# Basic sizing

Equation (15.12) shows the basis of sizing: since the air flow rate (Q) is known, the cross­sectional area of the duct (A) can be established if a suitable mean velocity (V) is chosen.

Q = AV (15.12)

There is no general agreement on duct system classification but low velocity systems are often regarded as those in which the maximum mean velocity is less than 10 ms-1, medium velocity as having maximum mean velocities between 10 and 15 m s’1 and high velocity systems as those with maximum mean velocities not exceeding 20 m s_1. As a general principle, velocities should be kept as low as is reasonably possible and 20 m s_1 should never be exceeded. Duct systems are classified in HVCA (1998) by pressure as well as velocity, low pressure being up to +500 Pa or down to -500 Pa, medium pressure up to +1000 Pa or down to -750 Pa, and high pressure up to +2500 Pa or down to -750 Pa. Large negative pressures are undesirable in comfort air conditioning systems because extract ducts with large sub-atmospheric pressures are not stable, tending to collapse if deformed. On the other hand, large sub-atmospheric pressures are essential for industrial exhaust systems and systems used for pneumatic conveying, but such ducts are constructed with this in mind.

Three methods of sizing are used: velocity, equal pressure drop and static regain.

(a) Velocity method

A suitable mean velocity is chosen (CIBSE 1986a) for a section of the system that is considered to be critical, usually in terms of noise. This is often the main duct, after the fan discharge. Equation (15.12) is then used for sizing this section.

The volumetric airflow rate handled by subsequent sections of the supply main reduces as air is fed through the branches and reference to Figure 15.3 shows that if the velocity is kept constant the rate of pressure drop increases as the volumetric flowrate falls. This is
undesirable because the total pressure loss through the system becomes too large and the risk of regenerated noise increases. Hence it is necessary to reduce the mean air velocity in the main as air is fed through branches. Here lies the difficulty of using the method: it is not always easy to obtain recommended mean air velocities for the downstream main duct when it is handling less airflow. One approach is to consider the ducting at the end of the system that delivers air into the last air distribution terminal (supply grille, supply diffuser, variable air volume supply device etc.). Manufacturers invariably quote recommended velocities for good air distribution without the generation of undesirable noise. A conservative interpretation of these recommendations should be adopted. Common sense and engineering prudence may then be used to proportion velocities between the fan outlet and the air distribution terminals. Manufacturers’ maximum velocities should never be exceeded and supply air terminals should never be selected to operate at the extreme bounds of their quoted volumetric ranges.

EXAMPLE 15.1

Size the ducting shown in Figure 15.4, given that the velocity in the main after the fan is to be 7.5 m s“1 and the velocity in any branch duct is to be 3.5 m s’1.

Refer to Figure 15.4. Common sense suggests that the velocity in section BC should be the mean of 7.5 and 3.5, namely, 5.5 m s-1. Hence the following table is compiled, using

 Section Q M3 s“1 V M s’1 A M2 D Mm Ap Pa nT1 AB 1.5 7.5 0.2 505 1.15 BC 1.0 5.5 0.182 481 0.67 CD’ 0.5 3.5 0.143 All 0.34

15.2 Basic sizing 417 D

 A

 B

 C

 B’ C’ D’ Fig. 15.4 Duct layout diagram for example 15.1.

Equation (15.12) and making reference to the CIBSE duct sizing chart for the relevant pressure drop rates.

The duct run having the greatest total pressure drop is termed the index run. This is usually, but not always, also the longest duct run. It is evident that the pressure at C is enough to deliver the design airflow rate to the index terminal at D’ but is more than enough to deliver the design rate through the branch to C. A similar consideration applies at B. This is dealt with during commissioning when branch dampers at B and C are adjusted to absorb the surplus pressure and ensure the correct branch airflow. Sometimes it is possible to reduce the sizes of the branch ducts so that they absorb the surplus pressure without the need for dampering.

The correct and well-established method to be adopted for adjusting branch dampers is termed proportional balancing, developed by Harrison et al. (1965). A summary of the method is as follows. The main system damper is partly closed, the setting of the safety overload cut-outs on the supply fan motor starter are checked and the supply fan is switched on. After establishing the location of the index supply air terminal its balancing damper is fully opened and the airflow rate measured. In general this will be less than the design intention. Working backwards to the fan, successive air terminals are balanced to deliver the same percentage of the design airflow rate as that measured at the index terminal. After completing this and carrying out various system checks, the main system damper is opened, the total airflow rate measured and the fan speed adjusted to give the design duty. A similar technique is applied to extract systems. The detailed procedure given in the CIBSE Commissioning Code (1986b) must be followed.

(b) Equal pressure drop method

This method is commonly adopted for sizing low velocity systems. The following alternative approaches which, in principle amount to the same method, may be used:

(i) Pick a maximum mean velocity for a critical section of duct, size the duct using equation (15.12), note the pressure drop rate by means of a duct sizing chart and size the rest of the system on this rate.

(ii) Pick a pressure drop rate and limiting maximum mean velocity that experience has proved to be suitable and size the whole system on this pressure drop rate, subject to the limiting velocity, and using a duct sizing chart.

The second method has been commonly used with a pressure drop rate of 0.8 Pa m-1 and a limiting velocity of about 8.5 or 9.0 m s’1. ASHRAE (1997a) quotes a range of limiting velocities from 9 to 20 m s-1, leaving the exact choice to the designer.

418 Airflow in ducts and fan performance EXAMPLE 15.2

Size the duct system shown in Figure 15.4, using a constant pressure drop rate of 0.8 Pa m-1, subject to a velocity limit of 6.0 m s_I.