MECHANICAL ENCINEERING

TimeAH<med: 3 hours IIIIximum IIIIrks 300
Candidates should attempt Questions Nos. 1 and 5 which are compulsory, and any three of the remaining questions selecting at least one question from each Section.
Ifany data is considered insufficient, assume suitable value. Use ofpsychometric chait is permitted.

SECTION A

1. Answer any three of the followmg parts (answer to each part should not exceed 200 words) (20x3=60)
ConSider a Carnal cycle heal enllne operating m the outer space. Heal can be rejected from Ills engme only by thermal radiation, wllch is proportional to the radiator area and the fourth power of the absolute temperature of the radiator Show that for a given engme work oUllul and liven temperature of the IIgher temperature reservOlr the radiator area will be a ffilll1ffiUm when the ratioT,/TH=3/4

A fhll conlamed m a honzonla! cylinder fitted with a frictionless leak-pro of PiStOn, is continuously agitated by means of stirrer passmg through the cylinder cover The cylmder diameter lS 0.40 m Dunng the stimng process lasting 10 mmutes, the plSton slowly moves out a distance of 0.485 m agamst the atmosphere. The net work done by the flmd dunng the process lS 2 kj The speed of the electric motor dnVlng the stirrer IS 840 rpm Detenmne the torque m the shaft and the power oUllut of the motor

A Simple carburetor has a ventun throat diameter of 20 mm and the coeffiCient of flow lS 0.8 The diameter of the fuel onfice lS 1 14 mm and the coeffiCient of fuellS 0.65. The gasolme surface lS 5 mm below the throat Calculate­

The air-fuel ratio for apressure drop of 0.08 bar when the nozzle tip lS neglected;

The air-fuel ratio when the nozzle tip lS taken mto account;

The ffilmmum velocity of air or cntical air velocity reqUired to start the fuel flow when the nozzle tip lS proVIded Assume the density of air and fuel to be 1 20 kg/m3 and 750 kgim3 respectively

ConSlder a diffuse Circular disc of diameter D and area Aj and a plane diffuse surface of area A All The surface are parallel and lS located at a distance L from the centre of Aj Obtam an expressiOn for view factor

The configuration of a furnace can be approXimated as an equilateral triangular duct which lS suffiCiently long that the end effects are neglillble. The hot wall is maintained atT, 900 K and has an effilsSlvity 0.8 The col d walllS at 4 00 K and has an emlSS! vity co 0.8 The third walllS reradiating zone for which Q3 0 The accompanymg sketch illustrates the configuration Calcul ate the net radiation heat flux 1eavmg the hot wall


l.B
The diagram shows a truncated conical section fabncated from a matenal of thennal conductivity K The circular cross-section of the comcal section has the diameter D ax, where alS a constant and x lS the aXial distance of the section from the apex of the cone. The temperatures at the two end faces of the comcal section (at distances and from the apex) are respectively and while the lateral surface of the truncated cone lS thennally msulated


Denve an expreSSiOn for the temperature distribution m symbol1c fonn assunung one­dimenSl onal steady-state conditions. Sketch the temperature di stribution


Calculate the heat rate through the cone m x-direction


A refrigeration system operates usmg SImple saturated cycle with a certam refrigerant The condensmg and evap orating temp eratures for the refrigerant are 35°C and _15°C resp ectively Deternune the COP of the system If a liqUId vapour heat exchanger is mstalled m the system, with the temp erature of the vap our leavmg the heat exchanger at 15°C, what will be the change m the COP? Use the followmg data for the refrigerant used



"
" 69.5
181.0

SUpellleall!d


2Q K




"




0.731

0.663g i 216.4
0,7052


10 cu m of almosphenc atr at 25°C DBT and 12°C WBT is flOWIng per nunute through a duct Dry saturated steam at 100 DC lS mJected through the duct Dry saturated steam at 100 °C 1SmJ ecled mto the air stream with a rate of 1 2 kg/mm


What 1s the temp erature 0f air after m1Xmg the steam?


What 1s the relative hunudity of air after nuxmg the steam?




Sketch the axial-flow turbme cascade. Show the veloCIty with Its components at enlly exit mdicating the forces exerted by the flow on blades. State the expreSSiOn of Ideal lift m tenns of flow angles and show that itlS equal to pCm where Cm 1Sthe mean velo city and llS the circulation


The first aXial-flow air compressor stage Wlthoutmlet gUIde vanes lS operating at a speed of 15000 r.p.m m the almosphenc conditions of To 288 Po 101 bar. The rotor mean blade nng diameter lS 0.34 m and hub to tip ratio lS 0.5 Almosphenc air enters the stage with a velocity of 150 m/s. ConSlder constant 8111al velocity through the stage and take stage effiCIency as 0 86, mecharucal effiCIency as 0.97, work done factor as 0.97, Cp 1 005 kJ/kg/K and R 0 287 kJikg/K Sketching the 8111al compressor stage WIth velocity diagrams and labelling with most general notations used m practice, detennme the folloWIng for atlallllng relative velocity rali on across rotor (de Hall er numb er) 0f 0.73


Mass flow rate m kg/s


M8Xlmum Mach numb er at rotor blade at enlly




Angles made by relative and absolute veloCIty at rotor entry and exit with axial directi on

Power reqrnred to drive the compressor


Stage pressure ratio




SECTION II
Answer any three questions (20x3=60)
Sketching 'load curve' and 'load duration curve explam the1f purposes Define also 'demand factor' and 'plant-use factor The loads for certam mdustnes are tabulated below for 24 hours. Dunng load duration and 10 ad curve, find power reqUired for 40% 0f the time of the day If the capacity 0f the power pI antlS 35 MW, find the cap acity factor 0f the power plant
Time 6AM 8AM 9AM IIAM 2AM
o to to to to
8AM 9AM I lAM 2AM 5AM
Load 18 26 30 22 24
(in M1N)
Time 5PM 8PM 12PM 5PM
to to to to
8PM 12PM 5PM 6PM
Load 30 20 15 16
(in M1N)

If the load lS supplied by two power one lS acting as a base load planthavmg capaCIty of25 MW and other as peak load planthavmg capacity of 10 MW, find load factor, capaCIty factor and use factor for both power plants
The stator blades of a gas turbine are supplied with gas whose stagnation enthalpy ho and stagnation temperature To with radius r There is cylindncal flow through the stator blades lS reversible and adiabatic Show that, m the cross-sectional plane at exit from the stator blades

.. O"""a +Cdo
Hence, when the gas can be assumed to be a perfect gas and the stagnation pressure Po lS constant over the annulus, show that


A quarter-scale turbme modellS tested under a head of 10.8 m. The full-scale turbine lS reqUired to work under a head 0f 30 it and to run at 7. I4 rev/s. At what sp eed the model must run? Ifit (model) develops 100 kW and uses I 085 m3 of water per second at this speed, what power wlll be obtamed from the full-scale turbme, its efficiency bemg 3°10 better than that of model? WhatlS the dimensiOnless sp eCifi c speed 0f Full-scale turbme?


Steel ball beanngs 50 a =1.3 x 10.5 haVing a diameter of40 mm are heated to a temperature of 650°C and then quenched m a tank of oil at 55°C. If the heat transfer coefficient between the ball beanngs and the olllS 300 detenmne


the duration 0f time the beanngs must remam m 011 to reach a temp erature 0f 200°C;


the total amount of heat removed from each beanng dunng this time;




the mstantaneous heat transfer rate from the beanngs when they are first immersed m oil and when they reach 200°C

Define Rayletgh flow and mention its govemmg relations. Usmg them, establish the expreSSiOn for the flow m the form p Const, where G lS the mass flow rate per unit

area. Show the plot of this equation on h-s and p-v planes. Show also that at maximum enthalpy state


For the Rayleigh flow, establish the expression for TiT* tenns 0f Mach numb er, M


Air enters a 5 em diameter frictionless duct with a Mach number 2. Its static temperature lS 250°C and stagnation pressure 6 bar. For increasmg Mach number to find the amount of heat to be transferred and change m static temperature You may use the followmg table for


airhavmgy= 1.4
N TIT* PolPo ToiTo*
2 05289 0.3636 1503 0.7934
3 02803 0.1765 3.424 06534


Why lS the use of dust collector necess"'Y m case of thermal power plant? Discuss the location of electrostatic precipitator with reference to sulphur content of coal and flue gas temp erature


From the followmg data for the underfeed stoker boiler, find draft requued m mm of water colunm and power requued to dnve the fan


Mean temperatures of flue gases passmg through duct 227 °C PI enum pressure I 5 cm 0 f water Atmosphenc pressure 75 cm of Hg Mean velocity of flue gases m duct 900 m1nun Length of the duct 150m Mean Size ofthe non-circular duct 75 Numberof900bends 4 Numberof45°bends 4 Loss 0fdraftmevery90°bend 0 Icm 0fwater Draft avatlable from chimney I 5 cm of water Fuel bed reSiStance for underfeed stoker I 0 cm 0 f water Fan efficiency 60% Motor efficiency 92.5% Assummg that 45° bend is eqU1valentto one-half of 90° bend, reSiStance offered by non­circular duct lS 20% higher than a Similar circular duct, friction factor for arcular duct lS 0.006, find draft reqU1red to be produced by fan and the fan power for flue gases Take R 294.353ikg-K
To avOid havmg additional mlet and outlet pipes through the wall of the pressure vessel of
pressunsed water nuclear reactors, itlS usual to employ a steam -heated reheat cycle. Steam lS bled from the boiler delivery main to reheat the steam leaVing the high-pressure turbme before it enters the low-pressure turbme. The data for the cycle are as follows
Boiler outlet condition Saturated steam at 60 bar
turbme mlet pressure 5 bar
Condenser pressure 0 05 bar
HP turbine isentropic efficiency 0 80 bar
LP turbme lSentropic effiaency 0 87 bar
Reheat temp erature 270°C

The feed pump tenns can be neglected, and it may be assumed that the bled steam leaves the reheater at a temp erature equal to that at the high-pressure turbine exit, Determme the dryness fractions at the high-and low-pressure turbine exit and the cycle efficiency
Also detennme these quantities if no reheating were used. Comment bnefly on the result

lor ........n .-.1


..... tho SlID, ,h. w.... tIo, lIII{ ..I.....




,..
." ...-" ......", ._. 0000"•


... ._.._.
._.
.W


..
·n

.>0
....,... ."'".. ...."......,,, Ill
.....L... NIOII'
..,." •w,. ...,. .....,. ...-,. ....
,..

....,.,
trJ:l --...... ..-.

··u " ..." .-. ... ...

u..... _00

.U H,n

·n Dn," .-onL" .oil'
· ..". .oo oo,H """. oOL:N
H" ...t.!. 04"6
...·.1 ....., H,U

......, ...,.
••
• "".
. H 106:11: _.. ... •••...
... ,.. >oW ....,
...:1
.-....,. "m --....

·"
_..
.<OJ. .-...., ......


·n ,..
II
e·"" ..m
d" ....""".. ."" >om ..,...., ,,-...... .."W'
"""
_i.. ..,.., ....as ...... ..m ..,.." ..,....
." ..... ..,.36 ITtl
..,." .".. ..-.-...."
."... ...--". ......


""" ..-"m
.-..­
.,. ...", ..:IIl·4 ..,..I ".'11
""" 0""
... .-,-....n .m,.,...6 ...""" .."..
...

... ..... ...,.1 .."..
••• ...-."OJ
om, ."u
...... ...... "..",.. """om. .­
-.... ,-......""" .. ...., ......
..-• ••• ....,
Cumulative distribution function for the standard nonnal eli stribution
M

• •• ._. .-0":11.

.., .,..50,. """00 ...... """. -......,
•
"'....
u...n
... ... 511" "'.... .
......,
ali003
·., ""..,. ._. .-...

... "or.. ....

••• om. ._. .....9 Q"" r.,z;.
c·....
... .n"

... ."" on.
II 0·"""

GO:U
"".
.., ".,...
......, ....,.
.-..­
" ......" .."
" ....... -.... ..-.._'m.. ..-..",e



.mm
...
--.--.......

".. ._.
·,.. ".. ...."'.
....,

""".
... ....... 0 ...., _.. -n..u ...._.,,... 6411.1• .....
."." •
... n....'9 n.,.


... ...." 0071• ....

." .-.......

.•., ..., """"

._.

". ._. .......


."


..-••• _ro_.. .."

."
.....u -.....,. """.,·.1
-...



.......... .,.....,.

."
." .... ..." ..... ....

." .......... ......A

."
.­

.,.

-....

._. .

0...... .... 0.....' 2m