof a polymer

molecule by measuring viscosity? 4

c) How does the vapour pressure of a liquid vary with

temperature?

3

5.

a) Stateand deriveBragg s equation.

4

b) A cubic lattice have X-ray diffraction from (Ill), (200),

(220), (311) and (222) planes. Determine the type of the

cubic crystal. 3

c) What is law of symmetry?How many symmetryelemt:nts

are there in a simplecubic latticeand what are they? 3

6.

a) Whatdoyoumeanbydipolemoment?Whichone ispolar-

NH) orBF)?Explain. 2+2

b) Define specific rotation. On which factors does specific

rotationdepend? 3

[ Turn over

8/10/2019 2nd-1st sem-2011Q

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[ 4 ]

c State and explainNernst Distribution law.

3

7. a How can you distinguish between electrochemical cell and

electrolytic cell?

3

b What is calomel electrode?

3

c How can you titrate a weak acid by a strong alkali

potentiometrically? 4

8. a Compareconductanceof 0.1N HCIand 0.1N NaCI solution

and explain. 3

b Calculate the pH of a mixture of 10 ml 0.1 N AcOH

8/10/2019 2nd-1st sem-2011Q

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~\

V

BACHELOROFCHEMICALENGINEERINGEXAMINATION,011

( 2nd Year, 1st Semester)

NUMERICALMETHODS

2

f)-

2roL ~ C.4.l~)

E

ExlCh.E/T/215/11/20111SPL

Time: Three hours Full Marks: 100

(50 marks for each part)

Use a separate Answer-Script for each part.

.

PART- I

Answer ny three questions.

All questions do not carry equal marks.

1. a) Consider a general 3x3 symmetric matrix in the following

form :

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[2 ]

with the conditions, x ==Y==1 at t = o. Find the largest

possible step size that you can use in solving the above set of

equations by explicit Euler l11ethod. Perform one step

integration with the above determined step size value.

10+10=20

2.

a) Solve the following set of linearsimultaneousequations by

.

Thomas Algorithm:

[

~ : ~I

][

~

]

=

[

~

]

-1 3 x3 3

b) DeriveDoolittle s Algorithm for solving a generalized set

of linear simultaneous algebraic equation. What are the

advantages or disadvantages of this method over

conventionalGaussElimination? 8+7=I5

3.

Answer any three questions:

x5= 5

a) When and why will you use Pivoting strategy in solving a set

of simultaneous algebraic equations?

b) When will you call a system of equations to be ill-

conditioned? What is condition number?

c) Whatdo you meanby local truncationerror?How can you

assess the stiffness of a set of ordinary differential

equations?

d) In some commercial software for solution of ODEs, the step

size isvaried as the integration proceeds. Why is itdone so?

~

[ 3 ]

4.

a) Considerthe followingset of equations:

[

2.1 5.7

][

XI

] [

1

]

.8 10.3 x2 = 2

It was observed that an attemptto solve the above set of

equation by Gauss Elimination with two decimal place of

accuracy results in a wrong solution. Explain this

observationbasedonconditionnumber,derivedon the basis

of SpectralNorm.

b) Solvethe followingordinarydifferentialequation byHeun s

method (predictor-corrector method) from x

=

0.0 to

x =4.0 with a step size of 1.0.

:

=

4eoosx 0.5y with the initial condition y =2.0 at

5.

x=O.

a) Use Fadeev-Laverier s method to determine the

characteristic polynomial for the x coefficient matrix as

stated in problem 2(a).

8+7=15

b) Consider the following differentialequation, which can be

developed by steady-stateheat balance for a long thin rod

that is not insulated along itslength:

d2T + h

(

T

-

T

)

=

0 whereh is convective head transfer

dx2 a

coefficient (m-2) and Ta is the temperature of the

surrounding air. Use Shooting method to solve the above

[ Turn over

8/10/2019 2nd-1st sem-2011Q

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[ 5 ]

[4]

PART-II

Answer any three questions.

All questions carry equal marks.

7. Use the methodof exploration followedby the method of false

posi tion or chord) t o fi nd t he three roots of: 1.8xl - sin lOx

=

0

with an accuracy of 0.001.

equation for a 10m rod with h = 0.0Im-2, Ta=20C and

use the followingboundary conditions :

T 0)=40 and T 10)= 200.

Hint Takeinitial guessvaluesfor ~~ tobe 10and 20.)

7+8=15

6. The one-dimensionalheat conduction problem in a rectangular

fin can be expressed by the following parabolic partial

differentialequation:

8.

Solve the equation: 2 10glOx - ~ + 1

=

0

2

Startingwith the values x=1 and x=5 with an accuracy of 0.001

using Newton-Raphson Method.

Fitthe followingtabular data to theArrhenius equation:

k

=

Aexp - E

I

RT) by the method of least square where the

symbolshave their usual significance.

a T

-=a.-

at ax2

The initial and the boundary conditionsfor the above PDE can

be expressedas follows:

9.

i) At t = 0, T = 3 0, for all x , 0 ~ x ~ 1.

ii) At x = 0, T = 150 for t > 0 .

ill) At x = 1 ,

or ax

=0

Develop the solution scheme for solving the apove PDE by

Finite Difference FD) method taking 2 internal grid points

with Crank-Nicholson method being used for solution of

resultant set of ODE-IVPs. Develop the complete solution

algorithmand perform one iteration. 15

10. For the functiongiven as a table:

determine the value of the argument corresponding to the value

0.892914 of the function.

[ Turn over

T K)

310

350

380 410 450

k hr-l)

1.7x 10-4

0.018 0.31

3.53 54.7

x 1.435

1.440

1.445

Y 0.892687

0.893698

0.894700

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[ 6 ]

1

11. Calculate Jcosx dx using Simpson s formula by dividing the

0 l+x

interval 0, 1) into a total of four equal subintervals.

12. Find the first derivative at the point x

=

50 for the function given

as the following table:

x

50 55 60 65

f 1.6990 1.7404

1.7782 1.8129

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Ex/Ch.E/MErr/213/1O/20 II

sP

BACHELOROF CHEMICALENGINEERINGEXAMINATION,011

( 2nd Year, 1st Semester)

ENGINEERING THERMODYNAMICS

Time: Three hours Full Marks: 100

.

Answer Question No.1 and any four from the rest.

Steam and other tables are permitted if necessary.

Assume any unfurnished data, consistent with the problem.

.

.

1. A Define:Heat,Work,Environment.

vb)

x =6

Plot the following diagrams for water:

i) Isobaric processs on T-v plane from solid phase to

superheated vapour phase. @.

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[ 2 ] [ 3 ]

ill) specific heat supplied.

jV) Plot the process on T-vplane.

4+4+12=20

and 150C,doing work. Heat loss from the system to the

surrounding is 2 KJ during this process. Assuming the

surrounding to be at 25Cand 100KPa, determine

i) exergyof the steam atthe initial and final states.

3. a) State the First lawof Thermodyanicsfor a cycle and hence

deduce the first law for a non-cyclic process.

b) Ina steam p~wer plant steam leaves the boiler at 2 MPa and

300C. The steam then leaves the turbine and enters the

condenser at IS KPa and 90% quality. Finally, it leaves the

condenser and enters the pump at 14 KPa, 45C. The pump

work is 4 KJ/Kg. Determine

i) Turbine work.

ii) Heat transfer in condenser and boiler.

ill) Thermal efficiency of the plant.

iv) Plot the process on T-S diagram.

ii) exergy change of steam.

ill) exergy destroyed.

iv) The 2nd law of efficiency.

f ---

4+4+12=20

6.

a) Establish the Maxwell relations.

6

b) Define mean effective pressure.

2

8+12=20

c) An air-standard Dieselcycle has a compression ratio of 16

and a cut-off ratioof 2.At the beginningof the compression

process, air is at 95KPa and 27C. Determine

i) the temperature after the heat addition process.

.

4. a)/State the '2nd law of Thermodynamics' and show that

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...~ , entropy is a property.

~

~

~e.,,>' 7 ~~

j?

Onekilogramof Ammoniain a piston/cylinderarrangement -

D

'i/'\ at 50C, 1000 KPa is expanded in a reversible~ ~

.

of--

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