Lecture - 08
IC Engines
Department of Mechanical Engineering 1
Numerical Problems
Department of Mechanical Engineering 2
Numerical Problem # 01
The cubic capacity of a four stroke over-square spark ignition engine is 245 cc. the over-
square ratio is 1.1. the clearance volume is 27.2 cc. calculate the following:
o Bore of cylinder
o Stroke of Piston
o Compression ratio of the engine
Department of Mechanical Engineering 3
Numerical Problem # 01 (Solution)
Department of Mechanical Engineering 4
Numerical Problem # 01 (Solution)
Department of Mechanical Engineering 5
Numerical Problem # 02
The mechanical efficiency of a single cylinder four stroke engine is 80%. The frictional
power is estimated to be 25 kW. Calculate the indicated power (ip) and brake power (bp)
developed by the engine.
Department of Mechanical Engineering 6
Numerical Problem # 02 (Solution)
Department of Mechanical Engineering 7
Numerical Problem # 02 (Solution)
Department of Mechanical Engineering 8
Numerical Problem # 03
A 42.5 kW engine has a Mechanical Efficiency of 85%. Find the indicated power and
frictional power. If the frictional power is assumed to be constant with load, what will be
the mechanical efficiency at 60% of the load?
Department of Mechanical Engineering 9
Numerical Problem # 03 (Solution)
Department of Mechanical Engineering 10
Numerical Problem # 03 (Solution)
Department of Mechanical Engineering 11
Energy Flow of System
Department of Mechanical Engineering 12
Efficiencies
𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑑 𝑃𝑜𝑤𝑒𝑟 𝒊𝒑
𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑑 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 (η𝒊𝒕𝒉 ) = =
𝐸𝑛𝑒𝑟𝑔𝑦 𝑖𝑛 𝐹𝑢𝑒𝑙 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 𝑬
𝐵𝑟𝑎𝑘𝑒 𝑃𝑜𝑤𝑒𝑟 𝒃𝒑
𝐵𝑟𝑎𝑘𝑒 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 (η𝒃𝒕𝒉 ) = =
𝐸𝑛𝑒𝑟𝑔𝑦 𝑖𝑛 𝐹𝑢𝑒𝑙 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 𝑬
𝐵𝑟𝑎𝑘𝑒 𝑃𝑜𝑤𝑒𝑟 𝒃𝒑 𝒃𝒑
𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 η𝒎 = = =
𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑑 𝑃𝑜𝑤𝑒𝑟 𝒊𝒑 𝒃𝒑 + 𝒇𝒑
𝐴𝑐𝑡𝑢𝑎𝑙 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 η𝒓𝒆𝒍 =
𝐴𝑖𝑟 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐸𝑓𝑓𝑖𝑐𝑒𝑖𝑐𝑛𝑦
Department of Mechanical Engineering 13
Numerical Problem # 04
A four-stroke, four-cylinder diesel engine running at 2000 rpm develops 60 kW. Brake
thermal efficiency is 30% and calorific value of fuel (CV ) is 42 MJ/kg. Engine has a bore
of 120 mm and stroke of 100 mm. Take ρa = 1.15 kg/m3, air-fuel ratio = 15:1 and ηm = 0.8.
Calculate (i) fuel consumption (kg/s); (ii) air consumption (m3/s); (iii) indicated thermal
efficiency; (iv) volumetric efficiency; (v) brake mean effective pressure and (vi) mean
piston speed.
Department of Mechanical Engineering 14
Numerical Problem # 04 (Solution)
Department of Mechanical Engineering 15
Numerical Problem # 04 (Solution)
Department of Mechanical Engineering 16
Numerical Problem # 04 (Solution)
Department of Mechanical Engineering 17
Numerical Problem # 05
A single-cylinder, four-stroke hydrogen fueled spark-ignition engine delivers a brake
power of 20 kW at 6000 rpm. The air-gas ratio is 8:1 and the calorific value of fuel is 11000
kJ/m3. The compression ratio is 8:1. If volumetric efficiency is 70%, indicated thermal
efficiency is 33% and the mechanical efficiency is 90%, calculate the cubic capacity of
the engine.
Department of Mechanical Engineering 18
Numerical Problem # 05 (Solution)
Department of Mechanical Engineering 19
Numerical Problem # 05 (Solution)
Department of Mechanical Engineering 20
Numerical Problem # 06
Consider two engines with the following details:
Engine I: Four-stroke, four-cylinder, SI engine, indicated power is 40 kW, mean
piston speed 10 m/s.
Engine II: Two-stroke, two-cylinder, SI engine, indicated power is 10 kW.
Assume that mean effective pressure of both the engine to be same. Ratio of bore of the
engine I:II = 2:1. Show that the mean piston speed of engine II is same as that of engine I.
Department of Mechanical Engineering 21
Numerical Problem # 06 (Solution)
Department of Mechanical Engineering 22
Numerical Problem # 06 (Solution)
Department of Mechanical Engineering 23
Any Questions?
Department of Mechanical Engineering 24
