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1. INTRODUCTION
Heat is transferred when two objects are of different temperature and this transfer
continuous until equilibrium is reached. This property of heat is true to all materials. Three
materials are said to be in thermal equilibrium if first material has the same temperature as the
second material and the second material has the same temperature as the third material. There
are different ways in which heat transfer occurs.
Heat is lost from the pipe, or other surfaces to the room in two ways
1. by conduction through and air film, and then by convection in the bulk of the air
2. by direct radiation to the cooler walks of the room.
Heat loss in pipes is not a favorable phenomenon in which an industry comes upon.
Aside from the energy lost during the transfer, the surroundings near the pipes may get hotter
and employees may not be comfortable in working. However, this cannot be prevented due to
its properties thus, controlling actions may be done such as coating the pipes with an insulating
material to reduce the transfer of heat from the pipe to the surroundings. Thus, a study in
thermal transfer of pipes is really a good background for a student to start since most processes
involves this phenomenon.
In conduction, heat can be conducted through different mediums. Energy is transferred
by the motion of adjacent atoms. The transfer of heat by convection implies the transfer of heat
by bulk transport and mixing of macroscopic elements of warmer portions with cooler portions
of gas or liquids. These usually represents fluids.
Radiation differs from heat transfer by conduction and convection in that no physical
medium is needed for its propagation. Radiation is the transfer of energy through space by
means of electromagnetic waves in much the same way as electromagnetic light waves transfer
light.
2
2. THEORITICAL BACKGROUND
Heat transfer is a discipline of thermal engineering that concerns the generation, use,
conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is
classified into various mechanisms, such as thermal conduction, thermal convection, thermal
radiation, and transfer of energy by phase changes.. Generally, this heat transfer occurs from a
high temperature material to a lower temperature material
Heat conduction, also called diffusion, is the direct microscopic exchange of kinetic
energy of particles through the boundary between two systems. When an object is at a
different temperature from another body or its surroundings, heat flows so that the body and
the surroundings reach the same temperature, at which point they are in thermal equilibrium.
Convective heat transfer, or convection, is the transfer of heat from one place to another
by the movement of fluids, a process that is essentially the transfer of heat via mass transfer.
Bulk motion of fluid enhances heat transfer in many physical situations, such as (for example)
between a solid surface and the fluid. Convection is usually the dominant form of heat transfer
in liquids and gases.
When two bodies are at different temperatures and separated by distance, the heat
transfer between them is called as radiation heat transfer. In case of the conduction and
convection heat transfer there is a media to transfer the heat, but in case of the radiation heat
transfer there is no media. The radiation heat transfer occurs due to the electromagnetic waves
that exist in the atmosphere.
Heat transfer is very important since it is frequently used in most of the processes, and
if not, is a natural occurring phenomenon and is inevitable in production. Industrial processes
usually require steam for operations such as heating. This medium is usually transported via
metal pipes. However, it is inevitable to encounter heat losses in this arrangement because of
3
the inherent temperature difference existing between the hot pipes and the surroundings. This
can instead be minimized through insulations placed on bare pipes. On the other hand, if a
process requires enhancing heat losses then the use of fins would be more appropriate.
The heat loss of pipes is due to the temperature gradient between the pipe and the
surroundings. Temperature difference, the thermal resistance, and the heat transfer area are
common factors involving the rate of heat transfer. The most common approach in dealing with
heat loss in pipes is the installation of insulating materials in the surface of the pipes.
The rate of heat lost from a pipe carrying steam can be measured simply by determining
the rate of condensation of steam, m, which can be collected at a certain point interval of time.
By heat balance,
Equation 1
where,
Bare pipes are uninsulated kind of pipes. Pipes which are insulated are also called
lagged pipes.
To determine therefore the effectiveness of an insulation, it is just a matter of comparing the
heat lost from the pipe with an insulation with that from a bare pipe. Since heat lost is
4
proportional to the rate of condensation, and the weight of condensate is proportional to the
volume of condensate v, assuming temperatures and pressures of condensates are the same,
then the lagging efficiency may be determined using the equation.
Equation 2
In convection the heat transfer coefficient can be calculated by the equation
Convection coefficient, hc = 0.42(
∆𝑇
𝐷
)0.25
Equation 3
While in radiation
Radiation coefficient, hr =
1.73p[(
Ts
100
)
4
−(
Tr
100
)
4
]
ΔT
Equation 4
5
3. EXPERIMENTAL SECTION
3.1 Materials and Apparatus
- Boiler
- Test pipes – bare, paint, silver chrome paint, and 85% magnesia insulation
- Thermocouple
- Beakers
- Graduated Cylinder
- Stopwatch
3.2 Procedure
Two runs with steam at approximately 30 psig for each run was made.
1. The drain cock was cracked under the header to remove the water from the
steam line and header after adjusting the system to the desired pressure.
2. The four plug type valve was opened to blow out any condensate from the
pipes and was closed until only small amount of steam escapes along with
the condensate.
3. The condensate from each pipe was measured and collected over a time
interval of 15 minutes and the surface temperatures were read 20 inches
from the end of the pipe.
3.3 Specifications
LENGTH OF PIPE
PIPE NO. 1 2 3 4
COVERING
PAINT BARE PIPE SILVER-
CHROME
PAINT
85%
MAGNESIA
INSULATION
OUTSIDE
DIAMETER (in.)
1.3535 1.35 1.382 2.48
6
Table 3.3.1
EMMISIVITY 0.96 0.95 0.96 0.72
RUN NO.
BAROMETRIC
PRESSURE
1 atm
STEAM PRESSURE 30 psig
STEAM
TEMPERATURE
84°C ≈ 183.2°F
ROOM
TEMPERATURE
30°C ≈ 86°F
TIME/RUN 5 minutes
7
4. RESULTS AND DISCUSSION
. Heat is transmitted through the insulation by means of radiation, conduction and
convection. The relative amount of each of these three factors depends entirely upon the
construction of the insulating material. Offering some resistance to heat transfer such as
insulation can reduce the amount of heat that is to be transferred to the surroundings. The bare
pipes, the pipe having no coating or insulation, has the third highest temperature of the three
pipes. This is considered and error however, the difference between the temperature is very
small and considering the environment many errors are expected to occur especially it was an
open environment and the thermostats are not functioning consistently. However, for the pipe
that was coated with 85% magnesia, it shows to have the least temperature. This is true since
it has the thickest resistance while those covered with paints and silver chrome may have no
effect because of the deterioration of the insulating materials.
Pipe no. 1 2 3 4
Trial Point
location
Surface Temperature
1st
A 98°C 82°C 77°C 48°C
B 101°C 86°C 83°C 51°C
C 110.3°C 98.4°C 110.1°C 58.2°C
D 114°C 105.6°C 114°C 62.7°C
2nd
A 99°C 80°C 78°C 46°C
B 102.5°C 86°C 83°C 50°C
C 113°C 105.6°C 109°C 61°C
D 117°C 110.2°C 113°C 65.1°C
8
Table 4.1
Average Temperature 106.85°C
≈ 224.33°F
94.225°C
≈ 201.605°F
95.8875°C
≈
204.5975°F
55.25°C
≈ 131.45°F
Average Condensate Collected 85.5 ml 77 ml 50 ml 32 ml
Lagging Efficiency 8.97% 0% 33.3% 58.97%
Convection Coefficient 1.89 1.74 1.63 1.73
9
5. CONCLUSION
Insulated pipes tend to have higher lagging efficiency in order to minimize heat losses
in industrial and commercial applications. The one coated with the 85% magnesia showed to
have the least temperature. This supports the theory since its resistance is the greatest among
the pipes. This kind of insulation is very useful in dealing with pipes especially in the industry
since the usage pipes is inevitable. It can prevent too much energy loss and can provide comfort
to the workers since heat is controlled. The experiment is not as successful as expected however
the error is small.
It is possible that any errors in the results and data could be in the reading of the surface
temperature of the pipes. Another one is the inconsistency of the thermal couples. Also, the
insulation around the pipes seemed to deteriorate.
6. RECOMMENDATION
It is recommended to fix the thermal insulation materials found in the piping since the
students suspect that it could be the cause of the error. Another one the usage of a carefully
calibrated thermocouple.
10
7.REFERENCES
[1] https://www.engineeringtoolbox.com/emissivity-coefficients-d_447.html
[2] https://dokumen.tips/documents/heat-loss-for-bare-and-lagged-pipes.html
[3] https://www.process-heating.com/articles/87988-calculating-heat-loss
[4] https://en.wikipedia.org/wiki/Heat_pipe[
[5] http://www.environmentcentre.com/wp-
content/uploads/2016/08/5_Pipe_lagging_new_branding.pdf
8. APPENDIX
8.1 Tables and figures
LENGTH OF PIPE
PIPE NO. 1 2 3 4
COVERING
PAINT BARE PIPE SILVER-
CHROME
PAINT
85%
MAGNESIA
INSULATION
OUTSIDE
DIAMETER (in.)
1.3535 1.35 1.382 2.48
EMMISIVITY 0.96 0.95 0.96 0.72
RUN NO.
BAROMETRIC
PRESSURE
1 atm
STEAM PRESSURE 30 psig
11
Table 4.1
STEAM
TEMPERATURE
84°C ≈ 183.2°F
ROOM
TEMPERATURE
30°C ≈ 86°F
TIME/RUN 5 minutes
Pipe no. 1 2 3 4
Trial Point
location
Surface Temperature
1st
A 98°C 82°C 77°C 48°C
B 101°C 86°C 83°C 51°C
C 110.3°C 98.4°C 110.1°C 58.2°C
D 114°C 105.6°C 114°C 62.7°C
2nd
A 99°C 80°C 78°C 46°C
B 102.5°C 86°C 83°C 50°C
C 113°C 105.6°C 109°C 61°C
D 117°C 110.2°C 113°C 65.1°C
Average Temperature 106.85°C
≈ 224.33°F
94.225°C
≈ 201.605°F
95.8875°C
≈
204.5975°F
55.25°C
≈ 131.45°F
Average Condensate Collected 85.5 ml 77 ml 50 ml 32 ml
Lagging Efficiency 8.97% 0% 33.3% 58.97%
Convection Coefficient 1.89 1.74 1.63 1.73
12
8.2 Computations
8.2.1 Convection coefficient, hc = 0.42(
∆𝑇
𝐷
)0.25
a. Painted pipe
hc = 0.42(
224.33 −86
0.1128
)0.25
= 2.485
𝐵𝑡𝑢
ℎ𝑟∙𝑓𝑡2∙°𝐹
b. Bare pipe
hc = 0.42(
201.605 − 86
0.1128
)0.25
= 2.38
𝐵𝑡𝑢
ℎ𝑟∙𝑓𝑡2∙°𝐹
c. Silver-chrome Paint pipe
hc = 0.42(
204.69753 − 86
0.1152
)0.25
= 2.208
𝐵𝑡𝑢
ℎ𝑟∙𝑓𝑡2∙°𝐹
d. 85% Magnesia insulation
hc = 0.42(
131.35 −86
0.2067
)0.25
= 1.61
𝐵𝑡𝑢
ℎ𝑟∙𝑓𝑡2∙°𝐹
8.8.2 Radiation coefficient, hr =
1.73p[(
Ts
100
)
4
−(
Tr
100
)
4
]
ΔT
a. Painted pipe
hr =
1.73(0.96)[(
226.85
100
)
4
−(
86
100
)
4
]
226.85−86
= 0.3
𝐵𝑡𝑢
ℎ𝑟∙𝑓𝑡2∙°𝐹
b. Bare pipe
hr =
1.73(0.95)[(
201.605
100
)
4
−(
86
100
)
4
]
201.605−86
= 0.23
𝐵𝑡𝑢
ℎ𝑟∙𝑓𝑡2∙°𝐹
c. Silver-chrome Paint pipe
hr =
1.73(0.96)[(
204.7
100
)
4
−(
86
100
)
4
]
204.7−86
= 0.24
𝐵𝑡𝑢
ℎ𝑟∙𝑓𝑡2∙°𝐹
d. 85% Magnesia insulation
hr =
1.73(0.72)[(
131.35
100
)
4
−(
86
100
)
4
]
131.35−86
= 0.07
𝐵𝑡𝑢
ℎ𝑟∙𝑓𝑡2∙°𝐹
8.8.3 For the calculation of lagging efficiency (L.E.) =
WB−WL
WB
x100
13
a. Paint pipe
L.E. =
290 − 250
250
× 100 = 16.0%
b. Bare pipe
L.E. =
250 − 250
250
× 100 = 0%
c. Silver-chrome paint pipe
L.E. =
177.5 − 250
250
× 100 = 29.0%
d. 85% Magnesia pipe
L.E. =
170 − 250
250
× 100 = 32.0%

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Heat loss in Bare and Lagged Pipes- Ed Ryan M. Ruales

  • 1. 1 1. INTRODUCTION Heat is transferred when two objects are of different temperature and this transfer continuous until equilibrium is reached. This property of heat is true to all materials. Three materials are said to be in thermal equilibrium if first material has the same temperature as the second material and the second material has the same temperature as the third material. There are different ways in which heat transfer occurs. Heat is lost from the pipe, or other surfaces to the room in two ways 1. by conduction through and air film, and then by convection in the bulk of the air 2. by direct radiation to the cooler walks of the room. Heat loss in pipes is not a favorable phenomenon in which an industry comes upon. Aside from the energy lost during the transfer, the surroundings near the pipes may get hotter and employees may not be comfortable in working. However, this cannot be prevented due to its properties thus, controlling actions may be done such as coating the pipes with an insulating material to reduce the transfer of heat from the pipe to the surroundings. Thus, a study in thermal transfer of pipes is really a good background for a student to start since most processes involves this phenomenon. In conduction, heat can be conducted through different mediums. Energy is transferred by the motion of adjacent atoms. The transfer of heat by convection implies the transfer of heat by bulk transport and mixing of macroscopic elements of warmer portions with cooler portions of gas or liquids. These usually represents fluids. Radiation differs from heat transfer by conduction and convection in that no physical medium is needed for its propagation. Radiation is the transfer of energy through space by means of electromagnetic waves in much the same way as electromagnetic light waves transfer light.
  • 2. 2 2. THEORITICAL BACKGROUND Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes.. Generally, this heat transfer occurs from a high temperature material to a lower temperature material Heat conduction, also called diffusion, is the direct microscopic exchange of kinetic energy of particles through the boundary between two systems. When an object is at a different temperature from another body or its surroundings, heat flows so that the body and the surroundings reach the same temperature, at which point they are in thermal equilibrium. Convective heat transfer, or convection, is the transfer of heat from one place to another by the movement of fluids, a process that is essentially the transfer of heat via mass transfer. Bulk motion of fluid enhances heat transfer in many physical situations, such as (for example) between a solid surface and the fluid. Convection is usually the dominant form of heat transfer in liquids and gases. When two bodies are at different temperatures and separated by distance, the heat transfer between them is called as radiation heat transfer. In case of the conduction and convection heat transfer there is a media to transfer the heat, but in case of the radiation heat transfer there is no media. The radiation heat transfer occurs due to the electromagnetic waves that exist in the atmosphere. Heat transfer is very important since it is frequently used in most of the processes, and if not, is a natural occurring phenomenon and is inevitable in production. Industrial processes usually require steam for operations such as heating. This medium is usually transported via metal pipes. However, it is inevitable to encounter heat losses in this arrangement because of
  • 3. 3 the inherent temperature difference existing between the hot pipes and the surroundings. This can instead be minimized through insulations placed on bare pipes. On the other hand, if a process requires enhancing heat losses then the use of fins would be more appropriate. The heat loss of pipes is due to the temperature gradient between the pipe and the surroundings. Temperature difference, the thermal resistance, and the heat transfer area are common factors involving the rate of heat transfer. The most common approach in dealing with heat loss in pipes is the installation of insulating materials in the surface of the pipes. The rate of heat lost from a pipe carrying steam can be measured simply by determining the rate of condensation of steam, m, which can be collected at a certain point interval of time. By heat balance, Equation 1 where, Bare pipes are uninsulated kind of pipes. Pipes which are insulated are also called lagged pipes. To determine therefore the effectiveness of an insulation, it is just a matter of comparing the heat lost from the pipe with an insulation with that from a bare pipe. Since heat lost is
  • 4. 4 proportional to the rate of condensation, and the weight of condensate is proportional to the volume of condensate v, assuming temperatures and pressures of condensates are the same, then the lagging efficiency may be determined using the equation. Equation 2 In convection the heat transfer coefficient can be calculated by the equation Convection coefficient, hc = 0.42( ∆𝑇 𝐷 )0.25 Equation 3 While in radiation Radiation coefficient, hr = 1.73p[( Ts 100 ) 4 −( Tr 100 ) 4 ] ΔT Equation 4
  • 5. 5 3. EXPERIMENTAL SECTION 3.1 Materials and Apparatus - Boiler - Test pipes – bare, paint, silver chrome paint, and 85% magnesia insulation - Thermocouple - Beakers - Graduated Cylinder - Stopwatch 3.2 Procedure Two runs with steam at approximately 30 psig for each run was made. 1. The drain cock was cracked under the header to remove the water from the steam line and header after adjusting the system to the desired pressure. 2. The four plug type valve was opened to blow out any condensate from the pipes and was closed until only small amount of steam escapes along with the condensate. 3. The condensate from each pipe was measured and collected over a time interval of 15 minutes and the surface temperatures were read 20 inches from the end of the pipe. 3.3 Specifications LENGTH OF PIPE PIPE NO. 1 2 3 4 COVERING PAINT BARE PIPE SILVER- CHROME PAINT 85% MAGNESIA INSULATION OUTSIDE DIAMETER (in.) 1.3535 1.35 1.382 2.48
  • 6. 6 Table 3.3.1 EMMISIVITY 0.96 0.95 0.96 0.72 RUN NO. BAROMETRIC PRESSURE 1 atm STEAM PRESSURE 30 psig STEAM TEMPERATURE 84°C ≈ 183.2°F ROOM TEMPERATURE 30°C ≈ 86°F TIME/RUN 5 minutes
  • 7. 7 4. RESULTS AND DISCUSSION . Heat is transmitted through the insulation by means of radiation, conduction and convection. The relative amount of each of these three factors depends entirely upon the construction of the insulating material. Offering some resistance to heat transfer such as insulation can reduce the amount of heat that is to be transferred to the surroundings. The bare pipes, the pipe having no coating or insulation, has the third highest temperature of the three pipes. This is considered and error however, the difference between the temperature is very small and considering the environment many errors are expected to occur especially it was an open environment and the thermostats are not functioning consistently. However, for the pipe that was coated with 85% magnesia, it shows to have the least temperature. This is true since it has the thickest resistance while those covered with paints and silver chrome may have no effect because of the deterioration of the insulating materials. Pipe no. 1 2 3 4 Trial Point location Surface Temperature 1st A 98°C 82°C 77°C 48°C B 101°C 86°C 83°C 51°C C 110.3°C 98.4°C 110.1°C 58.2°C D 114°C 105.6°C 114°C 62.7°C 2nd A 99°C 80°C 78°C 46°C B 102.5°C 86°C 83°C 50°C C 113°C 105.6°C 109°C 61°C D 117°C 110.2°C 113°C 65.1°C
  • 8. 8 Table 4.1 Average Temperature 106.85°C ≈ 224.33°F 94.225°C ≈ 201.605°F 95.8875°C ≈ 204.5975°F 55.25°C ≈ 131.45°F Average Condensate Collected 85.5 ml 77 ml 50 ml 32 ml Lagging Efficiency 8.97% 0% 33.3% 58.97% Convection Coefficient 1.89 1.74 1.63 1.73
  • 9. 9 5. CONCLUSION Insulated pipes tend to have higher lagging efficiency in order to minimize heat losses in industrial and commercial applications. The one coated with the 85% magnesia showed to have the least temperature. This supports the theory since its resistance is the greatest among the pipes. This kind of insulation is very useful in dealing with pipes especially in the industry since the usage pipes is inevitable. It can prevent too much energy loss and can provide comfort to the workers since heat is controlled. The experiment is not as successful as expected however the error is small. It is possible that any errors in the results and data could be in the reading of the surface temperature of the pipes. Another one is the inconsistency of the thermal couples. Also, the insulation around the pipes seemed to deteriorate. 6. RECOMMENDATION It is recommended to fix the thermal insulation materials found in the piping since the students suspect that it could be the cause of the error. Another one the usage of a carefully calibrated thermocouple.
  • 10. 10 7.REFERENCES [1] https://www.engineeringtoolbox.com/emissivity-coefficients-d_447.html [2] https://dokumen.tips/documents/heat-loss-for-bare-and-lagged-pipes.html [3] https://www.process-heating.com/articles/87988-calculating-heat-loss [4] https://en.wikipedia.org/wiki/Heat_pipe[ [5] http://www.environmentcentre.com/wp- content/uploads/2016/08/5_Pipe_lagging_new_branding.pdf 8. APPENDIX 8.1 Tables and figures LENGTH OF PIPE PIPE NO. 1 2 3 4 COVERING PAINT BARE PIPE SILVER- CHROME PAINT 85% MAGNESIA INSULATION OUTSIDE DIAMETER (in.) 1.3535 1.35 1.382 2.48 EMMISIVITY 0.96 0.95 0.96 0.72 RUN NO. BAROMETRIC PRESSURE 1 atm STEAM PRESSURE 30 psig
  • 11. 11 Table 4.1 STEAM TEMPERATURE 84°C ≈ 183.2°F ROOM TEMPERATURE 30°C ≈ 86°F TIME/RUN 5 minutes Pipe no. 1 2 3 4 Trial Point location Surface Temperature 1st A 98°C 82°C 77°C 48°C B 101°C 86°C 83°C 51°C C 110.3°C 98.4°C 110.1°C 58.2°C D 114°C 105.6°C 114°C 62.7°C 2nd A 99°C 80°C 78°C 46°C B 102.5°C 86°C 83°C 50°C C 113°C 105.6°C 109°C 61°C D 117°C 110.2°C 113°C 65.1°C Average Temperature 106.85°C ≈ 224.33°F 94.225°C ≈ 201.605°F 95.8875°C ≈ 204.5975°F 55.25°C ≈ 131.45°F Average Condensate Collected 85.5 ml 77 ml 50 ml 32 ml Lagging Efficiency 8.97% 0% 33.3% 58.97% Convection Coefficient 1.89 1.74 1.63 1.73
  • 12. 12 8.2 Computations 8.2.1 Convection coefficient, hc = 0.42( ∆𝑇 𝐷 )0.25 a. Painted pipe hc = 0.42( 224.33 −86 0.1128 )0.25 = 2.485 𝐵𝑡𝑢 ℎ𝑟∙𝑓𝑡2∙°𝐹 b. Bare pipe hc = 0.42( 201.605 − 86 0.1128 )0.25 = 2.38 𝐵𝑡𝑢 ℎ𝑟∙𝑓𝑡2∙°𝐹 c. Silver-chrome Paint pipe hc = 0.42( 204.69753 − 86 0.1152 )0.25 = 2.208 𝐵𝑡𝑢 ℎ𝑟∙𝑓𝑡2∙°𝐹 d. 85% Magnesia insulation hc = 0.42( 131.35 −86 0.2067 )0.25 = 1.61 𝐵𝑡𝑢 ℎ𝑟∙𝑓𝑡2∙°𝐹 8.8.2 Radiation coefficient, hr = 1.73p[( Ts 100 ) 4 −( Tr 100 ) 4 ] ΔT a. Painted pipe hr = 1.73(0.96)[( 226.85 100 ) 4 −( 86 100 ) 4 ] 226.85−86 = 0.3 𝐵𝑡𝑢 ℎ𝑟∙𝑓𝑡2∙°𝐹 b. Bare pipe hr = 1.73(0.95)[( 201.605 100 ) 4 −( 86 100 ) 4 ] 201.605−86 = 0.23 𝐵𝑡𝑢 ℎ𝑟∙𝑓𝑡2∙°𝐹 c. Silver-chrome Paint pipe hr = 1.73(0.96)[( 204.7 100 ) 4 −( 86 100 ) 4 ] 204.7−86 = 0.24 𝐵𝑡𝑢 ℎ𝑟∙𝑓𝑡2∙°𝐹 d. 85% Magnesia insulation hr = 1.73(0.72)[( 131.35 100 ) 4 −( 86 100 ) 4 ] 131.35−86 = 0.07 𝐵𝑡𝑢 ℎ𝑟∙𝑓𝑡2∙°𝐹 8.8.3 For the calculation of lagging efficiency (L.E.) = WB−WL WB x100
  • 13. 13 a. Paint pipe L.E. = 290 − 250 250 × 100 = 16.0% b. Bare pipe L.E. = 250 − 250 250 × 100 = 0% c. Silver-chrome paint pipe L.E. = 177.5 − 250 250 × 100 = 29.0% d. 85% Magnesia pipe L.E. = 170 − 250 250 × 100 = 32.0%