# AIR DISTRIBUTION SYSTEM, DUCTWORK Friction Loss Calculation

These are the general principles:

• No internal friction

• Noncompressible gas

• Isothermal

• Stationary

• Bernoulli theorem is applicable

 (9.138) P + + pgb = constant

Because the influence of gravitation pgh is negligible for horizontal (distri­bution) systems, this term is ignored in the equations.

Friction losses in ductwork are (9.139)

In which

А is friction factor, dimensionless L is length, m d is internal diameter, m p is density, kg nr3 v is average air velocity, m s-1

The friction factor А for laminar flow (Re 2300) is In which Re is Reynolds number: Re = vd/v, in which

V is the average air velocity v is kinematic viscosity

 Re > 3500 For turbulent flow the empirical formula of Colebrook-White applies:

(9.140)

This expression is difficult to use, as iteration is required. A simplified expres­sion can be used with sufficient accuracy: / 5.74 0.901 ‘  / (9.141)

The formulas are represented in the Moody diagram, which allows a quick solution.

In the transient field where 2300 < Re < 3500, the flow may be laminar or turbulent, and A is expressed by the following formula:

_ ^230o(3500 — Re) + A3soo(R-e ~ 2300)

3500-2300 ’

In which A23oo and A3500 are the calculated A values at Re = 2300 and Re = 3500, respectively.

9.7.1 .1 The Surface Roughness Factor E

This factor is material dependent. The values in Table 9.8 could be applied. The value for flexible plastic ducts (* in the table) can be estimated by

A = 510J^/d)6{S/s)’ if Re s 5 • 104 , (9.142)

In which

D is the internal diameter, m s is the depth of the winding, m S is the distance of the windings, m

Hydraulic Diameter

The hydraulic diameter is four times the flow area divided by the duct perimeter.

The formulas given before show the diameter d.

For rectangular and oval ducts, a corrected hydraulic diameter should be used.

Dh = 4\$, (9.143)

In which

A is surface area of the duct, m2 P is perimeter per unit length of the duct, m

TABLE 9.8 The Surface Roughness Factor e

 Duct type Material EOlHm) Seamless ducts Steel 0.045 Aluminum 0.045 Plastics 0.01 Spiral-type ducts Galvanized steel 0.15 Stainless steel 0.15 Aluminum 0.15 Ducts with beams Galvanized steel 0.07 Stainless steel 0.07 Aluminium 0.07 Flexible ducts Metal 0.5-3 Plastics » Internally insulated ducts Coated mineral wool 0.25 Masonry ducts Concrete 2 Brick 3

Pressure Loss Due to Local Resistance

(9.144)

The local friction resistance factor, depends on the geometrical shape of the ductwork and flow path through the various fittings used in duct systems.

Values for f are given in standard handbooks and are based on experi­mental measurements.

For computer applications, it is useful to have the friction factor in a mathematical expression (empirical).

Theoretical Background of Ј. One example for the case of a round col­lecting T-piece at 45° is shown in Fig. 9.59.

The impulse balance along the x axis is

 (9.145) PquiV1 cos a + A2p2 + Pqv2i’2 = A3p3 + Pqv3v3

In which

P is density, kg irr3 qv is volume flow’ rate, m3 s_1 v is air velocity, m s-1 A is surface area, m2

Because

Qvi — Qui

A2 — A3 P1 = P 21

Pl~Pi ~ Pv 3 Pv2PV3V1 Cos A + PV2V cos a —

Bernoulli’s law gives

 7 1 (9.146)  . pvT pvt Ap = Pv ^3 cos A + Pvi R. cos or The friction loss in this branch is expressed as Ap = 14

 / ILl / V V V
 T’-, r, f] y9 — 1+2 cos a——. Z/3I ^31/3
 (9.147) (9.1481 (9.149) C,23 = .1 — 2 cos a

 (9.150) Using the conservation law, a similar expression can be derived for other connection pieces. The general formula structure is

 ( ( 2 ( ( 2 ( V U2 V_2 Vx V2 + &-) + A3 + A A + a5 j N 4 VI ) V, V) 7
 C, — a0 + a j

Through d; are regression factors, calculated on the basis of the measured values.