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Question:
An eight cylinder automobile engine of 85.7 mm bore and 82.5 mm stroke with
a compression ratio of 7 is tested at 4000 rpm. on a dynamometer which has a
0.5335 m arm. During a 10 minutes test at a dynamometer scale beam reading
of 400 N, 4.55 kg of gasoline for which the heating value is 46,000 kJ/kg are
burnt, and air at 294 K and 10 × 104 N/m2 is supplied to the carburetor at the
rate of 5.44 kg per minute. Find
a) the brake power (b.p) delivered
b) the brake mean effective pressure (bmep)
c) the brake specific fuel consumption (bsfc)
d) the specific air consumption
e) the brake thermal efficiency
f) the volumetric efficiency
g) the air-fuel ratio (A-F Ratio)
Solution: 2 6 ( ) . 2 2 4000 400 0.5335 89.34 kW 60000 60000 . 89.39 kW ( ) 8( ) ( ) . 2 60000 60000 . 60000 89.39 60000 704.39 kPa 4 4 .0825 (85.7) 4000 4 10 704. a b p T NT b p n bmep Al N bmep Al N b b p x bmep b p lAN bmep 39 kPa ( ) Fuel consumed in one minute, 0.455 kg/min Fuel consumed in one hour, 0.455 60 kg/hr 27.3 kg/hr 27.3 kg/hr 0.306 kg/b.kWh . 89.34 kW 0.306 kg/b f f f f c w w w w bsfc b p bsfc .kWh ( ) Air consumption rate, 5.44 kg/min 5.44 60 kg/hr 326.4 kg/hr 326.4 kg/hr 326.4 kg/hr 3.653 kg/b.kWh . 89.34 kW 3.653 kg/b.kWh a a a a d w w w bsac w b p bsac 2 4 3 ( ) Brake Thermal efficiency, . 89.34 kW 89.34 kJ/s 0.455 kg/min 46000 kJ/kg 0.455 46000 kg/s kJ/kg 60 0.256 25.6% ( ) Piston displacement (0.0857) (0.0825) 4.76 10 m 4 b f b b e b p w HV f 4 3 3 /cycle At 4000 rpm and for four-stroke, eight-cylinder engine, Piston displacement 4.76 10 4000 8 m /min 7.62 m /min 2 Standard conditions of intake: Temperature (T) 298 K, 5 3 5 Pressure ( ) 1 atm 1.01325 10 Pa Volume of air used at intake conditions 5.44 287.1 298 4.593 m /min 1.01325 10 Volumetric efficiency, 4.593 100% 60.3% 7.62 60.3% ( ) A a v v p w RT p g ir : Fuel Ratio 5.45 11.98 0.455 A/F Ratio 11.98 a f w w
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Energy Losses (Heat Balance)
Only a part of the energy supplied to the engine is transformed into useful work whereas
the rest is either wasted or utilized for heating purposes. The main part of the unutilized heat
goes to exhaust gases and to the cooling system. In order to draw a heat balance chart for an
engine, tests should be conducted to give the following information.
(i) Energy supplied to an engine which is known from the heating value of the fuel
consumed.
(ii) Heat converted to useful work.
{Hi) Heat carried away by cooling water.
(iv) Heat carried away by exhaust gases.
(v) Heat unaccounted for (radiation etc.)
It is expected that the heat balance results of CI engine must differ from that of petrol engine
due to much higher compression and expansion ratios in the former. The higher compression
ratio results in lower exhaust gas temperature and also lower flame temperature that in turn
causes lower heat loss to the cylinder walls in CI engines.
The utilization of the fuel’s heat energy is also higher in CI engines because of its higher
compression ratio.
Although the actual value of heat utilization is dependent upon a number of factors like
compression ratio, engine load, fuel injection quantity, timing etc. some average figures for heat
Item S.I. Engine C.I. Engine
Heat converted to useful work (i.p.) 25 to 32% 36 to 45%
Heat carried away by cooling water 33 to 30% 30 to 28%
Heat carried away by exhaust gases 35 to 28% 29 to 20%
Heat unaccounted for 7 to 10% 5 to 7%
Total (= Energy supplied) 100% 100%
balances for both the engines are given below :
If the shaft work (b.p.) is considered instead of useful work, the mechanical losses are to be
accounted for or are generally included in the cooling water heat.
An eight cylinder automobile petrol engine of bore 85.7 mm and stroke 82.5 mm
with a compression ratio of 7: 1 was tested on a dynamometer which has an arm of
533.5 mm long. The dynamometer scale reading was 400 N and the speed of the
engine was 4000 RPM. During the 10 minutes run fuel consumption was 4.55 kg.
The heating value of fuel was 45980 kJ/Kg. Quantity of air supplied through the
carburetor was 5.44 kg per minute at a pressure of 0.1 MPa and at a temperature of
293 K. Find the following: (a) The brake power developed, (b) The brake mean
effective pressure, (c) The brake specific fuel and air consumption (d) The brake
thermal efficiency (e) the volumetric efficiency. Gas constant for air is 287.14 J/kg-K.
