PPE PROBLEM SET on STEAM GENERATOR
1. A water tube boiler has a heating surface area of 500 m 3. For a developed boiler Hp of 933. Determine the
percent rating of the boiler.
RBH =
HS 500
DB H 933 BHP
¿
¿
¿ 549.45 BHP %R=
%R=169.81 %
0.91 0.91
RBH 549.45 BHP
2. The factor of evaporation of the boiler is 1. 12 and a steam rate of 0.73 kg/s. what is the developed boiler hp?
KJ
ms [ hs−hf ] 0.73
hs−hf
hs−hf
KJ DBH =
kg
FE=
1.12=
hs−hf =2527.84
kJ ¿
2257
2257
kg
35322
kg
[
][
3600 s
KJ
2527.84
1hr
kg
KJ
35322
kg
][
]
DBH =188.074 BHP
3. The percent rating of water tube boiler is 200%, factor of evaporation is 1.1 and heating surface are is 300
m2.Find the rate of evaporation.
RBH =
HS 300
hs−hf
hs−hf
DBH
DBH
¿
1.1=
2=
¿ 329.67 FE=
hs−hf =2482.7%R=
DBH =659.34
0.91 0.91
2257
2257
RBH
329.67
DBH =
ms [ hs−hf ]
ms [ 2482.7 ]
659.34=
ms=9380.61 kg/hr
35322
35322
4. The actual specific evaporation of a certain boiler is 8. Factor of evaporation is 1.15. If the heating value is
26,000 KJ/kg., find the boiler efficiency.
FE=
hs−hf
hs−hf
ms [ hs−hf ]
2595.55
1.15=
¿ [ 8]
hs−hf =2595.55e=
e=0.8∨80 %
2257
2257
26000
msQn
[
]
5. The ASME evaporation units of a boiler is 24,827,500 KJ/hr. The boiler auxiliary consumes 2.5MW. What is the
net boiler efficiency if the heat generated by fuel is 32,000,000 KJ/hr.
ms [ hs−hf ] − Aux ¿
e=
ms Qh
[
24827500
KJ
hr
1000 kw
1
−[ 2.5 MW ]
kg
3600 s
1 MW
e=0.4946∨49.46 %
Kj
32 000 000
hr
kg 1
s
3600
][
]
[
[
]
]
6. A 150,000 kg of coal supplied to two boilers. One has a capacity of 350 kg/hr and the other boiler has a capacity
of 100 kg/hr. How many days to consume the available fuel?
ms=
m [ 350+ 100 ] kg
1 day
kg
=150 000 t=[ 333.33 hr ]
t=13.88=14 days
t
24 hr
hr
t
[ ]
7. A boiler operates at 82.5% efficiency while the mass of steam generated is 995,000 lbs in 5 hrs. The enthalpy of
steam is 1400 Btu/lb and feed is 250 Btu/lb while the fuel used for boiler has a heating value of 14,850 Btu/lb.
Find the mass of fuel needed in short tons per day.
995000 lbs
[ 1400−250 ] btu
5 hr
ms [ hs−hf ]
lb 1 short ton 24 hr
mf = 18679.73
e=
lb
hr
2000 lb
1 hr
msQh 0.825=
Btu
mf 14850
lb
mf =224.16 ton/day
[
]
[
[
]
][
][ ]
8. Two boilers are operating steadily on 94,000 kg of coal contained in a bunker. One boiler producing 1600 kg/hr
of steam at 1.2 factor of evaporation and an efficiency of 65% and another boiler produces 1464 kg/hr of steam
at 1.15 factor of evaporation and efficiency of 60%. How many hours will the coal in the bunker run the boilers if
the heating value is 7,600 kcal/kg?
kg
kg
[ 1.2 x 2257 ] KJ
1464
[ 1.15 x 2257 ] KJ
hr
hr
kg
ms [ hs−hf ]
mf 1=209.57
e=
kg
kg
hr 0.6=
mf Qh 0.65=
kcal
KJ
KJ
mf 7600
4.187
mf 2 [ 7600 kcal ] 4187
kg
kcal
kcal
[
]
1600
[
mf 2=199.08
[
][
]
]
[
]
kg
m
mf = t=230.03 hrs
hr
t
9. A typical steam generator with an efficiency of 75% is producing 10kg/s of steam. The enthalpy of the entering
water is 125.7910KJ/kg and is superheated to an enthalpy of 3034.8KJ/kg. The fuel used has heating value of
42,1501KJ/kg. The A/F ratio by weight is 14. Determine the amount of air needed has heat in kg/hr.
10
0.75=
e=
ms [ hs−hf ]
mf Qh
kg
3034.8−12579 ] KJ /kg
s
KJ
mf 42150
kg
kg
¿ 3312.75
hr
kg air
14=
kg
3312.75
hr
kg
kg air=46378.52
hr
[ ][
[
]
10. A steam generator evaporated 20,000 kg of water per hour from feed water with enthalpy of 461.3KJ/kg of
steam with enthalpy of 2706.31KJ/kg. Coal consumption is 2100 kg/hr. its heating value as fired is 28,300 KJ/kg.
Calculate the boiler horsepower.
kg
[ 2706.3−461.3 ] KJ /kg
ms [ hs−hf ] 2000
DBH =
DBH =1271.16 BHP
hr
35322 ¿
35322
[
]
11. Steam boiler on a test generates 858,000 lb of steam in a 4 hr period. The average steam pressure is 400 psia,
the average steam temperature is 700F, and the average temperature of the feedwater supplied to the boiler is
280F. If the boiler efficiency for the period is 82.5%, and if the coal has a heating value of 15,350 Btu/lb as fired,
find the average amount of coal burned in short tons per hour.
@table 3 400 psi∧700 ℉ hs=1362.5
Btu
250 218.52280 h 1300 269.61250 219.56280 h 2300 270.53
lb
858000 lb
[ 1362.5−249.9 ]
4 hr
ms [ hs−hf ]
0.825=
0 249.174400 249.948500 250.142e=
mf Qh
btu
mf 15350
lb
[
]
[
[
mf = 18844.52
]
ton
lb
1 ton
mf =9.42
hr 2000 lb
hr
][
]
12. Steam is admitted to the cylinder of an engine in such a manner that the average pressure is 120psi. The
diameter of the piston is 10inch and the length of the stroke is 12inch. What is the h of the engine when it is
making 300rpm?
P=
2 πTN ¿ 2 120 lb ¿ ¿
P=171.4 HP
33000
i n3
[
]
13. 24.5 kg of steam per second at 5 MPa and 400°C is produced by a steam generator. The feed water enters the
economizer at 145°C and leaves at 205°C. The steam leaves the boiler drum with a quality of 98%. The unit
consumes 2.75 kg of coal per second as received having a heating value of 30000 Ki/kg. What would be the
overall efficiency of the unit in percent?
@Table 3 :5 MPa∧400 ℃hs=3195.7@table 1 :145 ℃hf =610.63
e=
24.5[3195.7−610.63]
2.75 [ 30 000 ]
e=0.77∨77 %
14. Determine the vacuum efficiency of a surface condenser which operates at a vacuum of 635 mm Hg and exhaust
steam enters the condenser at 45.81°C. The barometric pressure is 760mm Hg.
45 9.59345.81 10.00246 10.098 P=10.002 kPa x 760
¿
mmHg
Patm−P
¿ 75.02 mmHgev =
101.325 kPa
Patm−Psat
760−125
e=0.927∨92.7 %
760−75.02
15. If coal having a hat of combustion of 16,000 Btu per lb is used in a heating plant of 50% efficiency, how many
pounds of steam of 50% quality and 212°F temperature can be made per pound of this coal from water whose
initial temperature is 70°F?
@table 1 212 ℉hf =180.10hfg=970.3hs=hf + xhfg¿ 180.16+0.5 ( 970.5 ) ¿ 665.31@table 1 70 ℉
hf =38.09e=
ms [ hs−hf ]
ms 065.31−3809 ms
0.5=
=12.8
mf
16000
mf
mf Qh
[
]
16. Find the degree superheat of steam at 0.89MPa and 180°C.
@ table 2 0.89 Mpa
Tsat =174.90° SH =Tg−Tsat¿ 180−174.9° SH =5.1℃
17. The heat transferred to the engine is at a rate of 60MW. Compute the thermal efficiency of the heat engine
when the rate of waste heat rejection from a nearby reservoir is 40MW.
e=
QA−QR 60−40
¿
e=0.3333∨33.33 %
QA
60
18. A typical steam generator with an efficiency of 80% is producing 15kg/s of steam. The enthalpy of the entering
water is 133.98Kj/kg and is superheated to an enthalpy of 3256.4 KJ/kg. The fuel used has a heating value of
43,250 KJ/kg. The A/F ratio by weight is 17.5.
Determine the amount of air needed in kg/hr.
15
e=
ms [ hs−hf ]
mf Qh 0.8=
17.5=
kg
3256.4−133.98 ] KJ
s
kg α kgair
kg 3600 s
¿ 4873.14
=
mf = 1.35
kg
hr f kgfuel
s
1 hr
KJ
mf 43250
kg
[ ][
[
]
[
][
]
kgair
kg
kgair=85279.97
4873.14
hr
19. A boiler uses 2000 kg of coal per hour. The amount of air needed for the combustion of one kg coal is 20 kg. If
ash loss is 15%, calculate the mass of gas entering the chimney.
ma
kg
=20ma=20 mf m ash=0.15 mf mg=ma+ mf −mash¿ 20 mf + mf −0.15 mf ¿ 20.85 mf ¿ 20.85 2000
mf
hr
mg=41700 kg/hr
[
]
20. A steam generator evaporated 22,000 kg/hr of water from a feedwater with enthalpy of 481.2KJ/kg to steam
with enthalpy of 2,508.9KJ/kg. Coal consumption is 2200kg/hr. Its heating value as fired is filer horsepower.
kg
[ 2508.9−481.2 ] KJ /kg
ms [ hs−hf ] 22000
DBH =
DBH =1263 BHP
hr
35322 ¿
32322
[
]
21. The rated boiler horsepower of a water tube generator is 164kw. The heating furnace area is?
RBH =
HS
1 HP
HS
164 kw x
=
HS=200 m2 ¿HS=2154 f t 3
0.929
0.745 Kkw 0.91
22. A fire tube boiler which has a heating surface area of 2960 sq. ft. at a height of 10ft is to convert to water tube
type. Feedwater temperature of 33 C and pressure of 0.1Mpa delivers to the furnace area passing right after the
economizer. Determine the heating surface area difference of the conversion.
[
m
2
2
]
2 1
ft
HS
HS
HS
2960 f t 3.281 ¿ 249.97 RBH =
RBH =
249.97=
HS 2=227.47∆ HS=HS1−HS2
¿
1.1
0.91
0.91
1.1
¿ 274.97−227.47¿ [ 47.5 m
2
]
[
1002 cm
∆ hs=4.75 x 105 c m 2
1 m2
]
23. A steam boiler generates 600,000 kg of steam in a 4-hour period. The steam pressure is 2750kpa and 370°C. The
temperature of the feedwater is 138C. If the overall thermal efficiency is 82% and the fuel is at 28 API, find the
average amount of fuel burned per hour.
@table 3 2.75 Mpa∧370 ℃hs=3166.9@table 1 138 ℃hf =580.54Qn=41130+139.6 API
kg
600 000
KJ
ms ( hs−hf )
4 hr [ 3166.9−580 ] mf =10504.6 kg /hr
e=
¿ 41130 +139.6 [ 28 ]¿ 45038.8
kg
mf Qn 0.82=
mf [ 45038.8 ]
24. 25kg of steam at 5MPa and 400°C is produced per second by a steam generator. The feedwater enters the
economizer at 145°C and leaves at 205°C. Determine the overall efficiency given the ultimate analysis of coal of:
C=75.2,H=8.3,0=12,S=4.2 and Ash=0.3 where it consumes 3kg/s.
@table 3 :5 Mpa∧400 ℃hs=3195.7@table 1 145 ℃hf =610.63QH =35629.82e=
¿
ms [ hs−hf ]
mf Qh
25 [ 3195.7−610.63 ]
e=0.605∨60.5 %
3 [ 35629.82 ]
25. A boiler operating at 11kg/cm2 is required to generate a minimum of 13.89 kg per second of saturated steam.
Feedwater enters the boiler at 80°C. The furnace is designed to fire coal at an average rate of 3 kg per second
and the overall efficiency is 85%. Compute the gross calorific value.
kg 1002 c m 2 9.81 N 1 KN
x
x
¿ 1079.1 kPA@Table 2=1.0791 Mpa1.06 2780.31.0791 2780.96
cm
1kg 1000 N
1 m2
KJ
ms [ hs−hf ]
13.89 [ 2780.96−334.9 ]
Qh=13 323.82
1.08 2781@table 1=80 ℃hf =334.91e=
0.85=
kg
mf Qh
3 Qh
Btu
Qh=5727.5
lb
11
26. A boiler operating at 11kg/cm2 is required to generate a minimum of 19 kg per second of saturated steam.
Feedwater enters the boiler at 80°C. The furnace is designed to fire coal at an average rate of 1.5 kg per second
and the boiler efficiency is 85%. Compute the rated boiler horsepower of 112% rating.
@table 2=1.0791 Mpahf =2780.96@table 1=80 ℃hf =334.91%R=
19 kg /s [
1.12=
DBH
RBH
3600 s
][2780.96−334.91]
1 hr
RBH =4229.2 BHP
RBH
27. What is boiler in a pan on a stove in sea level? During 10 minutes of boiling. It is observed that 200grams of
water has evaporated. What is the rate of heat transferred?
[
Q=mLv¿ [ 0.2 kg ] 2257
KJ
KJ
¿ 451.4
Q=45.14 KJ /min
10 min
kg
]
28. Find the net boiler efficiency of a water tube boiler whose heating value is 45,000KJ/kg at 3kg/s fuel rate, actual
specific evaporation of 20 and factor of evaporation of 1.3 with auxiliaries of 60KW.
FE=
hs−hf
hs−hf
ms [ hs−hf ] 20 [ 2934.1 ]
1.3=
hs−hf =2934.1e=
¿
e=1.30∨130 %
2257
2257
mf Qh
45000
29. Feedwater temperature of 78°C enters the boiler. Find the developed boiler horsepower if the steam flow rate is
18kg/s at 11kg/cm2.
@table 2=1.0791 mPahs=2780.96table 1=78 ℃hf =326.51DBH =
ms [ hs−hf ]
35322
kg
18
s
¿
[
3600 s
[ 2780.96−726.51 ] DBH =4502.81 BHP
1 hr
35322
]
30. A steam boiler generating 8kg/s of 4.137kpa, 426.7°C
steam is continuously blown at the rate of 0.49kg/s.
Feedwater enters the economizer at 148.9°C. The furnace burns 0.7kg/s of 35322KJ/kg heating value. Calculate
the overall thermal efficiency of the boiler.
e=
ms 1hg +ms 2 hf −[ m1+ms ] hf 8 [ 3274.09 ] +0.49 [ 1097.02 ] + 8.49 [ 629.87 ]
¿
e=0.865∨86.5 %
mf Qh
0.7 [ 35322 ]
31. A steam plant operates with initial pressure of 1.7 Mpa and 370C temperature and exhaust to a heating system
at 0.17MPa. The condensate from the heating systemis returned to the boiler at 65.5°C and the heating system
utilizes from its intended purpose 90% from the steam it receives. The turbine efficiency is 7 of the energy
transferred from the steam it receives. The turbine efficiency is 75%. If the boiler efficiency is 86%, what is the
cogeneration efficiency of the system? Neglect pump work.
WT =e [ h 1−h 2 ]¿ 0.75 [ 3187.1−2670.75 ] ¿ 387.27QR=e [ h 2−h 3 ] ¿ 0.9 [ 2670.7−274.15 ]¿ 2156.93
QA=
[ h 1−h 4 ] ¿ 3187.1−274.15 e= output ¿ 287.27+2156.93
e
0.86
input
3387.10
¿ 0.7511∨75.11 %
32. Steam enters the superheaters of a boiler at a pressure 25bar and dryness of 0.98 and leaves at the same
pressure at a temperature of 370°C. Calculate the heat energy supplied per kg steam supplied in the
superheaters.
@table 3=2.5 Mpa∧370℃hs=3171.8@table 2=2.5 Mpahs=962.11hfg=1841hf =hf + xhfg
hf =962.11+0.98 ( 1841 )¿ 2766.29Q=m [ hs−hf ] ¿ 3171.8−2766.29Q=405.51 KJ /kg
33. A double pass condenser with a mass flow rate of 1000000kg/hr has a leaving flow velocity of 1.5m/s. The area
of the condenser tube is 0.0003m2. Calculate the number of tubes.
kg
100 000 /
M
kg
hr
ρ=
V 1000 3 =
v
m
V =1000
2
m3
m3
hr
[
V = Avn 1000
1
=0.0003 m
hr
hr
3600 s
[
][
]
1,5 m
[ n]
s
]
n=617.28 x 2n=1235
34. From the furnace, heat is transferred to a heat engine at a rate of 75MW. The rate of rejection of waste heat to
a sink is 440M111/. Compute the thermal efficiency of the heat engine.
e=
QA−QR 75−40
¿
e=0.4667∨46.67 %
QA
75
35. A water tube condenser has a total of 60tubes. If these are three tubes per passes, compute the number of
tubes per pass.
tubes no . oftubes tubes
tubes
=
=20
p ass no . of passes pass
pass
36. A water tube boiler evaporated5.05kg/s of water from a feedwater temperature of 104.44°C to steam at
1241.1kPa and quality of 0.97; weight of the coal per second is 0.57; heating value of coal as fired is
11,800Btu/lb. Determine the rate of heat absorption in KW.
@table 1=10449℃104 435.92104.44 437.78105 440.15hs=hf + xhfg ¿ 865.46+0.97 [ 1980.55 ]¿ 2726.59
@table 2=1.2411 Mpa1.24 805.28 1980.71.2411 805.46 1980.551.26 808.53 1978Q=m [ hs−hf ]
¿ 5.05 [ 2726.59−437.78 ]Q=11558.5 KW
37. A water tube boiler evaporated 5.05kg/s of water from a feedwater temperature of 104.44°C to steam at
1241.1kPa and quality of 0.97; weight of the coal per second is 0.57; heating value of coal as fired is
11,800Btu/lb. Find the boiler horsepower.
hs=2726.59hf =437.78DBH =
m [ hs−hf ]
35322
kg
5.05
s
¿
[
3600 s
[ 2726.59−437.78 ] DBH =1178 BHP
1 hr
35322
]
38. A water tube boiler evaporated5.05kg/s of water from a feedwater temperature of 104.44°C to steam at
1241.1kPa and quality of 0.97; weight of the coal per second is 0.57; heating value of coal as fired is
11,800Btu/lb. Find the boiler efficiency.
[
hs=2726.59hs=437.78Qh= 11800
¿
KJ
Btu
KJ
lb
ms [ hs−hf ]
¿ 27450.05
1.055
2.205
e=
kg
lb
Btu
1 kg
Mf Qh
][
][
]
5.05[2726.59−437.78 ]
e=0.7387∨73.87 %
0.57( 27450.05)
39. A steam condenser receives 18kg/s of steam with an enthalpy of 275010/kg. Steam condenses into liquid and
leaves an enthalpy of 16010/kg. Cooling water passes through the condenser with temperature increase from
13°C to 24°C. Calculate the cooling water flow rate.
mCp ∆ T =ms [ h 1−h 2 ]m [ 4.187 ] [ 24−13 ]=18 [ 2750−160 ]m=1012.22
Kg
s
40. An HRT boiler is 4.25m long, 1950mm inside diameter has one hundred 100mm by 2.60mm tubes. The shell is
16mm thick. Setting walls touch the shell at the horizontal diameter. Calculate the heating surface of tubes.
Di=do−2t¿ 100−2 ( 2.6 )¿ 94.8H . S=πDi ln¿ π
94.8
4.25 ] H . S=126.6 m2
1000
[ ][
41. An HRT boiler is 4.25m long, 1950mm inside diameter has one hundred 100mm by 2.60mm tubes. The shell is
16mm thick. Setting walls touch the shell at the horizontal diameter. Calculate the heating surface of shell.
1
1 1982
[ 4.25 ] H . S=13.23 m2
Do=Di+ 2t ¿ 1950+2 [ 16 ]¿ 1982 H . S= π Do L¿ π
2
2 1000
[ ]
42. A. HRT boiler is 4.25m long, 1950mm inside diameter has one hundred 100mm by 2.60mm tubes. The shell is
16mm thick. Setting walls touch the shell at the horizontal diameter. Calculate the heating surface of tube
sheets, assuming C=0.67.
2
π 2¿
1.99
2
H . S= D
π
2 ¿
3 [ 1.95 ] ❑ 0.67 H . S=2.97 m
4
4
[
]
43. An HRT boiler is 4.25m long, 1950mm inside diameter has one hundred 100mm by 2.60mm tubes. The shell is
16mm thick. Setting walls touch the shell at the horizontal diameter. Calculate the total heating surface.
π
2
H . S= A 1+ A 2+ A 3− A 4 ¿ 13.23+126.6+2.97− [ 0.1 ] H . S=142.79 m2
4
44. An HRT boiler is 4.25m long, 1950mm inside diameter has one hundred 100mm by 2.60mm tubes. The shell is
16mm thick. Setting walls touch the shell at the horizontal diameter. Calculate the rated boiler horsepower.
RBH =
HS 142.8
¿
RBH =130 BHP
0.91 1.1
45. A boiler plant is to furnish steam for a 100hp engine using 17Ib of steam per hp-hr. The auxiliaries used 25% as
much as the engine. The efficiency of the boiler, furnace and grate is 70%. Steam pressure is 100psi, quality is
98%, feedwater temperature is 200°F. Coal contains 13,000Btu/lb. How much coal will the plant use in an hour.
@table 1=200 ℉hf =168.07@table 2=100 psihf =298.61hfg=889.2hs=hf + xhfg¿ 298.61+0.98 ( 889.2 )
¿ 1170.03e=
lb
ms [ hs−hf ]
lb
¿
0.7=[ 100 Hp ] 17 −hr 1170.5−168.07 ¿
mf =187.2
hp
hr
mf Qh
mf [ 13000 ]
[
]
46. A steam boiler having 153.4m2 of heating surface has a steaming capacity of 6800kg/hr. Steam is generated at
1.724MPa and 249°C from 138°C feedwater. Calculate the rated boiler horsepower.
RBH =
HS
m2
RBH =168.6 HP
¿ 153.4
0.91
0.91
47. A fuel of 12300Btu was burned in the furnace of a 2400sq.ft water tube boiler which was generating 12000lb
steam per hr at 200psi, dry and saturated from 228°F feed at a time when fuel consumption was 13501b/hr.
Determine the percent rating of the boiler.
@table 2=200 psihs=1199.3@table 1=228 ℉hs=196.3DBH =
ms [ hs−hf ]
33480
DBH
12000lb /hr [ 1199.3−196.3 ] btu/lb
2400 ft 2
¿ 359.5RBH =HS/10¿
¿ 240%R=
RBH
33480
10
359.5
¿
=1.49∨149 %
240
¿
48. A fuel of 12300Btu was burned in the furnace of a 2400sq.ft water tube boiler which was generating 12000lb
steam per hr at 200psi, dry and saturated from 228°F feed at a time when fuel consumption was 1350lb/hr.
Determine the overall thermal efficiency.
@table 2=200 psihs=1199.3@table 1=228 ℉hf =196.3e=
ms [ hs−hf ]
mf Qh
lb
[ 1199.3−146.3 ] btu/ lb
hr
e=0.725∨72.5 %
lb
1350 [ 12300 ] btu /lb
hr
1200
¿
49. A simple water tube boiler of 20,000m2 heating surface is offered by a salesman for installation in a steam plant
where 80,000 lb of dry and saturated steam are to be produced at 190psig from 210°F feedwater. Using the
babcock formula verify whether this area is adequate by assuming mass flow of 5000Ib/hr-ft. Furnace and
chimney temperatures of 1800°F and 450°F respectively.