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, Air-Conditioning (HVAC) trade is to size equipment and ductwork based on a thermal ton per a location-dependent square footage of conditioned interior. For example, air-conditioning 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.

 

Square-footage 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 energy-efficient homes may be properly cooled by a ton of air-conditioning 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 right-sizing the equipment to energy-efficient 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 lb-mass 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 cross-sectional 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 left-hand 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) Q₁ - Q₂ = 0

C) Q₂ - Q₃ - Q₉ = 0

D) Q₃ - Q₄ - Q₈ = 0

E) Q₄ - Q₅ - Q₇ = 0

F) Q₅ - Q₆ = 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
										.85-1.15
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
-5.1553E-11	Loop
1.89198E-11	Loop
-3.47194E-11	Loop
4.56492E-10	Loop
1.42109E-13	Node
-1.42109E-14	Node
-8.52651E-14	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 pre-selected 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, McGraw-Hill, 1992.

 

 

List of Works Consulted

 

ASHRAE Handbook Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning 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.