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Problems for Homework
n S.I. Engine has a fuel-air ratio of 0.07:1.
How
many kilograms of air per hour are
for an output of 75 kW at an overall efficiency
of 20%? How many m3of air are
per hour if the density of air is 1.2 ~ g / m ~ ?f the fuel vapor has density four
that of the air, how many m3 per hour of the mixture is required. The calorific
of the fuel is 43700 kJ/Kg.
n
engine develops 50 kW at
full
load.
If
its mechanical efficiency is 80%, what is the
power? What will be the mechanical efficiency if the load is halved, if the
efficiency and friction power remainsconstant?
two-stroke C.I. engine delivers 5000 kW while using 1000 kW to overcome frictional
It consumes 2300 Kg of
fuel
per hour at an air-fuel ratio of 20:l. The heating
of the fuel is 42000 kJIKg. Find the following: indicated power, mechanical
air consumption per hour, indicated thermal efficiency, and, brake thermal
haster
,----
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..
an ideal Otto cycle the compression ratio is 8. The initial pressureand temperature of
air are 1 bar and 100 oC. The maximum pressure in the cycle is 50 bar. For 1 kg of
calculate the values of the pressure, volume, and temperature at the all pointsof
cycle. What is the ratio of heat supplied to the heat rejected, mep, work done, and
of
compressionto expansionwork?
diesel engine has a cylinder of 25 cm diameter and 40 cm stroke. Cut-off takes place
5% of the stroke. Estimate the air standard efficiency & mep. Assume clearance
and pressureat the end of suction stroke are 1.2 litersand 1 bar respectively.
compression-ignitionengine working on diesel cycle operates at a compression ratio
15 using diesel fuel of calorific value 42000 kJ1kg. The inlet air pressure and
are 1 bar and 300 K. The air-fuel ratio is 21. Calculate the temperatureand
at salient points, air standard efficiency, and mep.
engine of compression ratio 6 uses fuel with calorific value 44000 kJ1kg. The air-
ratio is 15:1. The temperature and pressure of the charge at the end of the suction
are 60 C and 100 kPa respectively. Determine the maximum pressure in the
if the index of compression is 1.32 and the specific heat at constant volume is
as Cv = 0.71 + 20*10-~ kJ/kg.K, where T is in K.
R
= 0.287 kJ1kg.K.
this value with that for Cv = 0.71
8
kJ1kg.K.
an oil (Diesel) engine working on dual combustion cycle. The temperature and
at the beginning of compression are 90 C and 1 bar respectively. The
ratio is 13:
1.
The heat supplied per kg of air is 1675 kJ, half of which is
at constant volume and half is supplied at constant pressure. Calculate the
pressure of the cycle and the percentage of the stroke at which cut-off takes
Take Cv
=
0.71 + 20'10 T kJ/kg.K, where T is in K. Compare your results with
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The heat added is 1400 kJIkg. Using the air tables, determine the maximum cycle
temperature and pressure, thermal efficiency, power and the available portion of heat
rejected. The inlet conditions are 100 kPa and 300 K. Compare your results with those
at ideal conditions.
. A test was carried out on single cylinder, two-cylinder diesel engine, gave the following
data: cylinder diameter = 200mm, stroke
=
250mm, engine speed
=
300rpm, net brake
N-m, indicated mean effective pressure 4.9*105 ~ / m fuel consumption
=
rise of cooling water = 55K specific heat capacity of water =
mechanical efficiency, specific fuel consumption and draw up
an energy balance.
During the trial on a four-cylinder petrol engine running at 3000 rpm, the brake loadwas
267 N when all cylinders were working. When each cylinder was cut off in turn and the
speed returned to 3000 rpm the break readings were 178 N, 187 N, 182 N, and 182 N.
The engine brake power follows the following law :
BP
=
(W
RPM) 27300 kW, where W is the brake load in Newton. Determine the
brake power of the engine and estimate the indicatedpowerand mechanical efficiency.
The following readingswere obtained from a test on a single cylinder oil engine working
on the four stroke cycle: Area of the indicator diagram = 4.1 cm2, length of the indicator
diagram
=
6.25
crn
indicator spring rating
=
0.9mm, cylinder bore = 105mm, engine
stroke length
=
150mm, mean diameter of brakewhee
) =
0.6m, brake load
=
18kg, spring balance reading
=
3kg, engine speed
=
culate: brake power,
indicated power and mechanicalefficiency.
The air flow to a four-cylnder four-stroke il eryine is measured by means o f 5cm
diameter orifice having coefficient o f discharye of 0.6. During the
test
on this
engine the following data were recorded: 0ore = 1@5cmsfroke = 1Z5cm engine
speed
=
1200rpm brake torque
=
147N-m fuel consumption
=
55kg/hr calorific
value = 431m k m g head across orifice = 57cm o f water ambient conditionsare
1.013 bar and
20 L:
Calculate: brake thermal efficiency BMEP and volumetric
efficiency.
. A four stroke cycle petrol engine has six single-acting cylinders of
Z
cm bore
and 9 cm stroke. 73eeqine is coupled to a brake having a torque arm radius of 38
cm. At 3300 rev/min with all cylinders operating the net brake load is 324
N
When each cylinder in turn is rendered inoperative the average net brake load
produced at the same speed by the remainiry five cylinders is 245 N Estimate the
indicatedmean effective pressure of engine. With all cylinders operatiry the fuel
consumption is 0.3 @/mini fuel calorific value 42000 kJ/kg; the acket water flow
rate and temperature rise are 65 kg/min and 12
L:
On test the eryine is enclosed
in a thermally and acoustically insulated box throqh which the output drive
water fue[ air and exhaust connectionspass. Ventilatiry air blown up throwh fhe
box at the rate of
14
kg/min enters at
10
C and leaves at
OL
Draw up a heat
balance of the egine stating the items aspercentage o f total eneryy in.
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1 )
An S.I. Engine has a fuel-air ratio of 0.07: Mow many kilograms of alr per
hour are required for an output
o f 75
kW
a t an
overall efficiency of 20':'0' How
many m3 of air are required per hour if the density of air is 1.2 ~ g / n 1 ~ ?f the fuel
vapor has density four times that of the air, how many
m3 per hour of the mixture
is required? The calorific value of the fuel is 43700 kJ/Kg.
(2)
A diesel engine develops 5 kW. Its indicated thermal efficiency is 30% and
mechanical efficiency is 57%. Estimate the fuel consumption of engine in (a)
K g h ,
b)
litershr,
C)
indicated specific fuel consumption, and (d)
BSFC
Take
the density of diesel oil as 0.87 kg/m3. Take fuel calorific value = 42000 kJ/kg,
fuel SG
=
0.87.
(3)
An engine develops 50 kW at full load. If its mechanical efficiency is 80%,
what is the friction power? What will be the mechanical efficiency of the engine at
half load, if the mechanical losses (friction power) remains constant.
4)
A
two-stroke C.I. engine delivers 5000 kW while using 1000 kW to overcome
frictional losses. It consumes 2300 Kg of fuel per hour at an air-&el ratio of
20:
1
The heating value of the fuel is 42000 kJIKg. Find the following
(a) The Indicated power
(b) The mechanical efficiency
(6)
The air consumption per hour
( 4
The Indicated thermal efficiency, and,
(el The Brake thermal efficiency
(5)
A single cylinder, C I engine has thermal efficiency of 25% using fuel of
calorific value 39000 Wlkg. If the mechanical efficiency is 74%, calculate
ISFC,
BSFC, and, Indicated Thermal Efficiency.
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PROBLEMSFOR
PRACTICE
o
Basic Intend
Combustion Engines.
1 A
fwrr cylidx
engine
ojxxates on four stroke
cycle
ha stroke 7cm
and
bore 5cm.
The
p d m bas
a cavity
top of
it@aEasphere)of-e lcm3. 'Ihevokrme above the pistan
l d ~ i t i s a t ~ ~ ~ i s 8 c m ~ .
i b c d ~ p f c s s i o n d , e n g i n e ~ ~ a n d e a l g 2 n e ~
2. ~~
with ne t sketch
the
difikmce
between
the
ctu l and
theoretical
valve timing
6 r
4-
Stroke
S.L
engine.
3.
A
diesel
engine develops 5 kW. ts indicated thermal dc iency is
30
and mechanical
efficiency is 5 . Calculate:ISFC, IP,BSFC, BP,mfand thermal efficiency.
Air-Standard
Cydes
4. An engine working an the
tto
cycle has a compression r tio 8, total
cylinder
volume of 3.8
Liters,
The
i i
cmdtbm
are
P
14.95
ar
and
TI=
17
OC
at
the
begbmg
of
cmqms n
stroke. The amouut of heat added during the canstant
volume
combustion is 7.5.
Calculate
pressure and
kmpemtm
at all
pints,
MEP and Thermal Hliciency.
Take Cv
0.718W/Kg-K,y=
1.4fbr
air.
Z
5 The initial u m d i h fbr an air standard
d i d
cycle peding with
campression ratio
of 1 5 1
are 0.95 bar and 17 C. The heat added is 1800 M/kg.
Calculate
the pressure lnnd temperature at
the
end of
ewh process of
the cycIe
and
determine the engine's
e n d Bciency and
MEP.
TakeCp 1.005kJ/Kg-K,
y
1.4fbr air.
6 . Pnrvsthal k
ideal
air standarddiesel cyclef l l F 2 L
~ 4 m )
EngineTestingTechnque.
A
Stroke, QCyliodns petrol engine having
bore 86-
and
stroke
lOOnrm
wit compression
ratio
=
6. A test
was carried
out an
this
ngin
and
the
foblaving dab
was collected
engine
speed
2400
RPM,
Brake
Load
20
Kg,
Effective Brake
Arm
0.5
m,
IMEP
bar, Fuel
ammnption =10 Kg/hr. Fwl
Calorific Value =
44 kJ .
Caiculate: BP,
IP
FP BMEP,
FMEP
Brake Indicated ' I h e d EBciency, Brake
ndicated
SFC,
Mecholnical
and
Redative l icie.ucy. Takey 1.4fix air.
~ m d r e ~ o l ~ h ~ b c r e 5 7 n n n a d s b o k e = 9 0 m m ~
is 28
RPM and it is
tested
at
this
speed
@t a
brake which
has a torque arm of 0.356 m.
'ihe t et brake load is
155
N
and
the find amsumption is
6.74
Whr. The specific gravity
of
th
petrol used is 0.735 and
has a
lower calorific v lue of 44200 kJ/Kg. A
Marse
test
is carried
out
he
cylinders
ate
cut
out
in
th
order
1,2,3,4,
with
correqmdmg
brake
loads
of
111, 106.5,
104.2
and
111 N reqxxtively. Calculate
for this
speed,
the
engine Torque, BMEP BBSFC
IMH,,
Brake'llmml
andMechmical
mciency