Problems:
1.) As Becky was driving “Old Betsy,” the family station wagon, the engine finally quit being worn out after 171,000 miles. It can be assumed that the average speed over its lifetime was 40 mph at an engine speed of 1700 RPM. The engine is a 5 liter V8 operating on a four-stroke cycle. Calculate: a.) how many revolutions has the engine experienced? b.) How many spark plug firings have occurred in the entire engine? c.) How many intake strokes have occurred in one cylinder? Solution: a.)
b.)
c.)
in , = = 4.3610 = ;4 = = 4.3610 ( 4 ) / = 1.74410 1.7 4410 = = . = (1.74410 ) (8 ) = 2.1810
2.) A four cylinder, two stroke cycle diesel engine with 10.9cm bore and 12.6cm stroke produces 88kW of rate power at 200rpm. Compression ratio r c=18:1. Calculate: a.) engine displacement (cm3, L) b.) Brake mean effective pressure (kPa) c.) Torque (N-m) d.) Clearance volume of one cylinder (cm3) Solution:
= 4 = 4 410.912.6 = 4703 = 4.703 = 2 2 000 = (2 )0. 1 26 60 = 8.4 = 4 4 = 40.109 = 0. 0373 = 2 8.4 sec 0. 0 373 88 = 2 = 561 = 2
a.) Vd
b.) Bmep
c.) Torque
561 0. 0 04703 = 2 = 420 = 4 1 = 4703 4 = =1176 18 = 1176 = 69.2
d.) For one cylinder
3.) A four cylinder, 2.4 Liter engine operates on a four- stroke cycle at 3200rpm. The compression ratio is 9.4:1, the connecting rod length r=18cm, the bore and stroke are related as S= 1.06B. Calculate: a.) Clearance volume of one cylinder in cm3 and L b.) Bore and stroke in cm c.) Average piston speed in m/sec Solution: a.) Vc of 1 cylinder
= 2.44 = 0.6 = 600 = 9.4 = 600 = 71.43 0.07143 = 600 = 41.06 == 1.8.0967= 1.068.97
b.) B and S
= 9.50 = 22 3200 = ( )0.0950 ( 60 ) = 10.13/
c.) Up
4.) In problem 3, what is the average piston speed and what is the piston speed when the crank angle θ=90° aTDC in m/s? Solution:
a.) Problem3: Up=10.13m/s b.) Piston speed
= 2 = 0.096 = 0.0475 2 = = (320060)2()0.0465 = 15.9 /
5.) A five cylinder, 3.5 Liter SI engine operates on a four stroke cycle at 2500rpm. At this condition, the mechanical efficiency of the engine is 62% and 1000 Joules of indicated work
are
produced
each
cycle
in
Calculate: a.) Indicated mean effective pressure (Imep) (in kPa) b.) Brake mean effective pressure (bmep) (in kPa) c.) Friction mean effective pressure (fmep) (in kPa) d.) Torque (Nm)
each
cylinder.
Solution: a.) imep
1 = 1429 = = 0.0007 = = 0. 6 2 1429 = 886
b.) bmep
c.) fmep
= − = 1429 −886 = 543 = 4 886 0. 0 035 = 4 = 247 d.) Torque
6.) The engine operating at the conditions in problem 5 is square, with the stroke equal to the bore. Calculate: a.) Specific power (kW/cm2) b.) Output per displacement (kW/cm3) c.) Specific volume (cm3/kW) d.) Power lost to friction in kW. Solution: Vd= 0.0007m3
= 4 ; =
= = 0.0962 9.62 = = 4 = 4 9.664.265 = 0.178 = 64.4 = 3500 = 0.0185 / = = 364.5006 = 54.1 / a.) Specific Work
b.) Output per displacement
c.) Specific Volume
7.) The engine is connected to a dynamometer which gives a brake output torque reading of 205 N-m at 3600 RPM. At this speed air enters the cylinders at 85 kPa and 60°C, and the mechanical efficiency of the engine is 85%. Calculate: a.) brake power b.) indicated power c.) Brake mean effective pressure d.) Indicated mean pressure
e.) Friction mean effective pressure
Solution: a.)
b.)
c.)
d.)
e.)
= 2 3600 = (2 )( 60 sec) 205 = 77, 300 = = 77.0.385 = 90. 9 = ( 4 )205 = 0.003 = 859 = = 859 0. 8 5 ==1010 − = 1010 −859 = 151
8.) The engine in Example Problem 2-2 is running with an air-fuel ratio AF = 15, a fuel heating value of 44,000kJ/kg, and a combustion efficiency of 97%. Calculate: a.) rate of fuel into engine in kg/sec b.) brake thermal efficiency c.) indicated thermal efficiency
d.) Volumetric Efficiency Solution: a.)
b.)
c.)
d.)
= = 0.015005 = 0.000033 = (0.000033 )6(360060 sec)(1 ) 2 = 0.0060 / = = (0.006 sec )(77.44,3 0000) 0.97 = 0.302 30.2% = = 00..38025 = 0.355 = 35.5% = = (1.181 0.0005)0.0005 = 0.847 = 84.7%
9.) An SI, six-liter, V8 race car engine operates at WOT on a four-stroke cycle at 6000 RPM using stoichiometric nitromethane. Fuel enters the engine at a rate of 0.198 kg/sec and combustion efficiency is 99%. Calculate: (a) Volumetric efficiency of engine. [%] (b) Flow rate of air into engine. [kg/sec] (c) Heat added per cycle per cylinder. [kJ] (d) Chemical energy from unburned fuel in the exhaust. [kW] Solution: (a) Brake power using Eq. (2-43)
800 2π ̇ = 2πNτ = 1000W60 ⁄76 − = 6.365 mass flow rate of fuel
̇ = 0.1413 1000 60 ℎ = 1695 ℎ 1695 ̇ ℎ = ̇ = 6.365 = 266.3 −ℎ Eq. (2-60)
(b) displacement volume using Eq. (2-9)
= 4 = 1412.918.0cm = 2353 = 2.353 = 0.002353
Eq. (2-41)
− = 4πτ = 0.4π76 = 405, 7 00 002353 = 405.7 = 6.22.8276 353 = 405.7 or using Eq. (2-87)
or using Eq. (2-88)
3800652 = 405.7 = 10006. [2.353 60 ] (c)
from above
̇ = 6.365
(d) piston face area using Eq. (2-15)
= 4 = 412.9 = 130.7 6.365 = ̇ = 130. = 0. 0 487 7 = ̇ = .. = 2. 7 1 53 = 0.730 = ̇ = 2.6.3365 Eq. (2-51)
(e) Eq.(2-52)
(f) Eq. (2-53)
10.) A small single-cylinder, two-stroke cycle SI engine operates at 8000 RPM with a volumetric efficiency of Tlv = 0.85. The engine is square (bore = stroke) and has a displacement of 6.28 em 3. The fuel-air ratio FA = 0.067. Calculate: (a) Average piston speed. [m/sec] (b) Flow rate of air into engine. [kg/see] (c) Flow rate of fuel into engine. [kg/see] (d) Fuel input for one cycle. [kg/cycle] Solution: (a)
= 27. 7 8
(b)
. = 0.0847 = 8.47 k [. .]
(c)rate of fuel use during trip
[ 18 3. 7 85 0. 6 92 ] ̇ = [12.5ℎ3600 ℎ] = 0.001048 ℎ12.5ℎ] = 1.32 [0.001048 28 3600 1000 mass of CO
11.) A single-cylinder, four-stroke cycle CI engine with 12.9-cm bore and 18.0-cm stroke, operating at 800 RPM, uses 0.113 kg of fuel in four minutes while developing a torque of 76 N-m. Calculate: (a) Brake specific fuel consumption. [grnlkW-hr] (b) Brake mean effective pressure. [kpa] (c) Brake power. [kW] (d) Specific power. [kW/cm2] (e) Output per displacement. [kW/L] (f) Specific volume. [L/kW] (a) displacement volume of one cylinder Solution:
= 0.00056 . = = 41.12 = 4 =0.=00.0056 0860 = 1.12 = 1.120.0860 = 0.0963 3600 ̄ = 2SN = 2 0. 0 963 ∗ = 11. 5 6 60 = [159.3600260162] = 429. 8 − 8 ] = [6.282429. 5.6 = 964 (a)
Eq. (2-2)
(b) Eq (2-76)
(c) Eq (2-87)
12.) The engine operating at the conditions in problem 3 has a combustion efficiency of 97%.
Calculate: a.) Rate of unburned hydrocarbon fuel which is expelled into the exhaust system in kg/hr b.) specific emissions of Helium (gm/kW-hr) c.) Emissions index of Helium Solution: (a) mass flow rate of fuel into engine
̇ = 0.0060
mass flow of fuel not burned
̇ = ̇1− = 0.0060 1−0.973600 ℎ = 0.648 ℎ 648 ̇ ℎ = ̇ = 77.3 = 8.38 ℎ (b) Eq. (2-73)
(c) mass flow of unburned fuel emissions
[ 0. 6 48 1000 ] ℎ ̇ = 3600 ℎ = 0.18 0. 1 8 = ̇̇ = 0.0060 = 30 Eq. (2-74)
13.) A pickup truck has a five-liter, V6, SI engine operating at 2400 RPM. The compression ratio r c
= 10.2:1, the volumetric efficiency Tlv = 0.91, and the bore and stroke are related as stroke S =
0.92 B. Calculate: (a) Stroke length. [em] (b) Average piston speed. [rnlsec] (c) Clearance volume of one cylinder. [cm3] (d) Air flow rate into engine. [kg/see] Solution: a.)
b.)
c.)
d.)
= = 0.8333 = 833. 3 = 4 = 40.92 == 0.10.9249 = 0.9210.49 = =9.265 2400 = (2 )0. 0 965 ( ) 60 sec = 7.+72 / = 10.2 = 833.3 = 90.6 = 2400 1. 1 810. 0 050. 9 1 60 = 2 = 0.107 /
