Existing Duct Sizing Methods

The traditional duct sizing methods are Equal Friction and Static Regain [ASHRAE, 2001]. Both methods were developed as expedient practical procedures and neither addresses optimization. Available computer programs are simply automated versions of these manual procedures.

The Equal Friction method creates an "initial guess" for duct sizing by establishing a constant pressure loss per unit of duct length. A number of sources recommend using 25 Pa (0.1 in. WG) pressure loss per 30 m (100 ft) total length. This length is selected for the "critical path," which is the longest branch in an air distribution system. It is assumed that the longest run will have the highest sum of total pressure loss. However, the longest run is not necessarily the run with the greatest friction loss, however, because shorter runs may have more elbows, fittings, and other flow restrictions. The procedure for using the Equal Friction method for duct design, including system balancing, follows:

Step 1. Select the "critical path" as the longest branch between fan and terminal outlets.

Step 2.Assign total pressure losses to each section of the "critical path" as the recommended pressure loss per unit of length multiplied by the actual section length.

Step 3. Calculate cross sections for the "critical path" using previously assigned total pressure losses, and correct these if necessary in order to satisfy velocity and geometrical constraints. Pressure loss in junctions cannot be calculated until branched cross sections are assigned. At this time, the pressure loss in junctions can be ignored; a constant pressure loss can be assumed for any junction, or the same cross sections can be used in branches as in trunk ducts.

Step 4.Sum the pressure losses in the "critical path" and select a fan so that fan total pressure is close to the sum of total pressure losses in the critical path. This pressure is called the "root pressure." At this step the root pressure is the same as the fan pressure. If the selected fan does not satisfy the pressure requirement, change the assigned pressure loss per unit length and repeat the process from Step 2.

Step 5.Assign a total pressure at each node of the critical path. To achieve pressure balancing, node pressures must be dissipated in corresponding branch sections.

Step 6. Exclude sections that belong to the critical path and select the longest branch from the remaining sections. This will be the new critical path and the node pressure is its root pressure.

Step 7.Calculate the total pressure loss per unit length of the new branch as its root pressure divided by its length. This pressure loss should be larger than the initial pressure loss per unit length assumed for the main critical path in Step 2.

Step 8.Repeat the calculation process for the new critical path, starting from Step 2.

Step 9.Continue this process until cross sections are calculated for all sections.

The engineer should achieve pressure balancing by selecting proper duct cross-sections rather than by using dampers.

Note that during such a calculation process, the pressure loss in the "critical path," which is already calculated, will change because of the change of cross sections in the branches of junctions. A major problem in this process is to satisfy the noise and geometry criteria. For example, a short section located close to the fan must be balanced with the long "critical path." Often, this can only be done by dampening flow. However, this creates noise caused by high velocities in the damper. Occasionally, lowering fan pressure can prevent noise, but more often it indicates that the layout of the system must be modified.

The Static Regain method of duct sizing is based on Bernoulli's equation, which states that when a reduction of velocities takes place, a conversion of dynamic pressure into static pressure occurs. This is used as the major principle for sizing the ducts so that the increase in static pressure at each branch offsets the friction loss in the succeeding section of the duct. The static pressure should then be the same before each terminal and at each branch. This method provides a convenient means of designing a long duct run with several take offs so that the same static pressure exists at the entrance to each branch, outlet, or terminal take off. The Static Regain method applies to supply systems only. This method is also based on an arbitrary parameter, which is the velocity for the root section. The ASHRAE 2001 Fundamentals Handbook, Chapter 34, Table 10 [ASHRAE, 2001] gives the suggested range of velocities based on "engineering experience." When energy cost is high and installed ductwork cost is low, a lower initial air velocity is most economical. For lower energy costs and high duct costs, higher air velocity is most economical.

Like the Equal Friction method, the Static Regain method requires iterations. The major difference between the Static Regain and Equal Friction methods is that one uses the ratio of pressure loss to the length, and, in the other, the succeeding cross section is selected as a function of previously established air velocities at junctions:

(Pressure loss)1-2 = [(Velocity)12 - (Velocity)22] x (Density) / 2

Both methods are based on an initial guess.

The Static Regain method has been shown to have a number of deficiencies [Tsal and Behls, 1988]. The method has been partially modified [Brooks,1995] to compensate for some of these problems.

Popular traditional duct design methods, including Equal Friction and Static Regain [ASHRAE, 1997], provide engineers with design tools. However, these methods involve some engineering judgment and extensive manual recalculations, so air distribution systems designed by different engineers for identical situations will turn out to have different fans, duct sizes, costs, and overall system energy demands.

Tsal and Behls (1986) conducted a comprehensive analysis of existing duct-sizing methods . This analysis shows that these methods, after a number of iterations, can select cross sections that deliver the designed amount of flow to terminals; these methods cannot, however, select the most economically efficient design.

A large number of duct-sizing computer programs are available commercially. Most are based on manual sizing techniques. One example, the DUCTSIZE computer program developed by Elite Software, can size a duct system up to 500 sections using the Equal Friction, Static Regain, or Constant Velocity techniques. Ducts can be round, rectangular, or flat oval. DUCTSIZE calculates noise levels and required attenuation and presents a list of required materials. In addition, input data can be taken directly from a duct drawing file created by AutoCAD.

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