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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    2.1 A design engineer wishes to select an appropriate fan for the following galvanized steel duct

    system. Estimate the pressure loss for each branch of the duct system.

    Solution:

    There are two branches in this duct system: Branches 1-3 and 1-4.

    These branches are made up of multiple sections:

    Branch 1-3: Sections 1-2 and 2-3.

    Branch 1-4: Sections 1-2 and 2-4

    Find the pressure loss in each duct section to determine the pressure loss in each branch.

    Section 1-2

    This section is 50 ft long with a 10-in-diameter. The total flow rate through the section is 400 cfm.

    The equivalent length of this section is the sum of the actual length of the section, plus the equivalent

    length for the entrance from the large plenum:

    L1-2=Lduct+Le,entrance

    From Table A.4, the equivalent length for an abrupt, 90oentrance to the 10-in-diameter circular duct is

    found to be 25 ft. So,

    L1-2= 50 ft + 25 ft = 75 ft

    From the appropriate friction loss chart for round, straight galvanized steel ducts (Figure A.1), the

    pressure loss per 100 ft of duct is 0.09 in. of water. So, the pressure loss in this section is

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    Choose the 90opleated elbow since it has a lower equivalent length and lower losses. The 45

    oelbow is

    also pleated. Note that only 120 cfm of fluid enters section 2-4. Therefore, the wye is a diverging

    branch fitting.

    The equivalent lengths for this 6-in-diameter circular duct section are: Le,wye= 10 ft; Le,45 deg bend= 5 ft;

    Le,90 deg bend= 8 ft

    Hence,

    L2-4= 40 ft + 10 ft + 5 ft + 8 ft = 63 ft

    From the friction loss chart for round, straight galvanized steel ducts, the pressure loss per 100 ft of

    duct is 0.13 in. of water. Therefore, the pressure loss in this section is

    ft63ft100

    waterin.13.042

    P

    P2-4= 0.0819 in. of water

    The total pressure loss in each branch can be determined.

    Branch 1-3: P1-3= P1-2+ P2-3 = 0.0675 in. of water + 0.0445 in. of water

    P1-3= 0.112 in. of water

    Branch 1-4: P1-4= P1-2+ P2-4 = 0.0675 in. of water + 0.0819 in. of water

    P2-4= 0.149 in. of water

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    2.2 The duct system shown is one branch of a complete low-velocity air-distribution system. The

    system is a perimeter type located below the finished floor. The diffuser boots are shown,

    complete with the pressure losses. Design a round duct system, bearing in mind that a total

    pressure of 0.21 in. wg is available at the plenum.

    Possible Solution:

    Definition

    Size the round ducts for the given system. Select a suitable duct material.

    Preliminary Specifications and Constraints

    i. The working fluid will be air.

    ii. This is a low-velocity air-distribution system.

    iii. The total pressure available at the plenum is restricted to 0.21 in. wg.

    iv. The duct lengths, air flow rates, and pressure losses are constrained, as shown in the drawing.

    Detailed Design

    Objective

    To design a round air duct system. The size and material of the ducts will be determined.

    Data Given or Known

    i. The length of each duct section is given.

    ii. The air flow rates through the three diffusers are given as 80 cfm, 120 cfm, and 100 cfm.

    iii. The duct system is connected to an air plenum.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    Note that the equivalent lengths for the tee and the wye are for diverging branch fittings. Table A.4

    gives the equivalent lengths for each circular duct fitting. At this point, the diameter of the duct is not

    known. Assume that the duct diameter is 8 inches to find the equivalent length of the fittings.

    Therefore,

    Ltotal= 8 ft + 20 ft + 5 ft + 12 ft + 5 ft + (8 + 8 + 15) ft + 2(6 ft) = 93 ft.

    The total pressure available from the plenum is 0.21 in. wg.. For the longest branch of the duct system,

    the available pressure is the total pressure from the plenum less the pressure loss at the end of the

    longest branch.

    Thus, for sizing the ducts,

    ft100xft93

    wg.in.040210

    ..

    P

    = 0.18 in. wg. per 100 ft duct 0.2 in. wg. per 100 ft duct

    will be used.

    Size the duct sections

    The total volume flow rate of air from the plenum is (80 + 120 + 100) cfm = 300 cfm. The volume

    flow rate through the sections of the system are:

    Section 1: 300 cfm,

    Section 2: 80 cfm,

    Section 3: 220 cfm,

    Section 4: 120 cfm,

    Section 5: 100 cfm.

    The chart shown in Figure A.1 can be used to size the duct sections. Apply a pressure loss of 0.2 in.

    wg. per 100 ft duct. The duct sizes and velocities are:

    Section 1: 8 inches, 850 fpm,

    Section 2: 5 inches, 600 fpm,

    Section 3: 7 inches, 820 fpm,

    Section 4: 6 inches, 620 fpm,

    Section 5: 5 inches, 710 fpm.

    In all the sections, the duct velocity does not exceed 1200 fpm.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    A check should be conducted to ensure that the pressure loss in each of the branches does not exceed

    the total pressure available at the plenum. A similar check should be conducted for the longest branch.

    With 0.18 in. wg. per 100 ft duct, the pressure drop through the sections of the duct system are:

    Section 1: ft520xft100wg.in.0.18x

    ft100wg.in.0.18 throughtee,11 LLP = 0.045 in. wg.,

    Section 2: wg.in.0.05ft2710xft100

    wg.in.0.18x

    ft100

    wg.in.0.18 diffuserbranchtee,22 PLLP

    P2= 0.12 in. wg.,

    Section 3: ft512xft100

    wg.in.0.18x

    ft100

    wg.in.0.18 throughwye,33 LLP = 0.031 in. wg.,

    Section 4: wg.in.0.036ft1315xft100

    wg.in.0.18x

    ft100

    wg.in.0.18 diffuserbranchwye,44 PLLP

    P4= 0.086 in. wg.,

    Section 5: wg.in.0.04ft1231xft100

    wg.in.0.182x

    ft100

    wg.in.0.18 diffuserelbow45,55 PLLP

    P5= 0.12 in. wg.,

    For the longest branch:

    P1-3-5= P1+ P3+ P5= (0.045 + 0.031 + 0.12) in. wg. = 0.196 in. wg. < 0.21 in. wg.

    For branch 1-2:

    P1-2= P1+ P2= (0.045 + 0.12) in. wg. = 0.165 in. wg. < 0.21 in. wg.

    For branch 1-3-4:

    P1-3-4= P1+ P3+ P4= (0.045 + 0.031 + 0.086) in. wg. = 0.162 in. wg. < 0.21 in. wg.

    In this case, all the sections have lower pressure losses than that available from the plenum.

    Drawings

    The final drawing, showing the duct sizes is presented below.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    Conclusions

    Round duct sizes have been chosen for this system based on a pressure loss of 0.18 in. wg. per 100 ft

    of duct. This is larger than the standard 0.1 in. wg. per 100 ft of duct for small-sized, low-velocity duct

    systems. The constraint of 0.21 in. wg. of available pressure at the plenum forced a calculation of an

    appropriate pressure loss for the purposes of duct sizing.

    The assumption of an 8-inches duct to determine the equivalent lengths of the fittings is valid. In all

    cases, the duct sizes were 8 inches or less. This assumption resulted in a more conservative design

    since lower equivalent lengths are expected for duct sizes smaller than 8 inches. Absent from the

    design are losses due to transitions from larger duct sizes to smaller duct sizes. In all cases, the duct

    would be converging (becoming smaller) in the direction of air flow. Compared to other losses in the

    system, this loss is very small, with small equivalent lengths on the order of 3 ft, and was ignored.

    In branch 1-2 and 1-3-4, the pressure loss is lower than the main branch (branch 1-3-5). To balance the

    system, dampers may be installed to control the flow of air through these branches. These dampers

    should provide about 0.03 in. wg. of pressure drop.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    2.3 For most building design projects, the architectural trade tends to be the consultant (i.e. the lead

    consultant for the project) who hires the mechanical and the electrical trades as sub-consultants

    on the project. In most cases, the mechanical engineering sub-consultant has expertise in the

    design of ductwork to transport air for the purposes of heating and/or cooling an occupied space.

    The following section of a second floor tenant plan of an office building has been given by an

    architect.

    For the offices shown in the plan (complete with the occupant and work function), the architect

    has requested the design of a ductwork system to provide air at 75oF to heat the occupied spaces.

    A HVAC engineer has determined the amount of air required to maintain the space temperature,

    and they are shown in the following table.

    Office Space Heating Air Requirement

    Office 204 310 cfm

    Office 205 450 cfm

    Office 206 170 cfm

    Office 207 500 cfm

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    However, the engineer missed the fact that ASHRAE Standard 62 requires that 20 cfm per

    person of fresh outdoor air must be provided.

    a) To ensure an esthetically pleasing finish in the space, the architect has requested the design of

    a ductwork system based on round ducts. Due to the fact that most of the occupants of this

    section of the floor are managers and/or directors in the complex hierarchy of the clients

    company, the architect would like to have a dedicated fan installed with the ductwork for this

    section of offices. The fan is to be located on the roof above the offices, and it will be fitted with

    a plenum section.

    b) Based on the design of the ductwork, specify the minimum operating condition of the fan.

    a)Possible Solution:

    Detailed Design

    Objective

    To determine the sizes of round duct in a ductwork system, and show the system layout.

    Data Given or Known

    i. Office 204 has a length of 18 ft and a width of 10 ft.

    ii. The fan is complete with a plenum section.

    iii. Air at 75oF is required.

    iv. The amount of air, less the fresh air required by code, is provided by the HVAC engineer in tabular

    format.

    v. 20 cfm per person of fresh outdoor air is required.

    Assumptions/Limitations/Constraints

    i. Limit the friction loss everywhere in the duct system to approximately 0.1 in. wg. per 100 ft of

    duct. This is a standard industry guideline.ii. Limit the air velocity in the ductwork to 1200 fpm. Since this is an office space, a noisy, high-

    velocity duct system may not be desired. Therefore, a low-velocity duct system will be designed

    where the maximum velocity should be 1200 fpm.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    Office Space Total Air Requirement

    Office 204 330 cfm

    Office 205 470 cfm

    Office 206 190 cfm

    Office 207 520 cfm

    It was assumed that the pressure loss in the ductwork would be on the order of 0.1 in. wg. per 100 ft of

    duct. The friction loss chart for round, straight galvanized steel ducts will be consulted to determine the

    round duct sizes. For verification, the actual pressure loss per 100 ft of duct and the duct velocity will

    be provided to ensure that the design constraints were not violated.

    Duct Section Duct Diameter Air Velocity Air Flow Pressure Lossin. fpm cfm in. wg./100 ft

    1-2 16 1090 1510 0.1

    2- Office 204 9 730 330 0.1

    2-3 14 1150 1180 0.13

    3- Office 205 10 860 470 0.125

    3-4 12 920 710 0.11

    4- Office 206 7 750 190 0.15

    4- Office 207 10 980 520 0.15

    In all the sections, the pressure loss in the ducts is on the order of 0.1 in. wg. per 100 ft of duct and the

    air velocities are less than 1200 fpm.

    Drawings

    The layout, including the sizes of the ducts, is shown below.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    Conclusion

    The ductwork system has been designed as specified with round ducts. The velocities in all the duct

    sections were less than 1200 fpm. The friction losses were on the order of 0.1 in. wg. per 100 ft of

    duct. Some odd duct sizes are present. These may be increased to even numbers, if desired. However,

    to balance the systems, dampers may be needed in the branches at the diffusers.

    b) Specification of the minimum operating condition of the fan means that the minimum air flow rate

    and static pressure at the fan will be provided.

    The total air flow rate required for this system is 1510 cfm. Next, determine the total pressure drop in

    the longest branch of the duct system.

    The longest branch is labelled 1-2-3-4-5-Office 207. Determine the total length (straight duct length,

    plus equivalent lengths of fittings) of this branch (LLB).

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    207-5branch,5tee,54thru,4tee,43thru,3tee,32thru,2tee,21entranceLB LLLLLLLLLLL

    Assumptions will be made regarding the length of the duct sections. These lengths will be based on the

    length and width of Office 204, given in the problem statement. Assume that the entrance to the duct

    from the plenum is an abrupt 90oentrance. This will ensure that the fan is a bit larger. For duct sizes

    larger than 12 in., theLe/D ratio will be used to find the equivalent lengths. Duct contractions typically

    produce low losses, and are negligible.

    Therefore,

    LLB= (40 + 5 + 11 + 10 + 10 + 10 + 8 + 15 + 33 + 14) ft 156 ft.

    Hence,

    wg.in.0.156ft156xft100wg.in.10 duct .P

    There is also a pressure loss across the diffuser to Office 207. Thus, the total pressure required at the

    fan and plenum is

    Pstatic,fan= (0.156 + 0.05) in. wg.

    Pstatic,fan= 0.21 in. wg.

    Accordingly, the minimum operating condition of the fan is: 1510 cfm at 0.21 in. wg.

    Note that including losses due to the duct contractions would have increased the pressure loss to

    approximately 0.22 in. wg.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    2.4 A draw-through air handling unit (AHU) will be used to supply conditioned air as shown in the

    schematic below. Within the AHU assembly, the filter section has a pressure loss of 0.10 in. wg.,

    the heating/cooling coil section has a pressure loss of 0.20 in. wg., and the casing has a

    miscellaneous loss of 0.05 in. wg. The AHU is a modular unit complete with a fan that can

    produce 0.60 in. wg. of total pressure at the required design flows. Design a round ductwork

    system, ensuring that the location of and pressure drops across appropriate dampers for balancing

    the system is clear for the convenience of the mechanical contractor and the client.

    Possible Solution:

    Detailed Design

    Objective

    To design a round air duct system. The size and material of the ducts will be determined.

    Data Given or Known

    i. The length of each duct section is given.

    ii. The air flow rates through the diffuser boots are given.

    iii. The duct system is connected to an air handling unit (AHU).

    iv. The pressure losses in the AHU are given.

    iv. The total pressure available from the fan is 0.60 in. wg. for the design flows given.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    v. The pressure loss at the diffuser boots are given, with the typical boot equivalent length given as 20

    ft.

    Assumptions/Limitations/Constraints

    i. The maximum air velocity will be 1200 fpm. This is typical for low-velocity air-distribution

    systems. Low velocities will be chosen to ensure that the available total pressure from the fan is not

    exceeded.

    ii. Total friction losses available for the ductwork and component losses should be 0.60 in. wg. or less

    to meet the constraint at the fan.

    iii. Galvanized steel is typically used to fabricate air duct systems. It will be chosen as the material.

    iv. The entrance to the system at the plenum is a Bellmouth entrance. This reduces noise and losses.

    v. The elbows are pleated.

    Sketch

    A sketch of the system has been provided that shows the labels of each section of the duct system.

    Another sketch will be provided that clearly shows the locations of the appropriate dampers (if

    needed).

    Analysis

    In this design problem, the total pressure available at the fan is constrained to 0.60 in. wg. The designer

    is required to size the ducts within this constraint. If the fan is able to move air through the longest run

    of ductwork, then it will be able to move air through the side branches.

    Determine the pressure loss per 100 ft of duct

    The longest branch is the 1-2-3-4-9 branch. The total equivalent length of this branch is

    Ltotal=LBellmouth+L1+L2+L3+L4+L9+ 3(L90,elbow) + 4(Lwye,through).

    Note that the equivalent lengths for the wye are for diverging branch fittings. Table A.4 gives the

    equivalent lengths of the fittings in circular ducts. At this point, the diameter of the duct is not known.

    Assume that the duct diameter is 12 inches. This assumption will be used to find the equivalent lengths

    of the fittings. 12 inches was chosen because the total flow rate of air is large at 845 cfm.

    Therefore,Ltotal= 12 ft + 21 ft + 10 ft + 8 ft + 10 ft + 29 ft + 3(15 ft) + 4(8 ft) = 167 ft.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    The total pressure available from the fan is 0.60 in. wg. For the longest branch of the duct system, the

    available pressure is the total pressure from the fan less the pressure losses through the diffuser at the

    end of the longest branch and the losses in the AHU.

    Thus, for sizing the ducts,

    ft100x

    ft167

    wg.in.05.020.010.004.060.0

    P

    P= 0.13 in. wg. per 100 ft duct 0.15 in. wg. per 100 ft duct will be used.

    Size the duct sections

    The total volume flow rate of air from the fan is (250 + 120 + 150 + 200 + 125) cfm = 845 cfm. The

    volume flow rate through the sections of the main branch are:

    Section 1: 845 cfm,

    Section 2: 595 cfm,

    Section 3: 395 cfm,

    Section 4: 275 cfm.

    The chart shown in Figure A.1 can be used to size the duct sections. Apply a pressure loss of 0.15 in.

    wg. per 100 ft duct. The duct sizes, velocities, and actual pressure drops are:

    Section 1: 12 inches, 1100 fpm, 0.15 in. wg./100 ft.,

    Section 2: 10 inches, 1100 fpm, 0.19 in. wg./100 ft.,

    Section 3: 9 inches, 900 fpm, 0.15 in. wg./100 ft.,

    Section 4: 8 inches, 850 fpm, 0.15 in. wg./100 ft.,

    Section 5: 6 inches, 610 fpm, 0.13 in. wg./100 ft.,

    Section 6: 8 inches, 710 fpm, 0.12 in. wg./100 ft.,

    Section 7: 7 inches, 750 fpm, 0.15 in. wg./100 ft.,

    Section 8: 6 inches, 610 fpm, 0.13 in. wg./100 ft.,

    Section 9: 6 inches, 760 fpm. 0.18 in. wg./100 ft.

    In all the sections, the duct velocity does not exceed 1200 fpm.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    A check should be conducted to ensure that the pressure loss in each of the branches does not exceed

    the total pressure available at the fan. A similar check should be conducted for the longest branch. The

    pressure drop through the sections of the duct system are:

    Section 1:

    wg.in.095.0ft15*21221xft100wg.in.0.152x

    ft100wg.in.0.15 elbow,90bellmouth11 LLLP

    Section 2:

    wg.in.0.032ft710xft100

    wg.in.0.19x

    ft100

    wg.in.0.19 throughwye,22 LLP ,

    Section 3:

    ft78xft100

    wg.in.0.15x

    ft100

    wg.in.0.15 throughwye,33 LLP = 0.023 in. wg.,

    Section 4:

    ft510xft100

    wg.in.0.15x

    ft100

    wg.in.0.15 throughwye,44 LLP = 0.023 in. wg.,

    Section 5:

    wg.in.0.03ft51017xft100

    wg.in.0.13x

    ft100

    wg.in.0.13 diffuserelbow45,branchwye,55 PLLLP

    P5= 0.072 in. wg.,

    Section 6:

    wg.in.0.092wg.in.0.05ft1322xft100

    wg.in.0.12x

    ft100

    wg.in.0.12 diffuserbranchwye,66 PLLP

    Section 7:

    wg.in.0.081wg.in.0.04ft1314xft100

    wg.in.0.15x

    ft100

    wg.in.0.15 diffuserbranchwye,77 PLLP

    Section 8:

    wg.in.0.075wg.in.0.036ft1020xft100

    wg.in.0.13x

    ft100

    wg.in.0.13 diffuserbranchwye,88 PLLP

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    Section 9:

    wg.in.0.04ft8428xft100

    wg.in.0.18x

    ft100

    wg.in.0.18 diffuserelbow,90throughwye,99 PLLLP

    P9= 0.112 in. wg.,

    For the longest branch (1-2-3-4-9):

    P= PAHU+ P1+ P2+ P3+ P4+ P9

    P= (0.25 + 0.095 + 0.032 + 0.023 + 0.023 + 0.112) in. wg. = 0.54 in. wg. < 0.60 in. wg.

    For branch 1-6:

    P= PAHU+ P1+ P6= (0.25 + 0.095 + 0.092) in. wg. = 0.44 in. wg. < 0.60 in. wg.

    For branch 1-2-7:

    P1-2-7= PAHU+ P1+ P2+ P7= (0.25 + 0.095 + 0.032 + 0.081) in. wg. = 0.46 in. wg. < 0.60 in.

    wg.

    For branch 1-2-3-8:

    P1-2-3-8= PAHU+ P1+ P2+ P3+ P8= (0.25 + 0.095 + 0.032 + 0.023 + 0.075) in. wg. = 0.48

    in. wg. < 0.60 in. wg.

    For branch 1-2-3-4-5:

    P1-2-3-4-5= PAHU+ P1+ P2+ P3+ P4+ P5= (0.25 + 0.095 + 0.032 + 0.023 + 0.023 + 0.072)

    in. wg. = 0.50 in. wg. < 0.60 in. wg.

    From the above calculations, it is shown that all the sections have lower pressure losses than that

    available from the fan.

    Dampers with the specified pressure drops are required to balance the system on each section:

    Section 6: 0.16 in. wg.

    Section 7: 0.14 in. wg.

    Section 8: 0.12 in. wg.

    Section 5: 0.10 in. wg.

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    Intr oduct ion to Therm o-Fluid s System s Design, First Edition. Andr G. McDonald and Hugh L. Magande.

    2013 Andr G. McDonald and Hugh L. Magande. Published 2013 by John Wiley & Sons, Ltd.

    Drawings

    The drawing shows the duct sizes and the damper locations.

    Conclusions

    Round duct sizes have been chosen for this system based on a pressure loss of 0.13 in. wg. per 100 ft

    of duct. This is close to the standard 0.1 in. wg. per 100 ft of duct for small-sized, low-velocity duct

    systems. The constraint of 0.60 in. wg. of available pressure at the fan forced a calculation of an

    appropriate pressure loss for the purposes of duct sizing.

    The assumption of a 12-inches duct to determine the equivalent lengths of the fittings is valid. In all

    cases, the duct sizes were 12 inches or less. This assumption resulted in a more conservative design

    since, for the most part, lower equivalent lengths are expected for duct sizes smaller than 12 inches.

    Absent from the design are losses due to transitions from larger duct sizes to smaller duct sizes. In all

    cases, the duct would be converging (becoming smaller) in the direction of air flow. Compared to other

    losses in the system, this loss is very small, with small equivalent lengths on the order of 3 4 ft, and

    was ignored.

    The following table summarizes the design results.

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    Duct Section Duct Size Duct Velocity Total Pressure Loss

    in. fpm in. wg.

    1 12 1100 0.15

    2 10 1100 0.19

    3 9 900 0.15

    4 8 850 0.15

    5 6 610 0.13

    6 8 710 0.12

    7 7 750 0.15

    8 6 610 0.13

    9 6 760 0.18

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    2.5 A small-duct high-velocitysystem is to be developed to distribute conditioned air to a factory.

    This type of air distribution system results in smaller duct sizes, and is desired due to space limits

    and high construction costs. As a guide, Section 3.11 of the Air-Conditioning, Heating, and

    Refrigeration Institute (AHRI) Standard 210/240-2005 [10] requires that a cooling product

    contain a blower that produces at least 1.2 in. wg. of external static pressure when operating at

    the certified air flow rate of 220 to 350 cfm per rated ton of cooling. For high-velocity systems, a

    maximum velocity of 5000 fpm has been recommended [11]. Terminal boxeswill be introduced

    at the duct exit to the space to throttle the air to a low velocity, control the air flow, and reduce

    noise. The terminal boxes are usually designed to operate at a minimum pressure loss of about

    0.25 to 1.0 in. wg., that is, the branch pressure loss should be on the order of at least 0.25 to 1.0

    in. wg. The cooling product is an air-handling unit, capable of producing 5 tons of cooling.

    Based on the sketch provided below, design a round duct, high-velocity system to distribute air

    in the factory. Will the pressure drops across the terminal boxes be sufficient to balance the

    system? Make appropriate recommendations to the client.

    Possible Solution:

    Definition

    Size the round ducts for the given high-velocity system.

    Preliminary Specifications and Constraints

    i. The working fluid will be air.

    ii. This is a high-velocity air-distribution system.

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    iii. AHRI Standard 210/240-2005 specifies that a high-velocity blower should produce at least 1.2 in.

    wg. of external static pressure at 220 to 350 cfm per rated ton of cooling.

    iv. The air velocity should not exceed 5000 fpm.

    v. The branch pressure losses should be on the order of at least 0.25 to 1.0 in. wg.

    vi. The duct lengths, air flow rates, and pressure losses across the terminal boxes are constrained, as

    shown in the drawing.

    Detailed Design

    Objective

    To design a round air duct system. The size and material of the ducts will be determined.

    Data Given or Known

    i. The length of each duct section is given.

    ii. The air flow rate through the three diffusers is given as 460 cfm, 590 cfm, and 550 cfm.

    iii. The duct system is connected to an air handling unit.

    iv. The blower should produce at least 1.2 in. wg. of external static pressure at 220 to 350 cfm per

    rated ton of cooling.

    v. The air handling unit produces 5 tons of cooling.

    vi. The pressure losses across the three terminal boxes are given as 0.07 in. wg., 0.056 in. wg., and

    0.06 in. wg.

    Assumptions/Limitations/Constraints

    i. Galvanized steel is typically used to fabricate air duct systems. It will be chosen as the material.

    ii. The entrance to the system at the air handling unit will be a Bellmouth entrance. This reduces noise

    and losses.

    iii. The 45oelbows will be pleated.

    Sketch

    A sketch of the system is provided to show the labeling of each section to be evaluated.

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    Analysis

    Determine the maximum air velocity in the system

    According to the problem preamble, the air velocity in the duct cannot exceed 5000 fpm. From Table

    2.3 and for high-velocity duct systems, air flow rates between 1000 cfm and 3000 cfm require a

    maximum air velocity of 2500 fpm. Even though the volume flow rate in section 5 and the branch

    take-offs are lower than 1000 cfm, a maximum velocity of 2500 fpm will be used to size the round

    ducts.

    Size the duct sections

    The total volume flow rate of air from the air handling unit is (460 + 590 + 550) cfm = 1600 cfm. The

    volume flow rates through the sections of the system are:

    Section 1: 1600 cfm,

    Section 2: 460 cfm,

    Section 3: 1140 cfm,

    Section 4: 590 cfm,

    Section 5: 550 cfm.

    The chart shown in Figure A.1 can be used to size the duct sections. Use the maximum velocity

    constraint of 2500 fpm as a guide. The duct sizes, velocities, and pressure losses are:

    Section 1: 11 inches, 2500 fpm, 0.8 in. wg. per 100 ft,

    Section 2: 6 inches, 2500 fpm, 1.45 in. wg. per 100 ft,

    Section 3: 10 inches, 2050 fpm, 0.6 in. wg. per 100 ft,

    Section 4: 7 inches, 2250 fpm, 1.2 in. wg. per 100 ft,

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    Section 5: 7 inches, 2050 fpm, 0.95 in. wg. per 100 ft.

    In all the sections, the duct velocity does not exceed 2500 fpm. Higher pressure losses per 100 ft of

    duct in the shorter branch sections should facilitate system balancing (to prevent excess air from

    flooding branches with low pressure losses or low frictional resistances).

    Check the branch pressure losses to confirm minimum requirement for terminal box operation

    A check should be conducted to ensure that the pressure loss in each of the branches is at least 0.25 to

    1.0 in. wg., as required for operation of the terminal boxes. For a more conservative analysis, the

    pressure drop across the terminal boxes themselves will not be included.

    Section 1:

    wg.in.0.224ft820xft100

    wg.in.0.80x

    ft100

    wg.in.0.80 throughtee,11 LLP ,

    Section 2:

    wg.in.435.0ft2010xft100

    wg.in.1.45x

    ft100

    wg.in.1.45 branchtee,22 LLP ,

    Section 3:

    wg.in.114.0ft712xft100

    wg.in.0.60x

    ft100

    wg.in.0.60 throughwye,33 LLP ,

    Section 4:

    wg.in.0.336ft1315xft100

    wg.in.1.2x

    ft100

    wg.in.1.2 branchwye,44 LLP ,

    Section 5:

    wg.in.0.409ft1231xft100

    wg.in.0.952x

    ft100

    wg.in.0.95 elbow45,55 LLP

    For the longest branch:

    P1-3-5= P1+ P3+ P5= (0.224 + 0.114 + 0.409) in. wg. = 0.747 in. wg. > 0.25 in. wg.

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    For branch 1-2:

    P1-2= P1+ P2= (0.224 + 0.435) in. wg. = 0.659 in. wg. > 0.25 in. wg.

    For branch 1-3-4:

    P1-3-4= P1+ P3+ P4= (0.224 + 0.114 + 0.336) in. wg. = 0.674 in. wg. > 0.25 in. wg.

    In this case, all the branch sections have pressure losses that are greater than 0.25 in. wg., which is

    required for operation of the terminal boxes.

    Pressure drops across the terminal boxes

    Based on these calculations of branch pressure losses, without the pressure drops across the terminal

    boxes, it may be necessary to select different terminal boxes that will produce larger pressure losses in

    branches 1-2 and 1-3-4. The pressure drop across the terminal box in the longest branch will be held at

    0.06 in. wg. Therefore, the total pressure loss in the longest branch is

    P1-3-5,total= (0.747 + 0.06) in. wg. = 0.807 in. wg.

    The pressure drops required across the other terminal boxes are

    Pbox2= P1-3-5,total- P1-2= (0.8070.659) in. wg. = 0.15 in. wg.

    Pbox4= P1-3-5,total- P1-3-4= (0.8070.674) in. wg. = 0.13 in. wg.

    Given that 1600 cfm will be delivered by the blower on the 5 ton air handling unit, 320 cfm per ton

    will be required. Based on AHRI Standard 210/240-2005 at least 1.2 in. wg. of external static pressure

    should be provided by the blower. This will be sufficient to meet the pressure loss requirement (0.81

    in. wg.) of the longest branch and the rest of the system. In addition, at 1.2 in. wg. of external staticpressure, the blower will not be greatly over-sized for this application.

    Drawings

    The final drawing, showing the duct sizes is presented below. The pressure drops across the terminal

    boxes have also been modified to reflect the results of the analysis.

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    The following table summarizes the design results.

    Duct Section Duct Size Duct Velocity Total Pressure Loss

    in. fpm in. wg.

    1 11 2500 0.80

    2 6 2500 1.45

    3 10 2050 0.60

    4 7 2250 1.20

    5 7 2050 0.95

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    2.6 The National Research Council has decided to pursue research in the area of spray-dried

    agglomeration of nano-sized powder particles to produce micron-sized powder particles. Safety

    and health regulations permit only a limited amount of these particles to escape into the ambient

    air of the space. To that end, the Council has contracted the services of Alliance Engineering

    Corp. to design a high-velocityduct system for a FarrGold Series 10 dust collector. The dust

    collector will draw 4000 cfm of air in an effort to eliminate any powder particles from the space.

    The air will be drawn through a hood and filter system, as shown. High efficiency, open-pleat

    style cartridge filters with flame-retardant media and average pressure loss of 2.7 in. w.g. were

    used. A commercial shop environment will be provided by the Council, in which the maximum

    duct velocity can be on the order of 2500 to 6000 fpm. Size and specify the round ductwork

    between the hood and the duct collector. The layout, accessories, and fittings that are chosen

    should be such that losses are kept at a minimum. Specify an appropriate fan.

    Further Information: Given that this is an industrial application, the designer may consider

    specification of a utility or industrialcentrifugal fan.

    Possible Solution:

    Definition

    Size the round duct for a dust collector system.

    Preliminary Specifications and Constraints

    i. The working fluid will be air.

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    ii. This is a high-velocity air duct system.

    iii. The air velocity should be between 2500 to 6000 fpm.

    iv. The equipment dimensions and maximum air flow rate are constrained, as shown in the sketch.

    Detailed Design

    Objective

    To design a round air duct. The size and material of the duct will be determined. The layout,

    accessories, and fittings that are chosen should be such that losses are kept at a minimum.

    Data Given or Known

    i. The dimensions of equipment and distances between equipment are given.

    ii. The maximum air flow rate is 4000 cfm.

    iii. The air pressure loss across the filters is 2.7 in. w.g.

    Assumptions/Limitations/Constraints

    i. Galvanized steel is typically used to fabricate air duct systems. It will be chosen as the material.

    ii. The entrance to the system at the hood will be a Bellmouth entrance. The exit to the dust collector

    will also be a Bellmouth shape. This reduces noise and losses.

    iii. Any 90oelbows will be 5-piece, withR/D= 1.5. Pleated or mitered with vanes will be avoided to

    prevent accumulation of powder particles in the duct.

    Sketch

    A sketch of the system is not required here for this analysis. The final drawing will show the final duct

    layout and size.

    Analysis

    Determine the maximum air velocity in the systemAccording to the problem statement, the maximum air flow rate in the duct will be 4000 cfm. From

    Table 2.3 and for high-velocity duct systems, an air flow rate 4000 cfm will require a maximum air

    velocity of 3000 fpm. This will be the velocity constraint in this design.

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    Size the duct

    The total volume flow rate of air and the maximum velocity will be used to guide the sizing of the

    duct. The chart shown in Figure A.1 will be used to size the duct. The duct size, air velocity, and

    pressure loss are:

    16 inches, 2810 fpm, 0.6 in. wg. per 100 ft, respectively.

    In this case, the duct velocity does not exceed 3000 fpm.

    Determine the pressure losses in the duct system

    The total pressure loss in the duct system will be required to specify the requirements of the dust

    collector fan. Therefore,

    exitbend90entrancestraightfilter oxft100wg.in.0.60

    LLLLPP

    D

    LD

    D

    LD

    D

    LDLPP

    exitbend90entrancestraightfilter

    o

    xft100

    wg.in.0.60 .

    The length of straight duct is approximately,

    Lstraight= 50 in. + 24 in. + 20 ft = 27 ft.

    Table A.4 presents the equivalent lengths of the fittings for round ducts.

    Thus,

    12ft33.112ft33.112ft33.1ft27xft100

    wg.in.0.60w.g.in.7.2 P

    wg.in.2.3 P

    In this case, the fan should be able to move 4000 cfm of air and provide an external static

    pressure of 3.2 in. wg.

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    A Greenheck single-width industrial centrifugal belt drive fan will be selected for this application. The

    specifications are shown in the catalog sheet. The fan should provide at least 4000 cfm of air over at

    least 3.2 in. w.g. of external static pressure. From the performance curves for the Greenheck 15 BISW

    fan, a 2830 rpm speed and a 4.83 hp motor is selected.

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    Source: Greenheck Fan, Corp. (Reprinted with permission)

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    Drawings

    The final drawing, showing the duct size is presented below.

    Conclusions

    A round duct has been chosen for this high-velocity system based on a maximum air velocity of 3000

    fpm. Decisions were made throughout the analysis to ensure that this constraint was not violated and

    that the system losses were kept low.

    Throughout the design, it was decided to avoid the use of any fittings that produced abrupt changes in

    the duct or flow pattern. This will prevent the accumulation of powder particles in the duct, which may

    be difficult to clean or pose a risk of explosion.

    In this application, the fan was slightly oversized.

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    2.7 Refer to Problem 2.2 and redesign the system with rectangular ducts.

    Possible Solution:

    Definition

    Size the rectangular ducts for the given system. Select a suitable duct material.

    Preliminary Specifications and Constraints

    i. The working fluid will be air.

    ii. This is a low-velocity air-distribution system.

    iii. The total pressure available at the plenum is restricted to 0.21 in. wg.

    iv. The duct lengths, air flow rates, and pressure losses are constrained, as shown in the drawing.

    Detailed Design

    Objective

    To design a rectangular air duct system. The size and material of the ducts will be determined.

    Data Given or Known

    i. The length of each duct section is given.

    ii. The air flow rate through the three diffusers is given as 80 cfm, 120 cfm, and 100 cfm.

    iii. The duct system is connected to an air plenum.

    iv. The total pressure available at the plenum is 0.21 in. wg.

    v. The pressure loss at the three diffusers are given as 0.05 in. wg., 0.036 in. wg., and 0.04 in. wg.

    Assumptions/Limitations/Constraints

    i. The maximum air velocity will be 1200 fpm. This is required for low-velocity air-distribution

    systems.

    ii. Total friction losses available for the ductwork should be 0.21 in. wg. or less to meet the constraintat the plenum.

    iii. Galvanized steel is typically used to fabricate air duct systems. It will be chosen as the material.

    iv. The entrance to the system at the plenum is a Bellmouth entrance. This reduces noise and losses.

    v. The 45oelbows are pleated.

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    Sketch

    A sketch of the system will be provided to show the labeling of each section of the duct system.

    Analysis

    In this design problem, the total pressure available at the plenum is constrained to 0.21 in. wg. The

    designer is required to size the ducts within this constraint. If the plenum is able to move air through

    the longest run of ductwork, then it will be able to move air through the side branches.

    Determine the pressure loss per 100 ft of duct

    The longest branch is the 1-3-5 branch. The total equivalent length of this branch is

    Ltotal=LBellmouth+L1+Ltee,through+L3+Lwye,through+L5+ 2(L45,elbow).

    Note that the equivalent lengths for the tee and the wye are for diverging branch fittings. Table A.4

    gives the equivalent lengths of the fittings in circular ducts. At this point, the diameter of the duct is

    not known. Assume that the duct diameter is 8 inches to find the equivalents of the fittings.

    Therefore,

    Ltotal

    = 8 ft + 20 ft + 5 ft + 12 ft + 5 ft + (8 + 8 + 15) ft + 2(6 ft) = 93 ft.

    The total pressure available from the plenum is 0.21 in. wg. For the longest branch of the duct system,

    the available pressure is the total pressure from the plenum less the pressure loss at the end of the

    longest branch.

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    Section 3: ft512xft100

    wg.in.0.18x

    ft100

    wg.in.0.18 throughwye,33 LLP = 0.031 in. wg.,

    Section 4: wg.in.0.036ft1315xft100

    wg.in.0.18x

    ft100

    wg.in.0.18 diffuserbranchwye,44 PLLP

    P4= 0.086 in. wg.,

    Section 5: wg.in.0.04ft1231xft100

    wg.in.0.182x

    ft100

    wg.in.0.18 diffuserelbow45,55 PLLP

    P5= 0.12 in. wg.,

    For the longest branch:

    P1-3-5= P1+ P3+ P5= (0.045 + 0.031 + 0.12) in. wg. = 0.196 in. wg. < 0.21 in. wg.

    For branch 1-2:

    P1-2= P1+ P2= (0.045 + 0.12) in. wg. = 0.165 in. wg. < 0.21 in. wg.

    For branch 1-3-4:

    P1-3-4= P1+ P3+ P4= (0.045 + 0.031 + 0.086) in. wg. = 0.162 in. wg. < 0.21 in. wg.

    In this case, all the sections have lower pressure losses than that available from the plenum.

    Size the duct sections as rectangular ducts

    The equal friction and capacity chart (Table A.3) will be used to select an appropriate rectangular duct

    equivalent for the circular ducts. The aspect ratio will be 4 or lower.

    Therefore,

    Section 1: 8 in. x 7 in. (aspect ratio: 1.14),

    Section 2: 6 in. x 6 in. (aspect ratio: 1.00),

    Section 3: 7 in. x 6 in. (aspect ratio: 1.17),

    Section 4: 6 in. x 6 in. (aspect ratio: 1.00),

    Section 5: 6 in. x 6 in. (aspect ratio: 1.00).

    The smallest size available from Table A.3 is 6 in. x 6 in. This is gives an equivalent diameter of 6.6

    in. At this diameter, the pressure loss will be lower than the design equivalent diameters of 5 in. and 6

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    in., resulting in a system pressure loss. The increase in material is small. This should be acceptable

    from a cost and installation perspective.

    Drawings

    The final drawing, showing the duct sizes is presented below.

    Conclusions

    Rectangular duct sizes have been chosen for this system based on a pressure loss of 0.18 in. wg. per

    100 ft of duct. This is larger than the standard 0.1 in. wg. per 100 ft of duct for small-sized, low-

    velocity duct systems. The constraint of 0.21 in. wg. of available pressure at the plenum forced a

    calculation of an appropriate pressure loss for the purposes of duct sizing.

    The assumption of an 8-inches duct to determine the equivalent lengths of the fittings is valid. In all

    cases, the duct sizes were 8 inches or less. This assumption resulted in a more conservative design

    since lower equivalent lengths are expected for duct sizes smaller than 8 inches. Absent from the

    design are losses due to transitions from larger duct sizes to smaller duct sizes. In all cases, the duct

    would be converging (becoming smaller) in the direction of air flow. Compared to other losses in the

    system, this loss is very small, with small equivalent lengths on the order of 3 ft, and was ignored.

    While the aspect ratios of the ducts are close to 1, installers in the field would likely install an 8 in. x 8

    in. duct in Section 1 and a 7 in. x 7 in. duct in Section 3. This would result in marginal increase in duct

    material, while producing a duct aspect ratio of 1 and lower pressure drops.

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    In branch 1-2 and 1-3-4, the pressure loss is lower than the main branch (branch 1-3-5). To balance the

    system, dampers may be installed to control the flow of air through these branches. These dampers

    should provide about 0.03 in. wg. of pressure drop.

    The following table summarizes the design results.

    Duct Section Duct Size Duct Velocity Total Pressure Loss

    in. fpm in. wg.

    1 8 x 7 850 0.045

    2 6 x 6 600 0.12

    3 7 x 6 820 0.031

    4 6 x 6 620 0.0865 6 x 6 710 0.12

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    2.8 Refer to Problem 2.4 and redesign the system with rectangular ducts. Specify a fan from a

    manufacturers catalog.

    Proposed Solution:

    Detailed Design

    Objective

    To design a rectangular air duct system and select a fan. The size and material of the ducts will be

    determined.

    Data Given or Known

    i. The length of each duct section is given.

    ii. The air flow rate through the diffusers boots is given.

    iii. The duct system is connected to an air handling unit (AHU).

    iv. The pressure losses in the AHU are given.

    iv. The total pressure available from the fan is 0.60 in. wg. for the design flows given.

    v. The pressure loss at the diffuser boots are given, with the typical boot equivalent length given as 20

    ft.

    Assumptions/Limitations/Constraints

    i. The maximum air velocity will be 1200 fpm. This is typical for low-velocity air-distribution

    systems. Low velocities will be chosen to ensure that the available total pressure from the fan is not

    exceeded.

    ii. Total friction losses available for the ductwork and component losses should be 0.60 in. wg. or less

    to meet the constraint at the fan.

    iii. Galvanized steel is typically used to fabricate air duct systems. It will be chosen as the material.

    iv. The entrance to the system at the plenum is a Bellmouth entrance. This reduces noise and losses.

    v. The elbows are pleated.

    Sketch

    A sketch of the system has been provided that shows the labels of each section of the duct system.

    Another sketch will be provided that clearly shows the locations of the appropriate dampers (if

    needed).

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    Analysis

    In this design problem, the total pressure available at the fan is constrained to 0.60 in. wg. The designer

    is required to size the ducts within this constraint. If the fan is able to move air through the longest run

    of ductwork, then it will be able to move air through the side branches.

    Determine the pressure loss per 100 ft of duct

    The longest branch is the 1-2-3-4-9 branch. The total equivalent length of this branch is

    Ltotal=LBellmouth+L1+L2+L3+L4+L9+ 3(L90,elbow) + 4(Lwye,through).

    Note that the equivalent lengths for the wye are for diverging branch fittings. Table A.4 gives the

    equivalent lengths of the fittings in circular ducts. At this point, the diameter of the duct is not known.

    Assume that the duct diameter is 12 inches to find the equivalent lengths of the fittings. 12 inches was

    chosen since the total flow rate of air is large at 845 cfm.

    Therefore,Ltotal= 12 ft + 21 ft + 10 ft + 8 ft + 10 ft + 29 ft + 3(15 ft) + 4(8 ft) = 167 ft.

    The total pressure available from the fan is 0.60 in. wg. For the longest branch of the duct system, the

    available pressure is the total pressure from the plenum less the pressure losses through the diffuser at

    the end of the longest branch and the losses in the AHU.

    Hence, for sizing the ducts,

    ft100x

    ft167

    wg.in.05.020.010.004.060.0

    P

    P= 0.13 in. wg. per 100 ft duct 0.15 in. wg. per 100 ft duct will be used.

    Size the duct sections as circular ducts

    The total volume flow rate of air from the fan is (250 + 120 + 150 + 200 + 125) cfm = 845 cfm. The

    volume flow rate through the sections of the main branch are:

    Section 1: 845 cfm,

    Section 2: 595 cfm,

    Section 3: 395 cfm,

    Section 4: 275 cfm.

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    The chart shown in Figure A.1 can be used to size the duct sections. Apply a pressure loss of 0.15 in.

    wg. per 100 ft duct. The duct sizes, velocities, and actual pressure drops are:

    Section 1: 12 inches, 1100 fpm, 0.15 in. wg./100 ft.,

    Section 2: 10 inches, 1100 fpm, 0.19 in. wg./100 ft.,

    Section 3: 9 inches, 900 fpm, 0.15 in. wg./100 ft.,

    Section 4: 8 inches, 850 fpm, 0.15 in. wg./100 ft.,

    Section 5: 6 inches, 610 fpm, 0.13 in. wg./100 ft.,

    Section 6: 8 inches, 710 fpm, 0.12 in. wg./100 ft.,

    Section 7: 7 inches, 750 fpm, 0.15 in. wg./100 ft.,

    Section 8: 6 inches, 610 fpm, 0.13 in. wg./100 ft.,

    Section 9: 6 inches, 760 fpm. 0.18 in. wg./100 ft.

    In all the sections, the duct velocity does not exceed 1200 fpm.

    A check should be conducted to ensure that the pressure loss in each of the branches does not exceed

    the total pressure available at the fan. A similar check should be conducted for the longest branch. The

    pressure drop through the sections of the duct system are:

    Section 1:

    wg.in.095.0ft15*21221xft100

    wg.in.0.152x

    ft100

    wg.in.0.15 elbow,90bellmouth11 LLLP

    Section 2:

    wg.in.0.032ft710xft100

    wg.in.0.19x

    ft100

    wg.in.0.19 throughwye,22 LLP ,

    Section 3:

    ft78xft100

    wg.in.0.15x

    ft100

    wg.in.0.15 throughwye,33 LLP = 0.023 in. wg.,

    Section 4:

    ft510xft100

    wg.in.0.15x

    ft100

    wg.in.0.15 throughwye,44 LLP = 0.023 in. wg.,

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    Section 5:

    wg.in.0.03ft51017xft100

    wg.in.0.13x

    ft100

    wg.in.0.13 diffuserelbow45,branchwye,55 PLLLP

    P5= 0.072 in. wg.,

    Section 6:

    wg.in.0.092wg.in.0.05ft1322xft100

    wg.in.0.12x

    ft100

    wg.in.0.12 diffuserbranchwye,66 PLLP

    Section 7:

    wg.in.0.081wg.in.0.04ft1314xft100

    wg.in.0.15x

    ft100

    wg.in.0.15 diffuserbranchwye,77 PLLP

    Section 8:

    wg.in.0.075wg.in.0.036ft1020xft100

    wg.in.0.13x

    ft100

    wg.in.0.13 diffuserbranchwye,88 PLLP

    Section 9:

    wg.in.0.04ft8428xft100

    wg.in.0.18x

    ft100

    wg.in.0.18 diffuserelbow,90throughwye,99 PLLLP

    P9= 0.112 in. wg.,

    For the longest branch (1-2-3-4-9):

    P= PAHU+ P1+ P2+ P3+ P4+ P9

    P= (0.25 + 0.095 + 0.032 + 0.023 + 0.023 + 0.112) in. wg. = 0.54 in. wg. < 0.60 in. wg.

    For branch 1-6:

    P= PAHU+ P1+ P6= (0.25 + 0.095 + 0.092) in. wg. = 0.44 in. wg. < 0.60 in. wg.

    For branch 1-2-7:

    P1-2-7= PAHU+ P1+ P2+ P7= (0.25 + 0.095 + 0.032 + 0.081) in. wg. = 0.46 in. wg. < 0.60 in.

    wg.

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    For branch 1-2-3-8:

    P1-2-3-8= PAHU+ P1+ P2+ P3+ P8= (0.25 + 0.095 + 0.032 + 0.023 + 0.075) in. wg. = 0.48

    in. wg. < 0.60 in. wg.

    For branch 1-2-3-4-5:

    P1-2-3-4-5= PAHU+ P1+ P2+ P3+ P4+ P5= (0.25 + 0.095 + 0.032 + 0.023 + 0.023 + 0.072)

    in. wg. = 0.50 in. wg. < 0.60 in. wg.

    In this case, all the sections have lower pressure losses than that available from the fan.

    Dampers with the specified pressure drops are required to balance the system on each section:

    Section 6: 0.16 in. wg.

    Section 7: 0.14 in. wg.

    Section 8: 0.12 in. wg.

    Section 5: 0.10 in. wg.

    Size the duct sections as rectangular ducts

    The equal friction and capacity chart (Figure A.1) will be used to select an appropriate rectangular duct

    equivalent for the circular ducts. The aspect ratio will be 4 or lower.

    So,

    Section 1: 11 in. x 11 in. (aspect ratio: 1.00),

    Section 2: 9 in. x 9 in. (aspect ratio: 1.00),

    Section 3: 8 in. x 8 in. (aspect ratio: 1.00),

    Section 4: 8 in. x 7 in. (aspect ratio: 1.14),

    Section 5: 6 in. x 6 in. (aspect ratio: 1.00),

    Section 6: 8 in. x 7 in. (aspect ratio: 1.14),

    Section 7: 7 in. x 6 in. (aspect ratio: 1.17),Section 8: 6 in. x 6 in. (aspect ratio: 1.00),

    Section 9: 6 in. x 6 in. (aspect ratio: 1.00).

    Drawings

    The drawing shows the duct sizes and the damper locations.

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    Fan selection

    The AHU should include a fan that is capable of moving 845 cfm of air and provide at least 0.60 in.

    w.g. of external static pressure. A Greenheck single-width industrial centrifugal belt drive fan will be

    selected for this application. The specifications are shown in the following catalog sheet. From the

    performance curves for the Greenheck 9 BISW fan, a 2212 rpm speed and a 0.29 hp motor is

    selected. This fan will be able to provide 0.75 in. w.g. of external static pressure.

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    Source: Greenheck Fan, Corp. (Reprinted with permission)

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    Conclusions

    Rectangular duct sizes have been chosen for this system based on a pressure loss of 0.13 in. wg. per

    100 ft of duct. This is close to the standard 0.1 in. wg. per 100 ft of duct for small-sized, low-velocity

    duct systems. The constraint of 0.60 in. wg. of available pressure at the fan forced a calculation of an

    appropriate pressure loss for the purposes of duct sizing.

    The fan selected will be able to deliver a maximum of 850 cfm at 0.75 in. w.g. of external static

    pressure, which meets the requirements of the designed system.

    The assumption of a 12-inches duct to determine the equivalent lengths of the fittings is valid. In all

    cases, the duct sizes were 12 inches or less. This assumption resulted in a more conservative design

    since, for the most part, lower equivalent lengths are expected for duct sizes smaller than 12 inches.

    Absent from the design are losses due to transitions from larger duct sizes to smaller duct sizes. In all

    cases, the duct would be converging (becoming smaller) in the direction of air flow. Compared to other

    losses in the system, this loss is very small, with small equivalent lengths on the order of 3 4 ft, and

    was ignored.

    The following table summarizes the design results.

    Duct Section Duct Size Duct Velocity Total Pressure Loss

    in. fpm in. wg.

    1 11 x 11 1100 0.15

    2 9 x 9 1100 0.19

    3 8 x 8 900 0.15

    4 8 x 7 850 0.15

    5 6 x 6 610 0.13

    6 8 x 7 710 0.12

    7 7 x 6 750 0.15

    8 6 x 6 610 0.13

    9 6 x 6 760 0.18

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    2.9 Hot combustion gases from a large burner are being considered to heat cold water in a heat

    exchanger. To facilitate operation and maintenance of the two units, they have been separated

    and installed individually. The client failed to provide specific information regarding the heat

    exchanger and conduct verification of the presence of electronics and electrical boards on the

    unit. As per the 2006 National Fire Protection Association (NFPA) Standard 31, Section 4.3.6,

    oil-burning equipment must be installed so that a minimum 3 ft separation is maintained from

    any electrical panel-board. The design strategy will be to connect a duct to the burner and route it

    to the bottom of the heat exchanger. It is expected that 25,000 lb/hr of corrosive combustion

    gases at 600oF will be transported through the duct after combustion with a low air/fuel ratio.

    The duct will be routed through the concrete slab of the floor in a trench to provide insulation,

    support, and protection. Design and layout a low-velocity rectangular duct system.

    Further Information: For the system designed, the maximum length of straight duct will depend

    on the fact that the burner blower cannot provide more than 0.35 in. wg. of pressure.

    Possible Solution:

    Definition

    Design a rectangular duct system to transport hot combustion gases between a burner and a heat

    exchanger.

    Preliminary Specifications and Constraints

    i. The working fluid will be combustion gases.

    ii. This is a low-velocity duct system.

    iii. NFPA Standard 31, Section 4.3.6 require a minimum 3 ft separation between the burner and the

    heat exchanger.

    iv. The duct should be routed through the concrete slab of the floor.

    v. The burner blower cannot provide more than 0.35 in. wg. of pressure.

    Detailed Design

    Objective

    To size a rectangular duct. The material of the duct will be selected. The layout, accessories, and

    fittings will be chosen.

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    Data Given or Known

    i. The flow rate of the combustion gases will be 25,000 lb/hr.

    ii. The temperature of the combustion gases will be 600oF.

    iii. The duct will be connected to the bottom of the heat exchanger.

    Assumptions/Limitations/Constraints

    i. Fiber-reinforced polymer (FRP) will be selected as the duct material, given the corrosive nature of

    the combustion gases. Another alternative may be to use stainless steel. This may be expensive,

    especially to install. Stainless steel duct lined with a Halar coating is also an option.

    ii. The entrance and exit to the duct will be a Bellmouth shaped. This will reduce noise and losses.

    iii. Any 90oelbows will be mitered with turning vanes. In that case, high-temperature filters should be

    placed in the burner to ensure that ash particulates do not enter and accumulate in the duct.

    iv. Let the gas velocity in the duct be no more than 2200 fpm. For industrial applications, the

    maximum velocity for low-velocity ducts should be 1300 to 2200 fpm.

    v. Assume that the combustion gases have the same properties as air since the air/fuel ratio is low.

    vi. The duct will be connected close to the top of the burner to ensure that the hot, rising gases will

    enter the duct.

    Sketch

    Below is a sketch of the system. The final drawing will show the final duct layout and size.

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    Analysis

    Determine the flow rate of the gases

    The flow rate of the gases, coupled with the maximum velocity will be needed to size the duct.

    Therefore, from the mass flow rate,

    cfm132,11min60hr1x

    lb/ft03743.0

    lb/hr000,253

    mV .

    The properties are those of air at 600oF.

    Size the round duct

    The total volume flow rate of air and the maximum velocity will be used to guide the sizing of the

    duct. The chart shown in Figure A.1 will be used to size the duct. The duct size, air velocity, and

    pressure loss are:

    30 inches, 2200 fpm, and 0.18 in. wg. per 100 ft, respectively.

    In this case, the duct velocity does not exceed 2200 fpm.

    Determine the size of an equivalent rectangular duct

    With the circular duct size known, a rectangular duct with equivalent friction and capacity will be

    selected from Table A.3. The dimensions will be chosen so that the aspect ratio will be 4 or less.

    Choose: 32 in. x 24 in.

    In this case, the aspect ratio is 1.3 and the equivalent circular duct diameter is 30.1 in.

    Determine the length of duct

    The total pressure available from the blower will be used to specify the total length of duct. With thetotal length known, the layout of the system can be fully presented. Hence, based on the sketch,

    exitbend90entrancestraight o4xft100wg.in.0.18

    LLLLP

    D

    LD

    D

    LD

    D

    LDLP

    exitbend90entrancestraight

    o

    4xft100

    wg.in.0.18 .

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    Table A.4 presents the equivalent lengths of the fittings in round ducts.

    Therefore,

    12ft5.210ft5.2412ft5.2xft100

    wg.in.0.18wg.in.35.0 straight L

    ft34straight L .

    The length of straight duct cannot exceed 34 ft. For this design, restrict the duct length to 30 ft.

    Drawings

    The final drawing, showing the duct size and length is presented below. Note that the total length of

    straight duct is 30 ft.

    Note that since the dimensions of the duct are on the order of 24 to 32 inches, two pieces of 4 ft

    sections of duct were allocated for attachment to the burner and heat exchanger to facilitate

    installation.

    Conclusions

    A rectangular duct has been chosen for the transport of hot corrosive gases from a burner to a heat

    exchanger.

    An analysis was conducted to determine the maximum length of duct required, while avoiding adverse

    impact on the performance of the burner blower in terms of its ability to produce sufficient pressure to

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    move the gases through the duct. The final lengths of the duct sections in the drawing will need to be

    confirmed during the installation stage of the project, especially when additional information regarding

    the dimensions of the burner and heat exchanger are known.

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    2.10 Refer to Problem 2.5. The client has decided to upgrade the factory space that is serviced by the

    small-duct high velocity system such that it will be classified as a clean room space for use in

    fabrication of microelectronic devices. To that end, the client wishes to replace the existing

    terminal boxes with replaceable terminal ceiling filter modules based on HEPA or ultra-low

    penetration air (ULPA) technology. Specify and select an appropriate fan from a manufacturers

    catalog for this application. Details on the recommendation of filter modules should be provided

    for review by the client. Specify dampers, where required, to balance the air flow in the system.

    Most manufacturers may provide static pressure loss data for clean, new filters. Static pressure

    loss increases as the particulate matter accumulates on the filter over time. What impact will this

    have on operation of the fan? Will it stall? Comment.

    Possible Solution: (Note that the analysis for Problem 2.5 is included here)

    Definition

    Specify and select an appropriate fan and terminal filter modules for the given high-velocity system.

    Preliminary Specifications and Constraints

    i. The working fluid will be air.

    ii. This is a high-velocity air-distribution system.

    iii. AHRI Standard 210/240-2005 specifies a blower that produces at least 1.2 in. wg. of external static

    pressure at 220 to 350 cfm per rated ton of cooling.

    iv. The air velocity should not exceed 5000 fpm.

    v. The duct lengths, air flow rates, and pressure losses across the terminal boxes are constrained, as

    shown in the drawing.

    vi. The space will be a clean room for use in fabrication of microelectronic devices.

    vii. Terminal ceiling filter modules based on HEPA or ultra-low penetration air (ULPA) technology

    should be used.

    Detailed Design

    Objective

    To design a round air duct system and select an appropriate fan and filter modules.

    Data Given or Known

    i. The length of each duct section is given.

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    ii. The air flow rates through the three diffusers are given as 460 cfm, 590 cfm, and 550 cfm.

    iii. The duct system is connected to an air handling unit.

    iv. The blower should produce at least 1.2 in. wg. of external static pressure when 220 to 350 cfm per

    rated ton of cooling will be produced.

    v. The air handling unit produces 5 tons of cooling.

    Assumptions/Limitations/Constraints

    i. Galvanized steel is typically used to fabricate air duct systems. It will be chosen as the material.

    ii. The entrance to the system at the air handling unit will be a Bellmouth entrance. This reduces noise

    and losses.

    iii. The 45oelbows will be pleated.

    iv. The maximum pressure loss across the filters will occur when they are blocked by particles.

    Sketch

    A sketch of the system is provided to show the labeling of each section of the duct system. Since the

    pressure drops across the terminal filter modules are not yet known, they are not specified in the

    subsequent drawing.

    Analysis

    Determine the maximum air velocity in the system

    According to the preamble of Problem 2.5, the air velocity in the duct cannot exceed 5000 fpm. From

    Table 2.3 and for high-velocity duct systems, air flow rates between 1000 cfm and 3000 cfm require a

    maximum air velocity of 2500 fpm. Even though the volume flow rate in section 5 and the branch

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    take-offs are lower than 1000 cfm, a maximum velocity of 2500 fpm will be used to size the round

    ducts.

    Size the duct sections

    The total volume flow rate of air from the air handling unit is (460 + 590 + 550) cfm = 1600 cfm. The

    volume flow rates through the sections of the system are:

    Section 1: 1600 cfm,

    Section 2: 460 cfm,

    Section 3: 1140 cfm,

    Section 4: 590 cfm,

    Section 5: 550 cfm.

    The chart shown in Figure A.1 can be used to size the duct sections. Use the maximum velocity

    constraint of 2500 fpm as a guide. The duct sizes, velocities, and pressure losses are:

    Section 1: 11 inches, 2500 fpm, 0.8 in. wg. per 100 ft,

    Section 2: 6 inches, 2500 fpm, 1.45 in. wg. per 100 ft,

    Section 3: 10 inches, 2050 fpm, 0.6 in. wg. per 100 ft,

    Section 4: 7 inches, 2250 fpm, 1.2 in. wg. per 100 ft,

    Section 5: 7 inches, 2050 fpm, 0.95 in. wg. per 100 ft.

    In all the sections, the duct velocity does not exceed 2500 fpm. Higher pressure losses per 100 ft of

    duct in the shorter branch sections should facilitate system balancing (to prevent excess air from

    flooding branches with low pressure losses or low frictional resistances). For a factory-type setting

    (similar to a testing laboratory), the design criteria for noise should be NC 4555. For circular ducts, a

    maximum velocity of 2600 fpm will produce NC 35 for an occupied space. Given that all the velocities

    in the duct are less than 2600, it is expected that the noise levels will be lower than the NC 45 55

    criterion.

    Select the terminal filter modules

    Flanders Filters is one manufacturer of replaceable terminal HEPA/ULPA filter modules that can be

    specified for this application. An excerpt of their catalog is shown below. For this application, and

    given that the flow rates are greater than 440 cfm, the 48 in. long x 24 in. wide module will be chosen.

    It is expected that the velocity across the filters will be between 70 and 110 fpm (see catalog sheets),

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    which will serve to avoid filter damage. Given that specifications on the type of solid particulates were

    not provided, a conservative approach will be to choose a filter capable of removing 99.9995% of

    particles with sizes of 0.12 microns and larger. This choice will result in larger pressure drops across

    the filters. Thus, choose filter model number PF-GS591-2448. Given that the flow rates through the

    filter modules in the longest run of duct is 550 cfm, the static pressure loss will be taken to be 0.65 in.

    w.g.

    It is expected that the static pressure loss will increase as the particulate matter accumulates on the

    filter over time. For these filters, standard construction allows the modules to be operated at a pressure

    drop of 2.0 in. w.g. This is larger than the pressure drop of the clean filters at 0.65 in. w.g. (see catalog

    sheets). This suggests that as particulate matter accumulates on the filters, the pressure drop may be as

    high as 2.0 in. w.g. This will have an impact on the fan and the air flow rates that it will draw.

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    Source: Flanders, Corp. (Reprinted with permission)

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    Check the branch pressure losses for fan sizing and balancing

    A check should be conducted of the pressure loss in each of the branches.

    Section 1:

    wg.in.0.224ft820xft100wg.in.0.80x

    ft100wg.in.0.80 throughtee,11 LLP ,

    Section 2:

    wg.in.435.0ft2010xft100

    wg.in.1.45x

    ft100

    wg.in.1.45 branchtee,22 LLP ,

    Section 3:

    wg.in.114.0ft712xft100

    wg.in.0.60x

    ft100

    wg.in.0.60 throughwye,33 LLP ,

    Section 4:

    wg.in.0.336ft1315xft100

    wg.in.1.2x

    ft100

    wg.in.1.2 branchwye,44 LLP ,

    Section 5:

    wg.in.0.409ft1231xft100

    wg.in.0.952x

    ft100

    wg.in.0.95 elbow45,55 LLP

    For the longest branch:

    P1-3-5= P1+ P3+ P5+ Pfilter= (0.224 + 0.114 + 0.409 + 0.65) in. wg. = 1.40 in. wg.

    For branch 1-2:

    P1-2= P1+ P2+ Pfilter= (0.224 + 0.435 + 0.65) in. wg. = 1.31 in. wg.

    For branch 1-3-4:

    P1-3-4= P1+ P3+ P4+ Pfilter= (0.224 + 0.114 + 0.336 + 0.65) in. wg. = 1.32 in. wg.

    In this case, the minimum pressure loss requirement for operation of the terminal boxes is no longer

    applicable because the boxes have been replaced with terminal filter modules. Since the longest branch

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    will require 1.40 in. w.g. of external static pressure loss, a new fan will be needed (Example 2.5

    required a fan to produce 1.2 in. w.g. of external static pressure). Also, this larger value of static

    pressure satisfies the requirements of AHRI Standard 210/240-2005.

    Damper sizes

    In order to balance the system, dampers will be needed in branches 1-2 and 1-3-4 since the pressure

    losses in those branches are less than 1.40 in. w.g.

    Therefore, the pressure drops across the dampers are

    For branch 1-2: 0.09 in. w.g.

    For branch 1-3-4: 0.08 in. w.g.

    Fan selection

    The AHU includes a fan that is capable of moving 1600 cfm of air and provide 1.40 in. w.g. of external

    static pressure. A Greenheck single-width industrial centrifugal belt drive fan will be selected for this

    application. The specifications are shown in the catalog sheet. From the performance curves for the

    Greenheck 10 BISW fan, a 3118 rpm speed and a 0.98 hp motor is selected . This fan will be able

    to provide 1.50 in. w.g. of external static pressure.

    If the filter module has collected particulates such that the pressure drop is 2.0 in. w.g., the fan will be

    required to provide 2.75 in. w.g. of external static pressure. In that case, the fan will only be able to

    provide approximately 1100 cfm of air at the same motor horsepower. Though the flow rate would be

    lower, the operation of the fan would be well outside the stalling region and far from the free delivery

    point.

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    Source: Greenheck Fan, Corp. (Reprinted with permission)

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    Drawings

    The final drawing, showing the duct sizes is presented below. The pressure drops across the terminal

    boxes have also been modified to reflect the results of the analysis.

    Conclusions

    Round duct sizes have been chosen for this high-velocity system based on a maximum air velocity of

    2500 fpm. Decisions were made throughout the analysis to ensure that this constraint was not violated.

    In branch 1-2 and 1-3-4, the pressure loss is lower than the main branch (branch 1-3-5). To balance the

    system, dampers were installed. It should be noted that dampers are also available with the terminal

    filter modules. However, since they are included with all the modules, they will not contribute to

    decreasing the static pressure difference between the branches. Therefore, the additional dampers will

    be required in branches 1-2 and 1-3-4. Effort was taken to size the branch ducts such that the pressure

    loss per 100 ft of duct was larger than the main branch. Absent are the losses when the duct converges

    to smaller diameters. These losses are small compared to the others and were ignored.

    The effect of including the filter modules based on HEPA or ultra-low penetration air (ULPA)

    technology to meet the clients requirements was an increase in the size of the fan required for this

    application.

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    2.11 A researcher at a local university has decided to install new equipment in a laboratory booth that

    will be used to fabricate fiber-reinforced polymer (FRP) composites for the construction industry

    on a pilot scale. The production process will produce gases (volatile organic compounds, VOCs)

    and non-flammable small-particle contaminants (carbon fiber particles) that will need to be

    exhausted. The researcher has engaged a mechanical engineer to design and layout a circular

    duct exhaust system, complete with a fan and other accessories such as dampers and filters. The

    researcher is also an engineer and has requested the use of HEPA filters to protect the fan from

    particle damage and to avoid their discharge to the open external ambient, a sidewall mounted

    exhaust fan, and a damper at the inlet to the fan. The elevation plan, complete with the

    equipment, has been provided by the researcher. Four 10 in. diameter openings in the top of the

    booth were provided to allow installation of ductwork. The client will supply 4 exhaust hoods

    (dimensions: 5 ft long by 3 ft wide opening)for connection to the ductwork system, and as such,

    selection of the hoods is outside the scope of this problem. The tentative location of the exhaust

    fan has also been specified by the client in the drawing. Design the required system by referring

    to the client-supplied drawing of the elevation plan and through consultation with the

    International Building Code, the International Mechanical Code and NFPA Standard 704. Most

    manufacturers may provide static pressure loss data for clean, new filters. Static pressure loss

    increases as the particulate matter accumulates on the filter over time. What impact will this have

    on operation of the fan? Will it stall? Comment.

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    ii. The total friction losses available for the ductwork should be about 0.1 in. of water per 100 ft of

    ductwork, as per industry standard. In this case, the fan will be sized after the ductwork system has

    been designed.

    iii. The entrance to the system at the hood will be a Bellmouth entrance. The exit to the dust collector

    will also be a Bellmouth shape. This reduces noise and losses.

    iv. Any 90o elbows will be 5-piece, with R/D = 1.5. Pleated or mitered elbows with vanes will be

    avoided to prevent accumulation of powder particles in the duct.

    v. Assume that this problem falls in an industrial setting.

    vi. For non-flammable exhaust materials, the codes do not provide much guidance regarding gas flow

    velocity in the ducts. Based on experience with NFPA Standard 96 for commercial cooking

    exhaust systems, the gas velocity should be at least 500 fpm. In order to maintain a low-noise, low-

    vibration ductwork system, the gas velocity should not exceed 2200 fpm in the main duct and 1800

    fpm in the branch duct. Therefore, a target maximum velocity of 1800 fpm will be chosen for the

    duct system for a conservative design