ANALYSIS OF PRESSURE LOSS COMPONENTS IN AN INDUSTRIAL EXTRACT DUCT SYSTEM

The frictional head loss and the loss through fittings are computed for branch duct runs of an industrial extract ventilation system. Results show increases of both of the aforementioned loss components with increase in duct length. Furthermore, the fraction of the total loss due to fittings decreases from 0.60 to 0.45, with a corresponding increase of the fraction due to friction (from 0.40 to 0.55).Representative fractions of head loss components, obtained in the manner of this study, are shown to facilitate loss estimates and extract fan selection.


INTRODUCTION
The total head loss in an index duct run of an extract ventilation system comprises the losses through duct friction, fittings (such as elbows, tees and enlargements) and duct accessories (such as grilles, weather louvers and sound attenuators).The ventilating fan static pressure (which needs to be carefully estimated for proper fan selection) should exceed the sum of this total loss and the terminal pressure at the fan discharge.Usually, the estimation of the frictional loss and that due to fittings requires a greater effort than determining the other components of the fan pressure; the latter components being easily determined from the equipment manufacturer's technical specifications.To aid this effort, an earlier study had been carried out where a relationship between the total frictional loss and total loss due to fittings in composite index runs had been obtained, for varying duct complexities in an extract ventilation system serving groups of toilet rooms [1].Thus, a representative fraction due to all installed fittings in an index duct run may simply be added to the frictional loss to obtain a total and, thereby, serve in facilitating the fan selection procedure.
The present study is a case of an industrial ventilation system serving a canteen, kitchen and ablution spaces.The variation of the loss components, the total loss, and the fraction of the loss due to duct fittings with varying lengths of index run in the duct configuration are studied.
Recommended ventilation rates of 0.34m 3 /min per person, 0.60 m 3 /min/m 2 of floor area and 1.2 m 3 /min/m 2 of floor area, respectively, for cafeteria, toilets and kitchens [2] are utilized.b.
On account of reducing sound levels in the ductwork, flow velocities between 4.5 m/s and 8.0 m/s are recommended in ventilation ducts [3].An average value of 6.25m/s is utilized.c.
Pressure losses through duct accessories, such as intake grilles, weather louvers and sound attenuation, whose values are usually provided by their specialist manufacturers, are not included in the analysis.However, such loss values should normally be added to obtain a total head loss.

METHODS ADOPTED
The system parameters are calculated by the following methods.

Duct Sizing
By utilizing the flow velocity of 6.25 m/s and the respective air quantities q (in m 3 /s) in each duct section, the round duct size for each section is obtained as:

Calculation of Frictional Losses
For composite duct runs, the total friction head loss friction h as obtained as [4].
where f is the duct section friction factor, l is the section length (in m); i denotes the th i duct section and n is the number of sections in the composite run; q and d are as defined earlier; f is a function of the flow Reynolds number Re given as: where  is the air density (taken as 1.2kg/m 3 ),  is the flow velocity, and  is the air dynamic viscosity (taken as 1.8 x 10 -5 kg/ms).Expressing  in terms of flow rate and duct diameter, Re may then be expressed as: For the determination of f in the turbulent flow regime 3000 ≤ Re ≤ 200000 (which includes the range of Re realized in this study), the Blasius equation [5]: is found useful in determining f for use in equation 2.

Calculation of Loss through Duct Fittings
For a composite duct run, the total loss due to fittings is given as [4]:

08256
. 0 (6) where  is the head loss coefficient of the particular type of fitting [6]; j denotes the th j fitting and  is the number of fittings in the composite run; q and  are as defined earlier.
Furthermore, the head loss through duct enlargements is given as [4]: where e is the head loss coefficient through the enlargement.1 and 2 are, respectively, the upstream and downstream diameters at the enlargement.Values of e for various values of 2/1 and for various conical angles of enlargement are given in the literature [6]. Figure 3 illustrates the fittings.
Tables 1 and 2 give values of  for radius elbows and tees, and in order to achieve reduced head losses through fittings and to achieve uniformity of flow parameters (for the sake of proper comparison of results), 90 elbows and radius tees are utilized, while the enlargements are made of 30 conical angle.Thus, for the different values of

CALCULATION OF HEAD LOSS COMPONENTS FOR THE FIRST INDEX DUCT RUN 0, 1, 2, …,12
The loss components in the index run 0, 1, 2, ---, 12 are calculated as an illustration of the general procedure for the other runs listed in section 2 above.

Air Quantities
Using the recommended ventilation requirements stated earlier and the estimated numbers of users or the floor area for each room (as required), the ventilation air quantities are obtained.Hence, with the chosen number of air inlet terminals, the air quantity per inlet is obtained.Table 3 summarizes the calculation of the air quantities.Hence, the cumulative quantity for each air duct section is obtained and shown in Figure 2.

A Typical Head Loss Calculation
The head loss calculations are illustrated as follows using duct section 10-11.Air quantity in duct section, q = 3.88 m 3 /min = 0.065 m 3 /s, duct diameter (from Equation 1), d= 0.115 m.
Thus, a standard 100 mm size is taken.Re = 5154 .8 Now, there is one 100 mm x 150 mm enlargement, one elbow and one radius tee in this duct section.From Tables 1 and 2 the respective k values for the elbow and radius tee are 0.16 and 0.2.For the enlargement, 5 . 1 100 Following a similar procedure as for duct section 10-11, all other duct runs are analysed.Table 4 gives the complete computation of frictional and fitting loss components in the index duct run 0, 1, 2, ---, 12. Thus, the total frictional loss in the index run is 6.275 m while the total loss through duct fittings is 3.896 m.Table 10.Head loss computations for index run 'g' (

RESULTS AND DISCUSSIONS
Similarly, Tables 5 to 12 give the head loss computations for the other index runs enumerated as 'b' to 'i' in section 2 above, while Table 13 gives a summary of the computed losses as well as the fractions of the loss due to duct fittings for the different index runs.The graphs of Figure 5 show general increases of both the frictional loss and the loss due to fittings and, hence, the total system pressure loss with increasing length of index duct run.The increases occur in accordance with equations 2, 6 and 7. Furthermore, the plot of Figure 6 depicts the variation of the fraction of loss due to duct fittings with length of index duct run.This graph shows a general decrease of the fraction of loss due to fittings with increasing length of duct run (with a corresponding increase of the fraction due to friction).This decrease has resulted from the reason that as duct lengths increase, the numbers of duct fittings added into the duct runs are not proportionately increased.The fraction of head loss due to duct fittings decreases from 0.60 to 0.45 as the length of duct run increases from 6.6m to 25.5m.Thus, an average value of 0.525 may be utilized to approximate the fraction of loss due to fittings for the range of duct lengths utilized in this study.Hence, having obtained the frictional loss in an index run by the methods illustrated in this paper, the total loss is readily obtained by adding the relevant fraction due to fittings.
In the duct configuration utilized, it is observed that the largest total loss of 10.171 m occurs in the index run designated as 'a' in Table 13.This loss in the first index run is, thus, utilized in the extract fan selection [2,7].
Alternatively, having obtained the frictional loss of 6.275m for this duct run, applying the average fraction of 0.525 of the total to account for the loss through fittings gives the total loss through the first index run as follows: Let the loss through fittings = x .Then,

CONCLUSIONS
Within the range of lengths of duct run utilized in the study, the frictional and fitting head loss components are comparable in magnitude as can be deduced from Figure 5.It would, therefore, be a misnomer to refer to the fitting loss component as 'minor loss'.This conclusion has also been observed in earlier studies on ventilation and air conditioning ducts [1,8,9].
Representative fractions of head loss through duct fittings, obtained in similar manner to that discussed, for other configurations of extract duct would facilitate loss estimates and extract fan selection.For configurations which are not too different from the one analysed in this paper the results obtained may be applied.
of ke are obtained from the graphs of Figure 4[6].

Fig. 5 .
Fig. 5. Variation of Head Losses with Length of Index Run.

Fig. 6 .
Fig. 6.Variation of Fraction of Loss due to Fittings with Length of Index Run.
525 and x = 6.936 m.Total loss = 6.275 + 6.936 = 13.211 m.This figure, being larger than 10.171 m, gives a margin of safety in extract fan selection.

Table 3 .
Calculation of ventilation air quantities.