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Article # 0035
ACCA Manual D Spreadsheet Tool
By James A. Lacy, P.E.
August, 2007
Abstract
The purpose of this paper is to describe a spreadsheet tool which may be used for residential duct design. In adjunct with ACCA Manual D, it quickly models the values for air velocity, air flow, duct diameter, and pressure drops.
Disclaimer
Neither the author nor publisher is responsible for the use of this information. The accuracy or completeness of any information published is not guaranteed and neither the author nor publisher shall be responsible for any errors, omissions, or damages arising out of the use of this information.
Problem
Manual D, Duct Design for Residential Winter and Summer Air Conditioning and Equipment Selection describes an iterative process for sizing ducts. Ducts are available only in fixed sizes, e.g. 3", 4", 5", etc. When the calculated value calls for a 5.5" duct, the designer must choose either a 5" or a 6" duct. The result is either more or less air flow than optimum. Several iterations may be required before an acceptable solution is realized.
Partly because of the time involved in Manual D calculations, a common practice in the Heating, Ventilation, AirConditioning (HVAC) trade is to size equipment and ductwork based on a thermal ton per a locationdependent square footage of conditioned interior. For example, airconditioning may be estimated by 400, 500, or 600 square feet per ton (12,000 Btu per hour) of air conditioning. Ducts and terminals (registers) are likewise estimated by the size of the room to be conditioned. Occupants are not likely to feel mismatches due to the oversizing. That is, as long as it feels cold in the summer, then the equipment is assumed to be working.
Squarefootage per ton is being challenged by two changes: one is rising energy costs, and two is mandated energy codes. In some states, use of Manual J and Manual D is mandatory for sizing equipment. Better energyefficient homes may be properly cooled by a ton of airconditioning per up to 1200 square feet. By applying the 500 square feet per ton to one of these homes, the equipment would be grossly oversized.
By rightsizing the equipment to energyefficient homes, the terminals and duct sizes will also be affected. Both air flow and velocity are important to selecting proper terminals. Terminals which would have worked under a 500 square foot per ton rule will likely have insufficient throw under a 1200 sf per ton system. Immediate feedback to the designer on the effects of air flow, velocity, duct size, and pressure drop would reduce design time.
Theory
Residential HVAC sizing consists of several iterative steps. The first is understanding the building load by analysis with Manual J, Load Calculation for Residential Winter and Summer Air Conditioning.
Equipment sizing is then performed using Manual S, Residential Equipment Selection. This will also account for such things as evaporator air temperatures, outside air condenser temperatures, sensible versus latent heat, etc.
Air flows from Manual J and Manual S are allocated to room cubic feet per minute (CFM)s. Ducts are then sized using Manual D. Whereas Manual J computations are linear, that is, a temperature difference across a fixed thermal resistance will produce a heat flow; air movement in a duct is not linear.
Air movement down a duct has both frictional losses and dynamic losses. Assuming a standard air at 0.075 lbmass per cubic foot, the Darcy friction loss is:
_{ }= f(12L/D)(V/4005)^{2}
where
_{ } is friction loss, inches of water
f is the friction factor
L is the duct length in feet
D is the hydraulic diameter in inches
V is the velocity in feet per minute
Following Altshul and Tsal, friction loss f is further simplified and may be calculated by:
f = 0.11 (_{}
where _{ } is the duct roughness factor, in feet (galvanized steel is 0.0003)
R_{e}_{ }is the Reynolds number, and
R_{e}_{ }= 8.56 D V for standard air.
Dynamic losses from fittings and flow disturbances may be expressed in two ways. One way is to use the Manual D fitting loss and express these losses in equivalent lengths of duct. The other way is to use the equation:
_{ }
where
_{ } is the fitting pressure loss in inches water
C is the local fitting loss coefficient
Velocity and airflow rate are related as
V=144 Q/A
where
V is velocity in feet per minute
Q is airflow rate in cubic feet per minute
A is crosssectional duct area in square inches
Friction varies with the air velocity and duct diameter. Friction pressure and dynamic pressure vary with the square of air velocity. Friction charts of Manual D plot airflow in cfm, velocity in fpm, friction in inches water, and duct diameter in inches. Any two of these factors determine the values of the other two factors.
With the charts of Manual D, and the theory equations, the designer may calculate V, Q, D, and _{ }
Example
Assumptions
For residential HVAC, ideal terminal velocities are assumed to be 700 fpm. Duct and trunk velocities are assumed to be low speed, under 1,000 fpm. Available pressure to be allocated to ducts may be from 0.1 to 0.5 inches of water. Stack effect may be ignored for residential HVAC.
Model
A trunk and duct set may be modeled as shown in Figure 1, where segments 1 through 5 represent trunk elements, and segments 6 through 9 duct elements terminating in an air register. If there are no return ducts, then air moves to the central fan to be recirculated.
For the moment, let us assume that there is no duct leakage. Then the sum of air entering and leaving any individual node, such as B; C; D; E; or F, is zero. Our convention is that air flowing into a node is positive, and flowing out is negative.
Four loops are assigned to Figure 1. Taking node C as an example, the pressure across element 9 must equal the sum of pressures across element 3 and element 8. Our convention is to start in the upper lefthand corner of the loop, moving clockwise. Moving with air flow in elements 3 and 8 is positive for sign convention, moving against the air flow in element 9 is negative.
Using the theory equations, it is possible to solve for V, Q, and each element pressure drop _{ }, given D. The number of node equations plus loop equations must equal the number of elements.
To solve Figure 1, the node equations are:
B) Q_{1}  Q_{2} = 0
C) Q_{2}  Q_{3}  Q_{9} = 0
D) Q_{3}  Q_{4}  Q_{8} = 0
E) Q_{4}  Q_{5}  Q_{7} = 0
F) Q_{5}  Q_{6} = 0
The loop equations are:
Drop1 + Drop2 + Drop9  P_{F} = 0
Drop3 + Drop8  Drop9 = 0
Drop4 + Drop7  Drop8 = 0
Drop5 + Drop6  Drop7 = 0
These simultaneous equations could be solved for V by setting up matrices; instead, the Solver function of a spreadsheet can be used. The cells containing the 9 equations will be constrained to 0 as a value. The cells assigned to respective V’s will be iteratively changed by the spreadsheet until the constraints are satisfied.
The designer proceeds by setting up and filling in the spreadsheet entries of Figure 2 in accordance with Manual D . Duct diameter D is calculated per Manual D using the cfm and branch static design pressures. Figure 2 allocates an example design pressure of 0.15 IWG.

1 
2 
3 
4 
5 
6 
7 
8 
9 






Util 
Dining 
Guest 
Kitchen 
Duct diameter Inches 
12 
12 
12 
12 
5 
5 
8 
7 
7 
Measured Length of Section Duct FT 
5 
4 
2 
2 
2 
4 
6 
12 
4 
Beginning Fitting 









Equiv Length Fitting (D2) FT 
10 
20 


10 




Equiv Length Fitting (D2) FT 
20 






10 

Equiv Length Fitting (D2) FT 









Fitting C coefficient 






1.2 
1.2 
1.2 
Fitting C coefficient 









Fitting C coefficient 









Ending Fitting 









Equiv Length Fitting (D2) FT 



5 
10 
90 
90 
90 

Equiv Length Fitting (D2) FT 




90 




Fitting C coefficient 









Fitting C coefficient 









Total Effective Length of Run FT 
35 
24 
2 
2 
17 
104 
96.5 
113 
95.5 
Sum of C coefficients 
0 
0 
0 
0 
0 
0 
1.2 
1.2 
1.2 
Material Roughness Epsilon 
0.0003 
0.0003 
0.0003 
0.0003 
0.0003 
0.0003 
0.0003 
0.0003 
0.0003 
Diffuser pressure loss IWG 





0.007 
0.03 
0.03 
0.03 










Branch design static 
0.43 
0.63 
7.50 
7.50 
0.88 
0.14 
0.16 
0.13 
0.16 
CFM 



225 

56 
169 
114 
151 
Figure 2
Output calculations are shown in Figure 3. Drop1 _{ } is calculated as:
=((Vel1 / 4005)^2) * ((12* (0.11*((12*Eps1/Dsub1) +(68/(8.56*Dsub1*Vel1)))^0.25) * Lsub1/Dsub1) + Csub1 ) +Ptsub1
where
Eps1 is the material roughness factor
Ptsub1 is the register or diffuser pressure drop.
Air flow Q1 is calculated as:
=Vel1 * (PI()*(Dsub1 / (2*12))^2)
Calculations 




















.851.15 
IWG 




Target 


Target 

% 
0.019704043 
Drop1 

657 
Vel1, fpm 

516 
Q1, cfm 



0.013511344 
Drop2 

657 
Vel2, fpm 

516 
Q2, cfm 
490 

105% 
0.000646735 
Drop3 

483 
Vel3, fpm 

379 
Q3, cfm 



0.000312663 
Drop4 

322 
Vel4, fpm 

253 
Q4, cfm 



0.015289493 
Drop5 

464 
Vel5, fpm 

63 
Q5, cfm 



0.100535723 
Drop6 

464 
Vel6, fpm 
330 
63 
Q6, cfm 
56 
Util 
113% 
0.115825216 
Drop7 

542 
Vel7, fpm 
600 
189 
Q7, cfm 
169 
Dining 
112% 
0.116137879 
Drop8 

474 
Vel8, fpm 
500 
127 
Q8, cfm 
114 
Guest 
111% 
0.116784614 
Drop9 

512 
Vel9, fpm 
550 
137 
Q9, cfm 
151 
Kitchen 
91% 











Equations 










5.1553E11 
Loop 









1.89198E11 
Loop 









3.47194E11 
Loop 









4.56492E10 
Loop 









1.42109E13 
Node 









1.42109E14 
Node 









8.52651E14 
Node 









0 
Node 









0 
Node 









Figure 3
Results
Figure 3 shows the calculation results. Duct diameters have been adjusted to bring the calculated cfm air flow to within a target of + and  15% of the Manual J demanded air flow. However, the example calculated air velocities are below the desired air velocities for the example preselected air terminals. The consequences would be poor air mixing. Therefore, the example air terminals must change or the example pressure 0.15 IWG assigned to the ducts must be raised, and then reallocated.
Once the initial iteration is performed using the Manual D charts, subsequent iterations may be made quickly by changes on the spreadsheet. The designer may quickly identify velocities and air flows which are off target.
About the Author
James A. Lacy is a registered professional engineer in Texas. His publications include Systems Engineering Management: Achieving Total Quality, McGrawHill, 1992.
List of Works Consulted
ASHRAE Handbook Fundamentals, American Society of Heating, Refrigerating and AirConditioning Engineers, Inc.
International Energy Conservation Code Commentary 2000, International Code Council, Inc.
Manual D, Duct Design for Residential Winter and Summer Air Conditioning and Equipment Selection, Air Conditioning Contractors of America.
Manual J, Load Calculation for Residential Winter and Summer Air Conditioning, Air Conditioning Contractors of America.
Manual S, Residential Equipment Selection, Air Conditioning Contractors of America.
Article # 0035 TEST QUESTIONS: Coming Soon
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