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)

подпись: (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

AIR DISTRIBUTION SYSTEM, DUCTWORK Friction Loss Calculation

(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

AIR DISTRIBUTION SYSTEM, DUCTWORK Friction Loss Calculation

In which Re is Reynolds number: Re = vd/v, in which

V is the average air velocity v is kinematic viscosity

Re > 3500

подпись: 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:

AIR DISTRIBUTION SYSTEM, DUCTWORK Friction Loss Calculation

/

подпись: /

5.74

подпись: 5.74

0.901 ‘

подпись: 0.901 ‘

подпись:

/

подпись: /(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)

подпись: (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

AIR DISTRIBUTION SYSTEM, DUCTWORK Friction Loss Calculation

(9.146)

AIR DISTRIBUTION SYSTEM, DUCTWORK Friction Loss Calculation

AIR DISTRIBUTION SYSTEM, DUCTWORK Friction Loss Calculation

. pvT pvt

Ap = Pv ^3 cos A + Pvi R. cos or

The friction loss in this branch is expressed as

Ap = 1[1]4

/

ILl

/

V V

V

T’-, r, f] y9

— 1+2 cos a——.

Z/3I ^31/3

(9.147)

(9.1481

(9.149)

AIR DISTRIBUTION SYSTEM, DUCTWORK Friction Loss Calculation

C,23 = .1 — 2 cos a

 

(9.150)

подпись: (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.

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