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Unformatted text preview: John’s automobile has a threeliter SI V6 engine that operates on a fourstroke cycle at
3600 RPM The compression ratio 1s 9. 5, the length of connecting rods 1s 16. 6 cm, and the engine is square (B= S) At this speed, combustion ends at 20° aTDC.
Calculate: » 1. cylinder bore and stroke length
2. average piston speed
4* t 3. clearance volume of one cylinder
4. piston speed at the end of combustion 5. distance the piston has traveled from TDC at the end of combustion
6. volume in the combustion chamber at the end of combustion a) ’1’)’ For one cylinder, using Eq. (28) with S: B: . . .
Vd = Wow/6‘ _3L/6“ — 0.5 L— — 0.0005 m3 =(1'T/4)BZS = (7r/4)B3
B = 0.0860m = 8.600(1) 2 S 1,) 27 Using Eq. (2—2) to ﬁnd average piston speed: Up = ZSN= (2 strokes/rev) (0 0860 m/stroke) (3600/60 rev/sec)
= 10. 32 m/sec ' é) .3)’ Using Eq. (212) to ﬁnd the clearance volume of one cylinder:
rc = 9.5 = (V4 + Vc)/Vc = (0.0005 + Vc)/Vc
Vc = 0.000059 m3 = 59 cm3 4) 4r Crank offset,a = 3/2 = 0.0430m = 4.30cm
R = r/a = 16.6 cur/4.30m = 3.86 _ Using Eq. (25) to find instantaneous piston speed:
UP/Up =‘(1r/2)sin8[1 + (case/m»
= (6/2) sin(20°){1 + [comm/Wu
= 0.668 . '
U, '= 0.668 U = (0.668) (10.32 m/sec) = 6.89 m/sec e) ,5')‘ Using Eq. (2 3) to ﬁnd piston position:
s=acos0 + Vr2  azsinzo
= (0.0430 In) cos (20°) + V‘(0.166 m)2 — (0.0430 m)2sin2 (20°) = 0.206 :11 Distance from TDC:
x = r + a — s = (0.1661'n) + (0.043 m)  (0.206 m)
= 0.003 m= 0.3 cm
,‘1 ,6 Using Eq (214) to ﬁnd instantaneous volume:
' V/V.=1+1(r,—1){R+1—cose—\/m]
= 1 + §(9.5 — 1)[3.86 + 1  cos(20°)— W]
= 1.32 I , .
V = 1.32 V, = (1.32) (59 cm3) = 77.9 cm3 = 0.0000779 m3 This indicates that, during combustion, the volume in the combustion chamber has only
increased by a very small amount and shows that combustion in an SI engine occurs at almost constant volume at TDC 'l‘ne engme in Example r'roolem 21 15 connected to a aynamometer wmcn 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: 1. brake power
(H; 2 2. indicated power
3. brake mean effective pressure
4. indicated mean effective pressure
5. friction mean effective pressure
6. power lost to friction
‘7. brake work per unit mass of gas in the cylinder
8. brake speciﬁc power '
9. brake output per displacement
10. engine specific volume 09 J) Using Eq. (243) to find brake power:
Wb— — 27rNr — (271' radians/rev) (3600/60 rev/sec) (205 N~m) = 77,300Nm1’sec = 77 3 kW = 104 hp lb) 2) Using Eq. (2 47) to ﬁnd indicated power.
W3: Wb/nm = (77. 3 kW)/(0. 85): 90.9 kW = 122hp C) 35’ Using Eq. (241) to ﬁnd the brake mean effective pressure:
bmep = 4777/14; = (471' radianslcycle) (205 N—m) / (0.003 m3/cycle)
= 859,000 Ni‘m2 = 859 kPa = 125 psia d)“ Equation (237c) gives indicated mean effective pressure:
' imep = bmep/nm = (859 kPa)/(0.85) = 1010 kPa = 146 psia 5) Equation (237d) is used to calculate friction mean effective pressure:
fmep =‘imep — bmepl'= 1010 — 859 = 151 kPa = 22 psia
C) 6) Equations (215) and (244) are used to ﬁnd ﬁiction power lost:
AP = (1r/4)Bz— ‘ (qr/ti) (0. 086 m)2 = 0.0058] 1112 for one cylinder
Wr='A(1/2n)(fmep)
= (1/4) (151 kPa) (0.00581 mzlcyl) (10.32 misec) (6 cyl)
= 13. 6 kW—  18 hp 01‘, it can be obtained from Eq. (2 49):
' vie: W.— W, = 90.9? 77.3 = 13.6 kW _
7) First brake work 15 found for one cyiinder for one cycle using Eq. (229):
= (bmep) Vd = (359 kPa) (0.0005 m3) = 0.43 1:] It can be assumed the gas entering the cylinders at BBC is air: ma =_ PVBDC /RT = P(Vd + Vc)/RT = (85 kPa) (0.0005 + 0.000059)m3 / (0.287 kakgK) (333 K)
' = 0.00050 kg Brake speciﬁc Work per unit mass: = Wb/ma = (0.43 H) /_(0.00050 kg) = 860 kJ/kg = 370 B'I‘Uflbm ' 8) ‘ Equation (251) gives brake speciﬁc power:
BSP = 77. 7A1, = (77. 3 kW) /[(7r/ 4)(0. 086 m)2(6 cylinders)]
— 2220 kWiruz = 0.2220 lecmz— " 1 92 lip/in. 2 9) Equation (252) gives brake output per diSplacement: BOPD = Wb [VJ = (77.3 kW) / (3 L) = 25.8 kaL = 35 lip/L = 0.567 hplin.3
10) Equation (2—53) gives engine speciﬁc volume:
st = V. Min, = llBOPD = 1725.8 The engine in Example Problem 2—2 is running with an air—fuel ratio AF = 15, a fuel
heating value of 44;000 kJ/kg, and a combustion efﬁciency of 97%.
Calculate: ' L rate of fuel flow into engine 2. brake thermal efﬁciency 7 3. indicated thermal efﬁciency 4. volumetric efficiency 5. brake speciﬁc fuel consumption 09 «13‘ From Example Problem 22, the mass of air in one cylinder forone cycle is ma =
. 0.00050 kg. Then: mf = ma / AF = 0.00050/ 15 = 0.000033 kg of fuel per cylinder per cycle
Therefore, the rate of fuel flow into the engine is: I
”if = (0.000033 kg/cylcycle) (6 cyl) (3600/60 rev/sec) (1 cycle/2 rev)
= 0.0060 kg/sec = 0.01321bm/sec '
. b) ,2 Using Eq. (264) to find brake thermal efficiencyi
(1,0,, = Wb/meHv n; = (77.3 kW) / (0.0060 kg/sec)(44,000 kJ/kg) (0.97)
= 0.302 =.30.2% '
Or, :using Eq. (268) for one cycle of one cylinder:
(0)6 = Wb /meHV m. = (0.43 k1) /(0.000033 kg) (44,000 kJ/kg) (0.97)
= 0.302
a) 55 Indicated thermal efficiency using Eq. (265):
' (71,). = («nob/n... = (130210.85 : 0355 = 35.5%
cl) 4? Using Eq. ((269) with standard air density for volumetric efficiency:
a... = m. /p., Vd = (0.00050 kg)/(1.181 kg/Im3)(0.0005 m3)
= 0.847 = 84.7% e) 5? Using Eq. (2—59) for‘brake specific fuel consumption:
5 bsfc = ”if/WI, = (0.0060 kg/sec) / (77.3 W)
= 7.76 X 10—5 kg/kWsec : 279 gm/kW'hr = 0.459 lbmfhp—hr ...
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 Spring '10
 IbrahimHassan

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