Duct Design

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Duct Design

Table Of Contents

Introduction ............................................................................................................................................ 3 Fundamentals Of Duct Design .............................................................................................................. 3 Pressure Changes In A System ............................................................................................................ 8 Example 1 ............................................................................................................................................. 13 Duct Design Methods .......................................................................................................................... 15 Example 2 ............................................................................................................................................. 15

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Introduction The purpose of air conditioning ductwork is to deliver air from the fan to the diffusers which distribute air to the room. This air that is distributed is ultimately delivered in response to a pressure difference created by one or several fans. The required pressure differential required by the fan(s) is a function of duct design. The objective of duct design is to size the duct such that:    

Minimize pressure drop Minimize noise Minimized cost Simplify Balancing

Proper duct design required a knowledge of the factors that affect pressure drop and velocity in the duct.

Fundamentals Of Duct Design Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Pressure in a duct system is the sum of two components, static pressure and velocity pressure. Static Pressure is equal in all directions. Static pressure is a perpendicular outward component and is analogous to the pressure which pushes against the walls of a balloon (figure 1).

Figure 1. Static Pressure

Velocity pressure is due to the momentum of the air. Velocity pressure is directional. Imagine a ribbon tied to the outlet of a common prop fan. When the fan is off, the ribbon remains slack, even though subjected to an atmospheric static pressure of 14.7 lb/sq-in. As the fan starts and begins producing airflow, the ribbon begins to deflect in the direction of airflow. As the airflow increases, the ribbon becomes more taught in the direction of airflow (figure 2).

Figure 2. Velocity Pressure WN Mechanical Systems

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Velocity pressure plus static pressure is equal to total pressure. In a duct system, velocity pressure and static pressure can be demonstrated using a flat plate suspended from a hinge. The plate and hinge are located downstream of a fan connected to a duct system. Directly downstream of the hinged plate, the duct system is fitted with discharge dampers. When the fan is off and the dampers are open, the plate does not deflect (figure 3). The fan is not producing any static or velocity pressure.

Figure 3. Duct Pressure Measurement System

With the fan turned on and the discharge dampers closed, pressure is produced in the duct system. All of pressure produced is static pressure (otherwise known as block tight static pressure). Static pressure is equal in all directions. Thus, the hinged plated does not deflect (figure 4). Total pressure is equal to static pressure.

Figure 4. Dampers Closed

With the fan turned on and the discharge dampers partially opened, the duct system experiences a combination of both static and velocity pressure. The velocity pressure component is directional in the direction of the airflow. This pressure impedes on the plate causing it to deflect (figure 5). The magnitude of the deflection is a function of the magnitude of the velocity pressure. Total pressure is equal to the velocity pressure plus the static pressure.

Figure 5. Dampers Partially Open

Finally, with the fan on, the discharge dampers are fully opened. Assuming the length of the duct system is very short, the static pressure in the duct system approaches zero. The majority of the pressure in the duct system is velocity pressure. The hinged plate will deflect to its maximum position (figure 6).

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Figure 6. Dampers Fully Ope

One method for measuring pressure in a duct system is a u-tube manometer. A u-tube manometer is a u shaped tube filled with some water. When one end of a u-tube manometer is closed to a vacuum and the other is open to atmosphere, the water will deflect. The magnitude of the deflection is equal to atmospheric pressure. Atmospheric pressure at sea level will cause the water to deflect 407.1” or 33.97 ft (figure 7).

Figure 7. U-Tube Manometer

Pressures measured in duct system are ordinarily in the order of 0-5 in-wg. This makes the use u-tube manometers in duct systems impractical. The variations in duct pressure are too small to make out accurately within the vertical tubes. To solve this problem, a similar device called an inclined manometer is used. An inclined manometer is sloped at 1:10 ratio (horizontal to vertical axis respectively). Knowing this ratio, we can more accurately determine changes within a duct system (figure 8).

Figure 8. Inclined Manometer WN Mechanical Systems

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Before we can measure pressure in a duct system, we must first understand how pressure varies with cross section. A fan creates kinetic energy by imparting velocity to air particles. At the discharge of a housed centrifugal fan, the velocity is greatest at top of the duct and falls off sharply as we approach the bottom of the duct. Generally speaking, it takes 5-10 duct diameters before the pressure in a duct system becomes uniform (figure 9).

Figure 9. Velocity Profile in Ductwork

After 5-10 duct diameters, we have an even flow distribution profile with the velocity achieving its maximum magnitude at the center of the duct. As we approach the walls of the duct, the air velocity approaches zero. When measuring pressure in a duct, it is important that the readings are taken in a section of duct where the velocity profile is uniform. Note from the cross sectional velocity profiles that the air velocity is zero at the edge of the duct. Thus, any pressure measurement taken at the edge of the duct is going to be measuring static pressure only (figure 10).

Figure 10. Static Pressure

Recalling that static pressure plus velocity pressure is equal to total pressure, placing the positive port of the inclined manometer at the center of the duct is going measure total pressure (figure 11).

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Figure 11. Combination Velocity + Static Pressure

Finally, manipulating the equation for total pressure yields: Velocity Pressure = Total Pressure – Static Pressure Taking into account the equation above, velocity pressure can be found by measuring total pressure with the positive port and static pressure with the negative port of the inclined manometer. The total water displacement would then be equal to velocity pressure (figure 12).

Figure 12. Measuring Velocity Pressure

Knowing the velocity pressure, the actual velocity in the duct can be determined.

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Pressure Changes In A System The first principle to understand when describing pressure changes in a duct system is the interaction between static pressure and velocity pressure. Earlier, we found that:

If we have a frictionless system and velocity pressure increases, then static pressure must then decrease by the exact same amount. Said another way, in a frictionless system, total pressure does not change. That being the case, if velocity pressure is equal to

If we increase the velocity in a duct system, the corresponding velocity pressure will increase. Assuming a frictionless system, this must come at the expense of static pressure. This can be demonstrated with an airplane wing. The Upper surface of the wing has a greater area than the lower surface. Thus the velocity of the air particles flowing along the upper surface will be greater than the velocity of the particles flowing along the lower surface. This velocity differential causes a pressure differential, which in turn causes lift (figure 13).

Figure 13. Airplane Wing Analogy

To begin our analysis of pressure changes in a duct system, we will assume a frictionless duct transition. Recall that :

If the outlet area is larger than the inlet area, the velocity pressure at the outlet must decrease. With a frictionless system where total pressure remains constant (Pt), static pressure (Ps) must increase at the same rate that velocity pressure (Pv) decreases. This phenomenon is known as static regain (figure 14).

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Figure 14. Static Regain in Lossless Duct System

However, both ductwork and fittings introduce friction. In straight duct, friction losses are due to fluid viscosity and are the result of momentum exchange between molecules in laminar flow. In fittings, friction losses are caused by the individual particles of adjacent fluid layers moving at differing velocities in turbulent flow. Friction losses are irreversible and are the conversion of mechanical energy into heat. Generally speaking, friction losses per unit length of straight duct are less severe than friction losses in fittings. Frictional losses occur at the expense of static pressure. Frictional losses do not impact velocity pressure. Examining the same duct system with two lengths of straight duct connected by a transition, but accounting for friction losses, results in pressure profile similar to that of figure 15. Note that that the magnitude of the velocity pressure at any point of the duct system does not change. However, as the air travels down the first section of straight duct, the static pressure drops at a consistent rate to due frictional losses in the duct. As the airflow travels through the transition, it experiences frictional losses due to turbulence which increases the rate of static pressure loss. Finally, as the airflow travels down the last section of straight duct, the static pressure loss again experiences at constant rate of change per unit length due to frictional losses. The sum of the static pressure plus velocity pressure at any point equals the total pressure in the duct system. The loss in total pressure is a direct result of the loss in static pressure due to frictional and turbulence losses.

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Figure 15. Friction Losses in

As mentioned previously, frictional losses in a section of straight duct are due to momentum exchange between the air particles and duct particles, which in turn produce heat. Those variables would include the velocity in the section of duct, air density and the type of material used for the duct. ASHRAE has plotted the relationship between those variable and created graphical chart for various roughness of duct (figure 16). Note that figure 16 is applicable only at sea level (.075 lb/ft3 air density). Figure 16 should be corrected for altitudes other than sea level.

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Figure 16. Friction Chart For Round Duct (density = .075 lb/ft3 and Ɛ=.0003 ft)

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Using this chart, we can find the frictional loss per 100 feet of duct. Another method which simplifies the use of the ASHRAE chart is a ductilator. Either method provides an accurate representation of duct losses due to friction. The output is generally given as in-wg pressure drop per 100 feet of duct. The second type of duct loss is referred to as dynamic losses. Dynamic losses result from flow disturbances caused by duct mounted equipment or fittings that change the airflow path direction or area. As discussed earlier, friction losses are sacrificed at the expense of velocity pressure. As a result, losses are measured as a percentage of velocity pressure. The local loss coefficient C is a measure of the fittings efficiency. The pressure drop through a fitting is calculated as:

Recalling that velocity pressure is

Substituting the equation for velocity pressure, the pressure drop through a fitting becomes

ASHRAE gives the local loss coefficient for various types and sizes of duct fittings. For example, a common duct fitting is the 45 degree branch. ASHRAE table SR5-13 (figure x) gives the loss coefficients for a 45 degree entry branch diverging tee. Note that two loss coefficients are given; Cb and Cs. ASHRAE defines the subscripts: c = Common b = Branch s = Straight

Figure 17. ASHRAE Fitting Table WN Mechanical Systems

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Example 1 Determine the straight and branch pressure drops through a tee. Example one assumes a 45 degree branch diverging tee with 2000 CFM entering the common duct and 1000 CFM leaving both the straight and branch legs of the tee. The upstream connection is 20” wide x 10” high and the straight and branch outlets are both 10” wide x 10” high. Find the straight and branch pressure drop (figure 17).

Figure 18. Example One

Solution: First we must find the areas of the common inlet, and straight and branch outlet. The area of the common inlet, straight outlet and branch outlet respectively are:

Next, we find the area ratio of the straight outlet to common inlet and the branch outlet to common inlet.

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Finally, we find the ratio of airflow of the straight outlet to common inlet and the branch outlet to common inlet.

Given these values, we enter ASHRAE table SR5-13 and find that Cb = .73 and Cs = .04. The velocity at both the branch and straight outlets is

Finally, the pressure drop through the straight – common leg is:

And the pressure drop through the branch – common leg is:

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Duct Design Methods Three common methods of duct design are the velocity method, equal friction method and static regain method. The velocity method assumes a constant duct velocity for main ducts and branch ducts. Typical duct velocities for low pressure duct design are: Rectangular Duct Recommended Velocities (fpm): Duct Type Main Branch

Residence 700 500

Theaters, Libraries 1000 500

Office Buildings 2200 1600

Industrial Buildings 3000 2500

Office Buildings 2400 2000

Industrial Buildings 4000 3000

Round Duct Recommended Velocities (fpm): Duct Type Main Branch

Residence 900 600

Theaters, Libraries 1200 600

The procedure for the velocity method is to pick a constant velocity for the main trunk and branch ducts. At the selected velocity enter the ASHRAE charts or use a common ductilator to find the nearest size common duct. Having found the duct size, the friction loss per 100 feet can be determined from the chart/ductilator. Multiply the friction loss per 100 feet times the actual duct length to find the pressure drop through all the sections of main trunk duct and branch duct. Add the pressure drops through each path. The total static pressure drop through the duct system is the sum of the worst case path. The fan external static pressure is the sum of the worst case path. The procedure for the equal friction method is very similar to the velocity method. With the equal friction method, we select a constant friction loss per 100 feet for all main trunk ducts and branch ducts. Then using a common ductilator or the ASHRAE charts, find the nearest practical duct size. Based on the actual duct size, determine the actual friction loss per 100 feet. Add the pressure drops through each path and sum the worst case path. The sum of the worst case path is equal to the fan external static pressure.

Example 2. Determine round duct size and fan external static pressure of system shown in figure 18. Assume a design friction loss of 0.1”/100’ and all fittings will have a pressure drop of 0.1” w.g. (figure 18).

Figure 19. Example Two

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Solution: Create a chart assigning the duct segments and corresponding airflow. Segment

Airflow (CFM)

AB BE BC CF CD DG

2000 500 1500 1000 500 500

Round Duct Size (in)

Friction Loss per 100’

Duct Length (ft)

Pressure Drop

100 40 50 75 40 50

Starting at segment AB, find the nearest duct size that (rounding to the larger size) that gives us 0.1”/100 ft of friction loss. Entering the ASHRAE chart, we find that the nearest duct size (rounding up) is 18”. The friction loss for 18” duct at 2000 CFM is .09”/100’. Knowing the length of segment AB is 10 ft, we can calculate the actual static pressure drop through the segment as:

Filling in the chart for segment AB Segment Airflow (CFM) Round Duct Size (in) AB 2000 18” BE 500 BC 1500 CF 1000 CD 500 DG 500

Friction Loss per 100’ .09

Duct Length (ft) 100 40 50 75 40 50

Pressure Drop (in) .09”

Next, we repeat the process for each of the remaining segments and complete the chart. Segment Airflow (CFM) Round Duct Friction Loss Duct Length (ft) Pressure Drop Size (in) per 100’ (in) AB 2000 18” .09 100 .09” BE 500 12” .055 40 .022” BC 1500 16” .085 50 .0425 CF 1000 14” .09 75 .0675 CD 500 12” .055 40 .022 DG 500 12” .055 50 .0275 Finally, we add each of the paths in order to determine the worst case path. The three possible paths are:

Adding the static pressure losses for the three passes above, we get:

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The worst case path is the required external static pressure of the fan. In the case of example 2, path 3 is the worst case path. The fan should be sized to an external static pressure of 0.585 in-wg. Typically, the worst case path can be identified without adding each and every path of the duct system. However, if the worst case path is not obvious, it is necessary to examine several of the worst case paths in order to determine the exact amount of external static pressure required for fan sizing. Note that in order for the duct system to properly balance, each of the branches will need to have the same static pressure as worst case branch. It is for this reason we install balancing dampers in all of the duct branches. The procedure for determining rectangular duct sizes is very similar. After having determined the round duct size, AHRAE tables can be used to find the equivalent round duct sizes based on duct aspect ratio. An alternate method is to identify the equivalent rectangular duct size using a common ductilator. The static regain friction duct design method uses the principal of static regain. Recall that static regain is the conversion of velocity pressure to static pressure by increasing duct cross sectional area and thus decreasing velocity pressure (figure 19).

Figure 20. Static Regain

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The static regain duct design method employs the use of fittings that decrease the airstream velocity downstream of a branch takeoff. This decrease in velocity is used to compensate the loss in static pressure upstream of the takeoff. The goal is to keep the static pressure constant via static regain at each takeoff. If done correctly, the duct system is literally self-balances and requires no balancing dampers. The downside to the static regain method is that is requires a computer analysis tool and often requires more duct material (figure 20).

Figure 21. Static Regain Duct Design

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