Combustion
1. A diesel electric plant supplies energy for Meralco. During 24hrs period, the plant consumed 220 gallons of fuel
at 28°C and product 4000 kw-hr. Industrial fuel used is 28°API and was purchased at P15.50 per liter at 15,6°C.
What should be the cost of fuel to be produced per kw-hr?
SG15.6=
141.5
141.5
¿
¿ 0.887SG28=SG15.6 [ 1−0.0007 ][ 28−15.6 ]¿ 0.867 [ 1−0.0007 ][ 28−15.6 ]
131.5+ API 131.5+ 28
¿ 0.879V 1=
220 gal 3. 785 li
li
li
[ V 2 ] [P]
x
¿ 34.696 [ SG ] V 1=V 2 [ SG ]34.696 ¿V 2=34.39 cost=
=¿
24 hrs
1 gal
hr
hr
kw−hr
2. A 750 bhp diesel engine uses fuel oil of 30°API gravity, fuel consumption is 0.75 lb/bhp-hr. Cost of fuel is P17.95
per liter. For continuous operation, determine the minimum volume of cubical day tank in m3, ambient
temperature is 45°C.
lb
1 kg
kg
lb
¿ 255.1 ρ=mv
M =[ 750 BHP ] 0.75
−hr ¿ 562.5 x
1 kg
0.858
=
hr 2.205lb
hr
bhp
li
[
]
[ ]
255.1kg
li
hr v=297.27
hr
v
Vt =¿ v=7.135 m3
3. A diesel power plant uses fuel that has a density of 892.74 kg/m 3 at 15.66°C. Find the heating value.
SG15.6=SG15.6 [ 1−0.0007 ] P 15.00−15.6 ¿6.89274=SG15.6 [ 1−0.0007 ][ 15.00−15.6 ] SG 15.6=0.893
[
Qh=41130+139.6 API ¿ 41130 +139.6 [ 2699 ]¿ 44898.38
KJ
kg
][
1 Btu
1kg
Qh=19500.55 Btu /lb
1.055 kg 2.205 lb
][
]
4. A diesel power plant uses fuel with heating value of 45,038.81(1/kg. What is the density of fuel at 30°C?
Qn=41130+139.6 API 45038.8=41130 +139.6 API SG30=SG15.6 ¿¿ 0.887 [ 1−0.0007 ( 30−15.6 ) ]¿ 0.878
ρ=SG [ ρ H 20 ]¿ 0.878
kg
1 Kg
ρ=0.875
li
li
[ ]
5. A diesel engine consumed 940 liter of fuel per day at 30°C. If the fuel was purchased at 15°C and 30°API at
P4.00/Ii, determine the cost of fuel to operate the engine per day.
5 SG 15.6 =
14.5
141.5
¿
¿ 0.876SG 30=SG 15.6 [ 1−0.0007 ( 30−15.6 ) ]¿ 0.876 [ 1−0.0007 ( 30−15.6 ) ]
131.5+ API 131.5+ 30
¿ 0.867V 1 SG1=V 2 SG2940
¿ Php
li
li
li
4
=v 2 [ 0.876 ]V 2=930.52
P
P=V [ P ]¿ 930.52
day [ 0.867 ]
day
day
li
[
][ ]
3722
day
6. A cylindrical tank 3 m long and 2 m diameter is used for oil storage. How many days can the tank supply the
engine having 27°API with fuel consumption of 65 kg/hr?
7. The specific gravity of fuel oil having a heating value of 44,899.210/kg is:
Qh=41130+139.64 API44899.2=41130 +139.6 API API=27 SG=
141.5
141.5
¿
SG=0.893
131.5+ API 131.5+ 27
8. Steam flows into a turbine at a rate of 10kg/s, and 10kw of heat are lost from the turbine. ignoring elevation and
kinetic energy effects, calculate the power output of the turbine. Inlet conditions are 2.0Mpa and
350°C(h=3137KJ/kg) and 0.10Mpa & 100% quality (h=2675.5KJ/kg). Fuel oil used has25°API.
Q=m [ h 1−h 2 ]
¿
[ 3137−2675 ] KJ
W o =Q−L4615−10¿ 4605 KW
kg
s
[ ]
kg 10
9. A fuel is represented with C5H8 is burned with 40% excess air. If mass of fuel is 0.17kg, find the mass of air
needed.
32 ( 7 ) +3.76 ( 28 ( 7 ) )
A ma
ma
A 32 x +3.76 ( 28 x )
=
( 1+ e )¿
( 1+0.4 )¿ 19.78 = 19.78=
ma=3.36 kg
F mf
0.17
F
12 n+m
12 ( 5 ) +8
10. The analysis of a product of combustion on dry basis, when C6H18 was burned with atmospheric air, is as
follows: CO2=12%, C0=1.75%, 02=3.01%, N2=83.24%. Compute the actual air-fuel ratio.
1716 n N 2
1716 ( 6 ) ( 0.8324 )
A
A
¿
=
=14.75
Fa 47 ( co+ co2 ) ( 12n+ m ) 47 ( 0.0176+0.12 ) ( 12 ( 6 ) +18 ) Fa
11. A boiler burns fuel oil with 15% excess air. The fuel may be represented by C13H28. Calculate the molal air-fuel
ratio.
Given the following ultimate analysis: C=71%, N2=4%, H2=4%, 02=3%, S2=5%, Ash=6%, moisture=8%. Using 20%
excess air, determine the actual air-fuel ratio.
12. A certain coal has the following ultimate analysis C=70%, N2=4%, H2=2.5%, 02=3.5%, Ash=5%, Moisture=?
Determine the heating value of fuel in Btu/lb.
A
A
0
0.03
= 11.5 C+34.5 M − + 4.35 [ 1+ e ]¿ 11.5 ( 0.71 ) +34.5 0.04−
+ 4.3 ( 0.05 ) [ 1+0.2 ] =11.56
Fa
8
8
Fa
[
] ]
[
[
[
]
]
13. A fuel gas has the following volumetric analysis: CH4=68% C2H6.32%. Assume complete combustion with 15%
excess air at 101.325kpa,21°C wet bulb and 27°C dry bulb. What is the partial pressure of water vapor in kpa?
[
Qh=33820 C+144212 H−
¿
[
27299.65 KJ
kg
][
Btu
1.055 KJ
0.035
O
+9304 ( 0.07 )
+93045¿ 33820 ( 0.7 ) +144212 0.025−
8
8
][
]
(
)
1kg
Qh=11735.35 Btu/lb
2.205 lb
]
14. There are 23kg of flue gases formed per kg of fuel oil burned in the combustion of a fuel oil. What is the excess
air in percent?
FUEL+ AIR=PRODUCT 0.68 CH 4 +1.36 O2+ 1.36 [ 376 N 2 ] → 0.68CO 2 +1.36 H 2 O+1.36 [ 3.76 N 2 ]
0.326+1.36 O2 +1.36 [ 376 N 2 ] → 0.68 CO2 +1.36 H 2 O+1.36 [ 3.76 N 2 ]
15. Calculate the amount of air in kg necessary for combustion of 1 kg of octane with theoretical air.
A 32 x +3.76 [ 28 x ] 32 ( 12.5 ) +3.76 [ 28 ( 12.5 ) ] ¿ 15.05 kgair x=8+ 18 =12.5 15.05 kgair = kg air
=
¿
kgfuel
4
kgfuel
kgfuel
F
12n+ m
12 ( 8 ) +18
ma=15.05 kg
16. Calculate the mass in kg of the combustion products of 12kg diesel fuel oil C16H30 with 30% excess air.
32 ( 23.5 ) +3.76 [ 28 ( 23.5 ) ]
kgair
30
A kgair
A 32 x +3.76 [ 28 x ]
x=16+ =23.5 =
=
[ 1+e ] A =
[ 1.3 ]−18.89
kgfuel
4
F kgfuel
F
12n+ m
F
12 ( 16 ) +30
18.89=
kgair
m=226.7 kg air
12 kg
17. . Five kg-mol of octane are burned with stoichiometric amount of air. How much water is formed in the products
if the combustion is complete?
m 18
H 2 O= = =9¿ 9 [ 5 ] H 2 O=45 kg−mol
2 2
18. . Methyl alcohol CH3OH is burned with 30% excess air. How much unburned
fuel will there be in the products if the combustion is complete?
gen in kg-mol- oxygen/kg-mol-
CH 3 OH +1.5O2 +3.76 N 2=1 CO 2+ 2 H 2 O+3.76 N 2C−1H−4O−10−2 x 1.5=3N−2C−1 x 1=1
O−2 X 1=2H−2 x 2=4O−1 x 2=2N−2O=x e¿ 1.5 [ 0.3 ]O=0.45
19. Dodecane C12H26 is burned at constant pressure with 150% excess air. What is the air-fuel for this process?
32 ( 18.5 ) +3.76 [ 28 ( 18.5 ) ]
A
A 32 x+ 3.76 [ 28 x ]
=
[ 1+ e ]¿
[ 1+ 1.5 ] =37.34
Fa
FA
12n+ m
12 ( 12 )+ 26
20. A complete combustion of one kilogram of C16H32 resulted to 20 kilograms of products of combustion.
Calculate the percent excess air.
A
A
A 32 x+ 3.76 [ 28 x ] 32 ( 24 )+ 3.76 [ 28 ( 24 ) ]
=
¿
¿ 14.71 = ( 1+ e )20−1=14.71 (1+ e )
Fa Ft
Ft
12n+ m
12 ( 16 )+ 32
e=0.2917∨29.17 %
21. Calculate the heating value of coal having the following composition by weight using Dulong formula.
Carbon75%, Hydrogen5%, Oxygen6%, Nitrogenl.5%, sulfur3%, waterl.5% &ash8%.
[
Qh=33820 C+144212 H−
KJ x
O
0.06
+93045¿ 33820 ( 0.75 ) +144212 0.05−
+9304 ( 0.03 )¿ 31773.18
kg
8
8
]
[
]
Btu
1 kg
X
Qh=13658 Btu /lb
1.055 KJ 2.205lb
22. A power plant consumes 710 liters of fuel at 25°C in a day with 28°API. Find the fuel rate in kg/hr?
SG15.6=
141.5
14.5
¿
¿ 0.887 SG 25=SG 15.6 [ 1−0.0007 ][ 25−15.6 ]¿ 0.887 [ 1−0.0007 ][ 25−15.6 ]
131.5+ API 131.5+ 28
¿ 0.881 ρ=0.881 X
KG
kg
kg 1 day
kg
kg
li
=0.88 m=ρv ¿ 0.88
710
¿ 625.73
x
m=26.07
LI
li
li
day
day 24 hrs
hr
[
][
]
23.
24. Determine the volume of day tank in cu. Ft of 28°API fuel having a fuel consumption of 300kg/hr.
300 kg
0.887 x 1000 kg
kg
hr
141.5
=887 3
SG=
¿ 0.887 ρ=
3
131.5+ 28
m
m v= m = 887 k g
ρ
m3
f t3
v=287
day
25. A spherical with an area of 114m2 is used for oil storage. How many days can the tank supply the engine having
27°API with fuel consumption of 65 kg/hr?
0.893 x 1000 kg
kg
kg
141.5
=893 3 m=ρv= 893 3 [ 114 m 3 ]¿ 101772.87 kg
¿ 0.893 ρ=
3
131.5+ 27
m
m
m
m 65 kg 101772.87 kg
mf = =
=
t=65.2 days
t
hr
t
SG=
[
]
26. A 750 bhp diesel engine uses fuel oil of 27°API, fuel consumed is 0.851b/bhp-hr. Fuel cost of P8 per liter. For
continuous operation, determine the cost of fuel per day at 50°C.
SG15.6=
141.5
0.871 xli
=0.87
¿ 0.893 SG50=0.871ρ=
131.5+ 27
kg
289.11 kg
m
hr
li
lb
1 kg
kg
=331.84
m= [ 750 bhp ] 0.85
−hr x
=289.11 v= =
ρ
kg
hr
bhp
2.205 lb
hr
0.871
li
Php 8 24 hr
cost= [ 331.24 hr ]
cost=Php 63713.49/day
li
1 day
[
][
[
]
][ ]
27. A firm in Isabela Mexico operatesto a diesel electric plant to supply its energy electric requirements. During a 24
hour period, the plant consumed 300 gallons of fuel at 75°F and produced 3 Mwh. Heating value of fuel is
453181 KJ/kg and was purchased at 4pesos per liter at 60F. Determine the cost of fuel to produce one kilowatthr.
Qh=41130+139.6 API 45318=41130 +139.6 API API=30 SG15.6=
SG23.89=0.876 [ 1−0.0007 ][ 23.89−15.6 ]¿ 0.871
0.871
47 li
hr
[
300
141.5
¿ 0.876
131.5+ API
gal
x 1 day
day
li
x 3.785 li
mf =47
24 hr
hr
=0.876 mf
1 gal
]
Php 4
1.51
mf ( Php )
li
cost=Php
−hr
cost=
¿
kw
Load
hr
3000 kw−
24 hr
[ ][
]
28. Twenty two thousand cubic feet of a fuel gas are passed through a meter at a 5.0psig, 48°F. Barometer,
29.75"Hg. find the commercial sales volume of this gas.
P1 V 1=P2 v 2[ 22000 f t 3 ] [ 5+14.7 ] =14.62V 2V 2=29652.72 f t 3
29. Tank contains 7540 cu. ft of fuel oil at 52°F, SG = 0.945. Find the weight of this quantity of oil measure at 60/60.
SG52=SG 60 [1−0.0004 ( 52−60 ) ]0.945=SG60 [ 1−0.0004 ( 52−60 ) ] SG 60=0.941SG 60 V 60=SG 52 V 52
0.941 V 60=0.945 [ 7540 ]V 60=7564.13 f t 3m=ρv¿ [ ( 0.941 ) ( 62.4 ) ] [ 7564.13 ]m=444618.72lb
30. A firm in Isabela Mexico op ates a diesel electric plant to supply its electric energy During a 24 hour period, the
plant consumed 300 gallons of fuel at 75°F and produced 3MWh. Heating value of fuel is 45318KJ/kg and was
purchased at 4pesos per liter at 60°F. Determine the overall thermal efficiency of the plant.
141.5
¿ 0.876
131.5+ 30
kg
output
li
kg
¿ 41.21 e=
0.876
SG23.89=0.876 [ 1−0.0007 ][ 23−15.6 ]¿ 0.871m=ρv ¿ 4704
hr
input
hr
li
¿ 0.24∨24.1 %
Qh=41130+139.6 API 45318=41130 +139.6 API API=30 SG15.6=
[
][
]
31. A steam generator burns fuel oil with 22% excess air. The fuel oil is dodecane. The fuel gas leaves the preheater
at 0.3 MPa. Determine the actual air fuel ratio.
32 ( 18.5 ) +3.76 [ 28 ( 18.5 ) ]
A
A 32 x+3.76 [ 28 x ]
=
[1+ e ]¿
[1+0.22] =18.23
Fa
Fa
12 n+m
12 ( 12 )+ 26
32. A steam generator burns fuel oil with 22% excess air. The fuel oil is dodecane. The fuel gas leaves the preheater
at 0.30 MPa. Determine the partial pressure of water.
P=
¿
z
[∆ tm]
mt
26
2
26
12+ + [ 18.5 ][ 0.22 ] +3.76 [ 18.5 ][ 1.22 ]
2
[ 300 ] P=34.23 kPa
33. In the boiler, it is desired to have the flue gas exit temperature above the dew point. Estimate the dew point of
the flue gas produced by combustion having a gravimetric analysis of: N2=72;CO2=20;02= 4; h20= 4
0.04
z
18
P= [ ∆ tm ]¿
[ 101.325 ]¿ 6.675 kPa @ steam tbles 6.675 kPa=38.14
0.72 0.2 0.04 0.04
mt
+
+
+
28 44 32
18
34. Butane and nonane has the following volumetric analysis of 70% and 30% respectively. Assume a complete
combustion with 15%excess air, what is the partial water vapor pressure.
UEL+ AIR=PRODUCT 0.68 CH 4 +1.36 O2+ 1.36 [ 376 N 2 ] → 0.68CO 2 +1.36 H 2 O+1.36 [ 3.76 N 2 ]
0.326+1.36 O2 +1.36 [ 376 N 2 ] → 0.68 CO2 +1.36 H 2 O+1.36 [ 3.76 N 2 ]
35. The dry exhaust gas from oil engine has the following gravimetric analysis: CO2=17.6%;
02=2.2%;N2=80.2%. Specific heats at constant pressure for each gas in kcal/kgK are:
CO2=0.203;02=0.219;N2.248. Determine the name of the fuel being used.
1
1 ¿
MW =
0.176 0.022 0.802 ¿ 30 KGOnly 2carbon can fit 30; 30−2 ( 12 )=6:6 molecules ¿ hydrogen
+
+
εV
44
32
28
C 2 H 6 ; Ethane
36. Find the partial water vapor pressure of benzene having an excess air of 15%.
C 6 H 6 +7.5 O 2 +7.5 [3.76 N 2 ] →6 CO 2 +3 H 2 O+7.5 [ 3.76 N 2 ]mt =6+3+7.5 [ 3.76 ] [ 1.15 ] + [ 7.5 ] [ 0.15 ] =42.56
p=
z
3
=
[ 101.325 ] P=7.14 kPa
42.56
mt [ 101.325 ]
37. Find the air fuel ratio for a combustion process to which the fuel is Octane.
A 32 x +3.76 [ 28 x ] A 32 ( 12.5 ) +3.76 [ 28 ( 12.5 ) ] x=8+ 18 =12.5 A =15.05
=
=
4
Ft
F
12n+ m
F
12 ( 8 ) +18
38. There are 20 kg of flue gases formed per kg of fuel oil burned in the combustion of fuel oil C12H2. What is the
excess air in percent?
A [ x +3.76 x ][ 28.97 ] [18.5+ 3.76 (18.5 ) ] [ 28.97 ] A = A ( 1+ e )
=
¿
20−1=15.01 (1+ e ) e=26.61 %
Fa Ft
F
12 n+ m
12 ( 12 ) +26
39. If methane is completely burned, find the percent nitrogen in the products.
CH 4 +2 O2+ 2 [ 3.76 N 2 ] → CO 2+ 2 H 2 O+ 2 [ 3.76 N 2 ]%=
2 (3.76 )
%=0.715∨71.5 %
1+2+2 ( 3.76 )
40. Methane is burned completely with 25% excess air. Compute the number of moles of nitrogen in the products of
combustion per mole of fuel.
CH 4 +2 O2+ 2 [ 3.76 N 2 ] → CO 2+ 2 H 2 O+ 2 [ 3.76 N 2 ]¿ of moles N 2 =2 [ 3.76 ][ 1+ 0.25 ] N 2=9.4 moles
41. Calculate the heating value of coal having the following composition by weight using Dulong's formula.
C=75%;H2=5%;02=6%;N2=1.5%;S=3%;H20=1.5%;Ash=8%
[
QH =14500 C+62000 H −
Btu
O
0.06
+4000 S¿ 14500 [ 6.75 ] +62000 0.05−
+4000 [ 0.03 ] QH =13630
8
8
lb
]
[
]
42. At 25°API, what is the heating value of oil in Btu/lb?
[
QH =41130 +139.6 API ¿ 41130 +139.6 [ 25 ]¿ 44620
KJ
kg
][
1 Btu
1.055 KJ
][
Btu
1 kg
QH =19180.88
2.205 lb
lb
]
43. What is the specific gravity of an oil which has a Baume reading of 28 degrees?
SG=
140.5
140.5
¿
SG=0.886
130.5+ ° BVME 130.5+ 28
44. Determine the air fuel ratio of ethane using 20% excess air.
32 ( 3.5 ) +3.76 [ 28 ( 3.5 ) ]
6
A 32 x +3.76 [ 28 x ]
=
[ 1+e ] x=2+ =3.5 A =
[ 1+0.2 ]¿ 19.22
4
F
12n+ m
F
12 ( 2 )+ 6
45. A mixture contains 4 moles of 02, 6 moles of N2 and 5 moles of CO2 at 100°C and 225kpa. The partial pressure
of oxygen is :
P=
mo
4
¿
[ 225 ] kPa P=60 kPa
mt [ 225 ] 6+5+ 4
46. The composition of a mixture of gases is 60%CO2, 20%02 and 20%He by volume. What is the apparent molecular
weight of the mixture?
weight=0.6 [ 12+32 ] +0.2 [ 32 ] +0.2 [ 4 ]weight=33.6
47. A mixture compos of 60%CO2 and 40%He by volume analysis is contained at 0.5MPa. What is the partial
pressure in kpa of the helium in this mixture?
P=
He
[ 500 ] ¿ 0.4 +0.6 [ 500 ] kPa p=200 kPa
mt
0.4
48. A gaseous mixture of methane, ethane and propane has partial pressures respectively of 95kpa, 105kpa and
50kpa. What is the mass percentage of methane in the mixture?
P=vP95=V 1 [ 101.325 ]V 1=0.937 105=v 2 [ 101.325 ] v 2=1.036 50=v 3 [ 101.325 ] v 3=0.493
% CH 4 =
0.937 [ 16 ]
% CH 4 =0.2212∨22.12 %
0.937 [ 16 ] +1.036 [ 30 ] +0.493 [ 4 ]
49. The combustion gases from a steam power plant have the following Orsat
analysis:CO2=11.1%;CO=0.6%;02.7.8%; N2=80.5%. Determine the excess air used.
e=
O2−0.5 O
0.078−0.5 ( 0.006 )
¿
e=0.545∨54.5 %
0.26 N 2−[ O2−0.5CO ] 0.264 ( 0.805 )− [0.078−0.5 ( 0.006 ) ]
50. Determine the air fuel ratio of diesel oil.
A 32 x +3.76 [ 28 x ] x=12+ 24 =18 A 32 ( 18 ) +3.76 [ 28 ( 18 ) ] A =14.7
=
=
4
Ft
F
12n+ m
F
12 ( 12 )+ 24