Calculation of fan total and fan static pressure

The air volume handled determines the size of a fan and the purpose for which it is to be used dictates the type of fan to be chosen. The reason for calculating the fan total pressure is to establish the speed at which the fan should be run, most fans being belt-driven, and the power of the motor that ought to be selected to drive it.

EXAMPLE 15.7

For the system shown in Figure 15.17, size all ducts at a pressure drop rate of 1 Pa nT1, subject to a velocity limit of 8.5 m s“1, and calculate the fan total and fan static pressures. Use the CIBSE (1986a) duct-sizing chart and loss coefficients for fittings and the additional information provided below.

Air inlet at A square-edged louvres with 80 per cent free area and a mean face

Velocity of 4 m s“1

Filter at B pressure drop 90 Pa, face velocity 1.5 m s-1

Pressure drop 50 Pa, face velocity 3 m s ‘1 pressure drop 150 Pa, face velocity 2 m s_l pressure drop 50 Pa, face velocity 3 m s~’

Pre-heater at C Cooler coil at D Re-heater at E Fan inlet at F Fan discharge at G Supply grilles at I’ and J’ Bend at J

625 mm diameter 600 mm x 500 mm

Pressure drop 5 Pa, face velocity 2 m s_l centre-line radius 375 mm

Convert all circular duct sizes into equivalent rectangular sizes that have the same volumetric airflow rate and the same pressure drop.

Answer

The following information is determined from the CIBSE (1986a) or (1986c).

		Circular		Rectangular
Duct	Airflow	Pressure Diameter	Velocity	Dimensions	Velocity
Section	Rate	Drop rate mm	M s“1	H x w
	M3 s“1	Pa m“1		Mm mm	M s“1
HI	3.0	1.0 675	8.4	500 x 750	8.0
IJ & II’	1.5	1.0 520	7.1	350 x 750	5.71

The following additional calculations must now be done:

Fan discharge area: 0.6 x 0.5 = 0.3 m2

Fan discharge velocity: 3.0/0.3 = 10 m s-1

Fan inlet area: jt x 0.6252/4 = 0.3068 m2

Fan inlet velocity: 3/0.3068 = 9.778 m s’1

Establishing changes of total pressure is much easier than determining changes of static pressure. If the total pressure is known at a point in the duct system the static pressure at the same point can always be calculated by subtracting from it the velocity pressure, in accordance with Bernoulli’s theorem (see equation (15.18)).

1. Outside Air Intake at A

Enough static suction must be developed immediately behind the louvres to provide the source of energy for accelerating the airstream from rest (at an infinite distance from the outside face of the louvres) to the face velocity and for offsetting the loss by friction and turbulence. The CIBSE (1986a) loss coefficient is 1.4 and hence

Apt = 1.4 x 0.6 x 42 = 13.44 Pa

Which is negative in the direction of airflow.

Accumulated pressure downstream:

2. Expander AB to Filter

The area ratio for this sudden expansion is the reciprocal of the velocity ratio and is

1. 5/4.0 = 0.375 whence, the CIBSE loss coefficient is 0.39.

Apt = 0.39 x 0.6 x 42 = 3.7 Pa

Accumulated pressures downstream:

Pt = -17.14 Pa, pv = +1.35 Pa, ps = -18.49 Pa

Note that a static regain has occurred across the expander (from -23.04 Pa to -18.49 Pa) because the velocity has reduced, although this is irrelevant to the calculation of total pressure loss.

3. Filter at В

Apt — 90 Pa Accumulated pressures downstream:

P, = -107.14 Pa, pv = +1.35 Pa, ps = -108.49 Pa

4. Reducer BC to Pre-heater

This is a sudden contraction with an area ratio corresponding to 1.5/3.0, whence the CIBSE loss coefficient is 0.23.

Ap, = 0.23 x 0.6 x 32 = 1.24 Pa

Accumulated pressures downstream:

P, = -108.38 Pa, pv = +5.4 Pa, ps = -113.78 Pa

5. Pre-heater at С

Apt = 50 Pa Accumulated pressures downstream:

Pt = -158.38 Pa, pv = +5.4 Pa, ps = -163.78 Pa

6. Expander CD to Cooler Coil

The sudden expansion from a velocity of 3 m s-1 to one of 2 m s-1 implies an area ratio of 0.67 and the CIBSE loss coefficient is 0.11.

Apt = 0.11 x 0.6 x 32 = 0.59 Pa

Accumulated pressures downstream:

Pt = -158.97 Pa, pv = +2.4 Pa, ps = -161.37 Pa

7. Cooler Coil at D

Ap, = 150 Pa Accumulated pressures downstream:

Pt = -308.97 Pa, pv = +2.4 Pa, ps = -311.37 Pa

8. Reducer DE to Re-heater

For this abrupt reducer the area ratio corresponds to 0.67 for which the loss coefficient is 0.11.

Apt = 0.11 x 0.6 x 32 = 0.59 Pa Accumulated pressures downstream:

Pt = -309.56 Pa, pv = +5.4 Pa, ps = -314.96 Pa

9. Re-heater at E

Apt = 50 Pa Accumulated pressures downstream:

Pi = -359.56 Pa, pw = +5.4 Pa, ps = -364.96 Pa

10. Transformation EF to Fan Inlet

This is a gradual, symmetrical reducer and if we take the included angle as 45° the CIBSE loss coefficient is 0.04.

Apt = 0.04 x 0.6 x 9.7782 = 2.29 Pa

Accumulated pressures downstream:

Pi = -361.85 Pa, pv = +57.37 Pa, ps = -419.22 Pa

These are the pressures at the fan inlet.

It is now convenient to start at the index grille, J’, and work backwards to the fan discharge.

11. Index Discharge Grille, J’

The frictional loss is given by the manufacturers at 5 Pa and this is the change of static pressure across the grille. The total pressure loss is the sum of this friction and the kinetic energy loss from the system, corresponding to the velocity pressure at the grille face.

Api = 5 + 0.6 x 22 = 7.4 Pa

Accumulated pressures upstream:

Pi = +7.4 Pa, pv = +2.4 Pa, Ps = +5 Pa

12. Expander J"J’ to Index Grille

The air velocity falls from 5.71 m s“1 to 2 m s"1 so the area ratio is 2/5.71 = 0.35, whence the CIBSE loss coefficient is 0.42. Since it is a gradual expander with an included angle of 50° (Figure 15.17) there is a further multiplier which the CIBSE (1986c) gives as 1.0. In other words this included angle is the equivalent of a sudden expansion.

Api = 1.0 x 0.42 x 0.6 x 5.712 = 8.22 Pa

Accumulated pressure upstream:

Pt = +15.62 Pa, pv = +19.56 Pa, ps = -3.94 Pa

(Notice that there is actually a negative static pressure in the beginning of the expander, even though the ductwork is on the discharge side of the fan. This is quite possible and arises because the static regain is +8.94 Pa, i. e. from -3.94 to +5 Pa.)

13. Straight Duct JJ’

Apt = 1 Pa m_1 x 30 m = 30 Pa Accumulated pressures upstream:

Pt = +45.62 Pa, pv = +19.56 Pa, ps = +26.06 Pa

14. Bend at J

The value of h/W (the reciprocal of the aspect ratio) is 350/750 = 0.47 and the ratio of the centre-line radius to the width is 1.0. The CIBSE loss coefficient is therefore 0.31.

Apt = 0.31 x 0.6 x 5.712 = 6.06 Pa

Accumulated pressures upstream:

Pt = +51.68 Pa, pv = +19.56 Pa, ps = +32.12 Pa

15. Straight Duct IJ

Apt = 1 Pa m-1 x 60 m = 60 Pa Accumulated pressures upstream:

Pt = +111.68 Pa, pv = 19.56 Pa, ps = +92.12 Pa

16. Supply Branch Piece I

For flow through the main, the velocity ratio is 5.71/8 = 0.71. The CIBSE loss coefficient for this is 0.25, referred to the downstream main velocity pressure.

Apt = 0.25 x 0.6 x 5.712 = 4.89 Pa

A static regain occurs as the air flows through the main, past the branch.

Accumulated pressures upstream:

P, = +116.57 Pa, pv = +38.4 Pa, ps = +78.17 Pa

17. Straight Duct HI

Apt = 1 Pa m-1 x 60 m = 60 Pa Accumulated pressures upstream:

18. Expander GH at Fan Discharge

The area ratio corresponds to 8/10 = 0.8, whence the CIBSE (1986a) loss coefficient is less than 0.09 so this value can be taken as a simplification. The CIBSE (1986a) also quote a further multiplying factor of 0.8 because it is a gradual expander with an included angle of 30°.

Apt = 0.8 x 0.09 x 0.6 x 102 = 4.32 Pa

Accumulated pressures upstream:

Pt = +180.89 Pa, pv = +60 Pa, ps = +120.89 Pa

These are the pressures at fan discharge.

Using equation (15.21) for the fan total pressure we have

PtF = +180.89 — (-361.85) = 542.74 Pa

Also, by means of equation (15.22) we have

PsF = +120.89 — (-361.85) = 482.74 Pa

Equation (15.23) verifies this:

PsF = +542.74 — (+60) = 482.74 Pa

Clearly, using two decimal places in the above calculations is academic. More realistic results would be ptp = 543 Pa and psF = 483 Pa. These would be rounded off, upwards, after the application of margins (see section 15.18).

As is seen in later sections (15.18 and 15.19), it does not follow that the design duty will necessarily be obtained: a great deal depends on how the fan is installed in the system and the extent to which the kinetic energy in the airstream leaving the fan is converted to static pressure by suitable reductions in velocity.

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