Figure 1. Evasé expansion of the area may be accomplished by using any number of sides. The best results are obtained when the expansion angle ø is the same for all sides.
“You say the fan outlet size doesn’t match the ductwork size? Well, just cobble something up and get the fan installed!”

Is that an expedient solution? Of course! Is it good technical advice? Possibly not! Every fan engineer who has been out to a number of “trouble jobs” has his own favorite story about a technical nightmare that was created by “cobbling up” a solution when what was really needed was some careful thinking.

Figure 2. The highlighted area represents a simple evasé with uniform expansion on four sides.

Turbulence and Trig

When air is being moved or controlled, one has to remember that air does not like to change direction abruptly. If an abrupt change is unavoidable, then one must do all one can to encourage the change by adding guidance and direction.

Even when airflow is in a straight line, it is necessary to treat a directional change with respect. For straight-line airflow, directional change occurs when duct size either increases or decreases. Round ductwork is easier to deal with. The device used to change size is referred to as a cone or conical diffuser or evasé or conical reducer for smaller-to-large, or a reducer for larger-to-smaller. Rectangular ductwork presents a host of problems. In this case, the device used to change size is called a diffuser, an evasé, or a transition for smaller-to-larger, or simply a transition for larger-to-smaller.

The round duct, smaller-to-larger case is very simple. The angle at which the cone expands (increases) is constant at any point on the smaller diameter. We can call this angle the expansion angle. Since the angle is constant at any point on the smaller diameter, the change is balanced. Now, if the angle is small enough, the change is then both balanced and gradual. ANSI/AMCA 210 calls for a maximum (expansion) angle of 3.5 degrees. This often makes for a relatively long cone, but it is one in which the air can expand into the larger area so gradually that no turbulence results.

The length of the cone (conical diffuser, transition, etc.) is given by simple trigonometry:

L = (R – r) / tan 3.5 degrees


L = Axial length of cone (or height)

R = Radius of larger opening

r = Radius of smaller opening

For the round duct, larger-to-smaller case, one might expect that the same 3.5 degrees-angle would apply, but that is not so. ANSI/AMCA 210 calls for a maximum convergence angle on any side is 7.5 degrees. The length of the cone (conical reducer, transition, etc.) is once again given by simple trigonometry:

L = (R – r) / tan 7.5 degrees Where:

L = Axial length of cone (or height)

R = Radius of larger opening

r = Radius of smaller opening

The Rectangular Twist

A rectangular duct presents an entirely different case. Although a rectangular duct is made up of simple flat panels, the balance effect that was so easily obtained with a round duct may be more elusive. However, one point of consistency remains: the maximum expansion angle of 3.5 degrees and the maximum convergence angle of 7.5 degrees still hold true.

Balance is affected when a rectangular duct expands or converges on only one side, and, to a lesser extent, on three sides. Balance is much less of a problem when expansion or convergence takes place on two sides, and even less when four sides are involved. Just as the length of the transition (or diffuser or evasé) was determined by simple trigonometry for a round duct, it can be obtained for a rectangular duct by using the tangent of the expansion or convergence angle.

Troubling Transitions

For our purposes from here on, we will call the device — cone, reducer, transition, diffuser, or evasé — a transition. We will examine the transition, particularly the expanding transition, and you will see that it is a far more complicated device than one might imagine.

An expanding transition operates on a very simple principle: air flowing from the smaller area to the larger area loses velocity as it approaches the larger area, and a portion of the reduction in velocity pressure (∆Pv) converts to static pressure ∆Ps). This conversion is called regain. It is important to remember that only a portion of ∆Pv is regained as Ps. It is not possible, though some have tried, to use a very long transition to regain ALL the ∆Pv.

The percentage of ∆Pv regained as Ps depends on whether the transition is round or rectangular, and if rectangular, the number of sides which diffuse, the ratio of the larger to the smaller area. The highest percentage regain is for the smallest area ratio and the smallest expansion angle. In brief, the regain is greatest when there is the least ∆Pv to serve as a base. As an example, for a four-side expanding transition with all sides expanding at 10 degrees and having an area ratio of 1.5:1, the percentage regain is about 85%.

Many duct systems are space-restricted and must necessarily use relatively small ducts with high Ps losses. This in turn causes the owner of the system to pay high operating costs for the life of the system. However, if duct size is not severely restricted, using larger ductwork to move air at a lower velocity can be financially beneficial. As a rule of thumb, when design predicts that air velocity in a system will reach or exceed 15.2 meters/sec (3,000 ft/min), an expanding transition and larger ductwork should be considered.

Cobble with Caution

To return to the lead situation in this article, the basic question is whether the fan outlet size and the ductwork size have to match. Obviously, they do not. The only real requirement is that whatever is “cobbled up” should be cobbled with some thought beforehand so that the transition joining the fan and the ductwork disturbs the airflow as little as possible. Bear in mind that the air coming out of the fan discharge is already turbulent and nothing should be done to aggravate the situation. In those cases where a blast of air is required from a converging transition, the change from one area to another should also result in as smooth an airflow as is reasonably possible.

Some fan designs incorporate a transition at the fan outlet as part of the basic fan design. This helps the fan to perform more efficiently and often simplifies the installation process.

From the foregoing, it can be seen that the simple transition is far from simple, and that negotiating it carefully and thoughtfully can have a decided impact on the dollars spent on airflow. ES