Dr. Jivraj Mehta Institute of Technology / Subject name: Elements of Mechanical Engineering
Subject Code: 110006
Assignment –III
HEAT ENGINES
Q .1 Define heat engine. What are the essential requirements of heat engine?
Q .2 Derive thermal efficiency formulae of Rankine cycle. What is difference between Rankine cycle and Carnot vapour cycle?
Q .3 Derive expression for efficiency of Carnot cycle.
Q .4 Derive efficiency equation of Diesel cycle.
Q .5 Derive an expression for efficiency of Otto cycle.
Q .6 State the assumptions for made in air standard cycles?
Q .7 Give limitation of Carnot vapour cycle.
Q .8 It is required to find out the efficiency of an air standard Carnot cycle with the following data: minimum temperature of the cycle = 150 C minimum pressure in the cycle = 1 bar. Pressure after isothermal compression = 3.5 bar. Pressure after isentropic compression = 10.5 bar. Assume R = 0.287 kJ/kgK for air. What power would be produced if engine makes 2 cycle/sec.
Q .9 Calculate the air standard efficiency of a four stroke Otto cycle with the following data: piston diameter = 137 mm, length of stroke = 130 mm clearance volume = 280 cm3. Express clearance as percentage of swept volume.
Q .10 A car possesses a four stroke cylinder in line diesel engine with compression ratio 21:1 and expansion ratio 10:5:1. Find the cut-off ratio and air standard efficiency.
Q .11 A compression ignition engine working on an air standard diesel cycle has the following particulars. Cylinder diameter = 150 mm, stroke length = 250 mm. Clearance volume = 400 cm3. The fuel injection takes place at constant pressure for 5% of the stroke. Find the air standard efficiency. What will be the percentage loss in efficiency if fuel cut-off is delayed from 5% to 8% of the stroke. Assume that compression ratio remains the same.
Q .12 In an air standard Otto cycle the maximum and minimum temperature are 14000 C and 150C. The heat supplied per kg of air is 8000kJ. Calculate the compression ratio and the cycle efficiency. Also calculate the ratio of maximum to minimum pressures in the cycle. Take Cv = 0.718 kJ/kgK and γ = 1.4.
Q .13 A four cylinder petrol engine has a swept volume of 2000 cm3. And the clearance volume in each cylinder is 60 cm3. Calculate the air standard efficiency. If the introduction conditions are 1 bar and 240C and the maximum cycle temperature is 14000C. Calculate the mean effective pressure on the air standard Otto cycle.
Q .14 An ideal four-stroke Otto-cycle engine has compression ratio of 6.3. The temperature at the beginning of compression is 180 C. Heat supplied during combustion is 3225 kJ/kg. Using γ = 1.3 for air and R = 0.287 kJ/kg K. for 1 kg of air. Calculate
Q .15 In an engine working on ideal Otto cycle the temperature at the beginning and end of compression are 500 and 3730C. find the compression ratio and air-standard efficiency of the engine.
Q .16 An engine operating on the ideal Otto cycle has a bore of 100 mm and stroke of 127 mm. The compression ratio is 7. At the beginning of the compression stroke the cylinder contains air at 15.60 C and 1 bar. If the maximum cycle temperature is 16500 C. calculate 1. The pressure, volume and temperature at the cardinal points of the cycle 2. The air standard efficiency 3. The mean effective pressure of the cycle. For air take Cv = 0.718 kJ/kgK.
Q .17 An engine operating on the ideal Diesel cycle has a maximum pressure of 41 bar and a maximum temperature of 10930 C. At the beginning of the compression stroke, the air is at 210C and 1.0 bar. Given that γ for air is equal to 1.4, calculate the air standard efficiency of the cycle.
Q .18 Obtain an expression for the work done by an engine working on the Otto cycle in item of the maximum and minimum temperature of the cycle, the compression ratio r and the constants of the working fluid assuming it to be a perfect gas. Hence show that. The compression ratio for maximum work is given by
and
the intermediate temperature is given by
T3 = T4 =
Also find the expression for maximum work.
Q .19 In an air standard Otto cycle. The pressure and temperature of the air at the stast of compression are 1 bar and 330 K. respectively. The compression ratio is 8.
The energy added at constant volume is 1250 kJ/kg.
Q .20 An engine is working on an ideal Diesel cycle. The compression ratio is 18. The temperature and pressure at the beginning of the cycle is 320 C and 2bar respectively. 720 kJ of heat is added during the cyclic operation. Calculate (1) Temperature and pressure at every salient point (2) work done in the cycle / kg (3) Thermal efficiency (4) mean effective pressure of an ideal Diesel cycle. Take Cp = 1.005 kJ/kg K and Cv = 0.718 kJ/kg K for air.
Q .21 An engine working on ideal Otto cycle has a clearance volume of 0.03 m3 and swept volume of 0.12 m3. The pressure at the end of heat addition is 25 bar, Calculate.
a. Ideal efficiency of the cycle.
b. Temperature at the key point of the cycle.
Assume γ = 1.4 for air
Q .22 An air engine works on the following cycle :
Air is taken in at a pressure of 110 kPa and temperature of 160C and is compressed adiabatically up to 3500 kPa pressure. Heat is taken in at constant pressure. The expansion afterword taken place adiabatically. The ratio of expansion is 5. The air is exhausted at the end of stroke. The heat is rejected at constant volume. Calculate.
(i) Temperature at the key points of the cycle.
(ii) Ideal thermal efficiency of cycle
Take Cp = 1.0035 kJ/kg K
Cv = 0.7165 kJ/kg K
The following results refer to a test on i.c. engine. Indicated power = 42 kw
Frictional power = 7 kw engine speed
Specific fuel consumption per b.p. = 0.30 kg/kwh calorific value of fuel used =
43000 kj/kg
Calculate:
(i) mechanical efficiency (ii) brake thermal efficiency
(iii) indicated thermal efficiency
Following observations were recorded during a test on a single cylinder oil
engine.
Bore= 300mm ,Stroke= 450mm , Speed= 300r.p.m., i.m.e.p.= 6 bar
Net break load= 1.5 k.n., brake drum diameter= 1.8 m
Brake rope diameter= 2 cm. Calculate
(i) Indicated power (ii)brake power (iii)mechanical efficiency.
The following readings were taken during the test on a single cylinder four
stroke,
Oil engine :
Cylinder diameter = 270 mm , Stroke length = 380 mm
mean effective pressure = 6 bar , Engine speed = 250 rpm
net load on brake = 1000 n
effective mean diameter of brake = 1.5 m, fuel used = 10 kg/hr
C.v. of fuel = 44400 kj/kg
Calculate:-
(i) Brake power. (ii) Indicated power. (iii) Mechanical efficiency. (iv)
Indicated thermal efficiency.
A six cylinder 4 stroke ic engine is to develop 89.5 kw indicated power at 800
rpm. The stroke to bore ratio is 1.25: 1. Assuming mechanical efficiency of
80% and brake mean effective pressure of 5 bar. Determine the diameter and
stroke of the engine.
The following reading were taken during the test of four stroke single
cylinder petrol engine :load on the brake drum = 50 kg diameter of brake
drum = 1250 mm spring balance reading = 7 kg engine speed = 450 rpm fuel
consumption = 4 kg/hr calorific value of the fuel = 43000 kj/kg calculate: (i)
indicated thermal efficiency (ii) brake thermal efficiency. Assume
mechanical efficiency as 70%
During testing of single cylinder two stroke petrol engine following data
is obtained, brake torque 640 nm, cylinder diameter 21cm, speed 350 rpm,
stroke 28cm, mep 5.6 bar, oil consumption 8.16 kg/hr, c.v. 42705 kj/kg .
Determine mechanical efficiency indicated thermal efficiency brake thermal
efficiency brake specific fuel consumption
The following results refer to a test on c.i. engine
Indicated power ------3 7 kw , Frictional power ------06 kw
Brake specific fuel consumption------0.28 kg/kwh
Calorific value of fuel ---44300 kj/kg Calculate:
1. Mechanical efficiency 2. Brake thermal efficiency 3. Indicated thermal
Efficiency
During a test on a single cylinder four stroke engine having compression ratio
of 6, following data is recorded. Bore =10cm, stroke=12.5 cm, imep =2.6 bar,
dead load on dynamometer =60n, spring balance reading =19 n, effective
radius of flywheel =40cm, fuel consumption =1kg/hr.calorific value of
fuel is 42, 000 kj/ kg, speed =2000rpm, determine its indicated power, brake
power, mechanical, over all efficiency, air standard and relative efficiency.
A four cylinder 4-stroke petrol engine develops 200 kw brake power at 2500
rpm. Stroke to bore ratio is 1.2. If mean effective pressure is 10 bar and
mechanical efficiency is 81%, calculate bore and stroke of the engine. Also
calculate indicated thermal efficiency and brake thermal efficiency if 65 kg/hr
of petrol is consumed having calorific value of 42000 kj/kg
Explain with neat sketch working of 4-stroke diesel engine
Travel of piston from one dead centre to other dead centre is termed as
_____
(a) stroke length (b) swept volume (c) clearance volume (d) compression ratio
Define the terms (i)) brake thermal efficiency
What are the functions of (i) injector in diesel engine and (ii) carburetor in
petrol engine?
Explain how i.c engines are classified.
Explain with a sketch the working of a four stroke petrol engine.
Why diesel engines are called c.i. engines? Differentiate between s.i. and c.i.
engine.
Define the following terms :
(i) Indicated thermal efficiency. (ii) Compression ratio. (iii)scavenging.
Write the difference between two- stroke and four- stroke cycle.
Mechanical Engineering DepartmentDJMIT, Morgar / Prepared By:
Prof. Jagdish S. Talpada