ANSI/API Std 560: 2007 Fired Heaters for General Refinery Service (Eng)

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Key

X Reynolds number

(

)

m,a

123,9 or 123,9Re v d q d

μμ

=×⋅⋅ ×⋅

Y Moody’s friction factor, f

1 very rough lined ducts: E = 0,01 (where E is the relative roughness)

2 medium-rough lined ducts: E = 0,003

3 smooth unlined ducts: E = 0,000 5

Figure F.6 — Moody’s friction factor versus Reynolds number

F.8.3.3 Flue-gas and air viscosity

If the viscosities,

, of the combustion-air and/or flue-gas streams are not known at all pertinent locations within

the system,

, expressed in millipascal seconds (mPa⋅s) and

, expressed in centipoise (cP), may be calculated

using the generalized Equations (F.5) and (F.6), respectively, for both air and flue gas without introducing any

significant error into the pressure-drop calculations:

μ = 0,016 2 (T/255,6)

0,691

(F.5)

where

T is the absolute temperature, in kelvin (K).

μ = 0,016 2 (T/460)

0,691

(F.6)

where

T is the absolute temperature, in degrees Rankine (°R)

12)

12) Rankine is a deprecated unit.

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F.8.4 Pressure drop calculations

F.8.4.1 General

The following equations and figures are a distillation of the large quantity of available literature on the subject of

fluid flow. This material has been used successfully in the design of duct systems and it is thought to be

particularly useful in that type of calculation. Two formats of each correlation are presented: linear velocity basis

and mass velocity basis. Use of either format remains the preference of the designer, as both formats produce

similar results.

F.8.4.2 Pressure drop in a straight duct

F.8.4.2.1 Pressure drop

The correlations in Equations (F.7) to (F.11) may be applied to straight ducts with or without internal refractory

linings. Additionally, these correlations can be used to calculate fitting losses for any fitting with a hydraulic length.

For example, Figure F.8 provides the equivalent lengths of various physical configurations of cylindrical mitred

elbows. The mitred elbow’s hydraulic length that is used with Equations (F.7) to (F.11) can be obtained by

multiplying the elbow’s equivalent lengths (from Figure F.8) by its flow diameter.

The pressure drop per 100 m,

ΔP

/100, expressed in millimetres of water column (mm H

O), is given by

Equations (F.7) and (F.8):

SI mF

/100 (5,098 10 ) /Pf

=× ⋅⋅vd

d⋅

(F.7)

SI mF m,a

Δ /100 (5,098 10 ) /Pfq

=× ⋅ (F.8)

where

is Moody’s friction factor (see Figure F.6);

is the flowing bulk density, in kilograms per cubic metre;

v is the linear velocity, in metres per second;

m,a

is the areic mass flowrate, in kilograms per square metre per second;

d is the duct inside diameter, in millimetres.

The pressure drop per 100 ft,

ΔP

USC

/100, expressed in inches of water column (in H

O), is given by

Equations (F.9) and (F.10):

USC mF

/100 (3,587) /Pf

=⋅⋅vd (F.9)

USC mF m,a

Δ /100 (3,587) /

=⋅d⋅

d is the duct inside diameter, in inches.

(F.10)

where

is Moody’s friction factor (see Figure F.6);

is the flow density, in pounds per cubic foot;

v is the linear velocity, in feet per second;

m,a

is the areic mass flow rate, in pounds-mass per square foot per second;

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F.8.4.2.2

( (F.7) through (F.10) employ a diameter dimension, d, and hence are

applicable to round ducts. To use these equations for rectangular ducts, an equivalent circular duct diameter, also

whe

is the length of one side of rectangle, expressed in millimetres (inches);

es).

NOT ar duct.

ure drop in straight ducts can be reduced to a simplifying

chart, presented for convenience as Figure F.7. Any error introduced is not significant for most cases.

sing a

hydraulic mean diameter, it is necessary to apply the correlation shown on the curve rather than the one in

C⋅ (F.12)

where

is the corrected pressure drop per 30 linear m (100 linear ft), expressed in mm H

O (in H

O);

from Figure 7 b);

1,0

table refractory):

The calculati given in Equation (F.13):

Hydraulic mean diameter

Equations F.1) through (F.4) and Equations

referred to as the hydraulic mean diameter, needs to be calculated. A useful correlation, in SI or USC units, for the

hydraulic mean diameter, d

, expressed in millimetres (inches), is given in Equation (F.11):

= 2ab/(a + b) (F.11)

b is the length of adjacent side of rectangle, expressed in millimetres (inch

E When using d in Equation (F.11), use the actual velocity calculated for the rectangul

F.8.4.3 Pressure drop estimation in straight ducts

By making several assumptions, the calculation of press

Note that when the pressure drop, ΔP, as given in Equation (F.12), is determined from Figure F.7 u

Equation (F.11).

ΔΔPPC=⋅

ΔP

is the uncorrected pressure drop taken from Figure 7 a);

is a pressure-drop correction factor for temperature taken

is a roughness correction factor, as follows:

⎯ very rough (e.g. brick):

⎯ medium-rough (e.g. cas 0,68

⎯ smooth (e.g. unlined steel): 0,45

on for rectangular ducts is as

()

1,3 [( ) 0,25]

+⋅

0,65ab×⋅

(F.13)

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a) Uncorrected pressure drop

b) Temperature correction factor

Key

X1 flue-gas mass flow rate, 10

kg/h (10

lb-m/h)

Y1 pressure drop, Δp

, expressed as millimetres H

O per

30 linear m (inches H

O per 100 linear ft)

X2 flue-gas temperature, expressed in degrees Celsius

(degrees Fahrenheit)

Y2 pressure-drop correction, C

NOTE 1 Flue-gas relative molecular mass is 28.

NOTE 2 Gauge pressure in duct is 100 kPa (14,5 psi).

NOTE 3 The bullet points in the figure coincide with a

flue-gas velocity of 15 m/s (50 ft/s).

Figure F.7 — Duct pressure drop versus mass flow

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⋅

F.8.4.4 Pressure drop in fittings and changes in cross-section

The pressure drop, Δp, of formed round elbows, various fittings, shape changes and flow disturbances can be

calculated with the loss coefficients provided in Table F.2 and Equations (F.14) and (F.15) for SI units, with Δp

expressed in millimetres of water column (mm H

O), and Equations (F.16) and (F.17) for USC units with Δp

expressed in inches of water column (in H

O).

In SI units:

Δ (5,102 10 )pC v

−

=× (F.14)

m,a

(5,102 10 ) /pC q

−

=×

(F.15)

where

C is the fitting loss coefficient from Table F.2;

is the flowing bulk density, in kilograms per cubic metre;

v is the linear velocity, in metres per second;

m,a

is the areic mass flow rate, in kilograms per square metre per second.

In USC units:

Δ (2,989 10 )pC v

−

=×

⋅ (F.16)

m,a

(2,989 10 ) /pC q

−

=×

(F.17)

where

C is the fitting loss coefficient from Table F.2;

is the flow density, in pounds per cubic foot;

v is the linear velocity, in feet per second;

m,a

is the areic mass flow rate, in pounds-mass per square foot per second;

Consideration should be given to the use of turning or splitter vanes to improve the characteristics of high-

pressure-drop fittings.

As previously noted in F.8.4.2, the pressure drop of multiple-piece mitred elbows can be calculated with the use of

Equations (F.7) through (F.10) and the equivalent lengths provided. The hydraulic length of a mitred elbow can be

obtained by simply multiplying the equivalent length from Figure F.8 by the elbow’s flow diameter. Consideration

should be given to the use of turning or flow-straightening vanes to improve the flow characteristics of high-

pressure-drop fittings. Additional information on this subject can be found in the references cited in F.8.9.

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Table F.2 — Loss coefficients for common fittings

Fitting type Fitting illustration

Dimensional

condition

Loss coefficient

L/D or L/W

Elbow of N degree

turn (rectangular or

round)

No vanes

N/90 times the value for a similar 90°

elbow

90° round section

elbow

Mitre

R/D = 0,5

R/D = 1,0

R/D = 1,5

R/D = 2,0

1,30

0,90

0,33

0,24

0,19

Mitre, H/W = 0,25

R/W = 0,5

R/W = 1,0

R/W = 1,5

1,25

0,37

0,19

Mitre H/W = 0,5

R/W = 0,5

R/W = 1,0

R/W = 1,5

1,47

1,10

0,28

0,13

Mitre H/W = 1,0

R/W = 0,5

R/W = 1,0

R/W = 1,5

1,50

1,00

0,22

0,09

4,5

90° rectangular

section elbow

Mitre H/W = 4,0

R/W = 0,5

R/W = 1,0

R/W = 1,5

1,35

0,96

0,19

0,07

110

90° mitre elbow with

vanes

= 0,1 to 0,25

Mitred tee with vanes

Equal to an equivalent elbow (90°)

(base loss on the entering velocity)

Formed tee

Equal to an equivalent elbow (90°)

(base loss on the entering velocity)

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Table F.2 (continued)

Fitting type Fitting illustration

Dimensional

condition

Loss coefficient based on

velocity in smaller area

Sudden contraction

= 0,2

= 0,4

= 0,6

= 0,8

0,32

0,25

0,16

0,06

Gradual contraction

= 30°

= 45°

= 60°

0,02

0,04

0,07

Slight contraction,

change of axis

≅ A

≤ 14°

0,15

Flanged entrance

0,34

Entrance to

larger duct

0,85

Bell or formed

entrance

0,03

Square-edged orifice

at entrance

= 0,2

= 0,4

= 0,6

= 0,8

1,90

1,39

0,96

0,61

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Table F.2 (continued)

Fitting type Fitting illustration

Dimensional

condition

Loss coefficient based on

velocity in smaller area

Square-edged orifice

in duct

= 0,2

= 0,4

= 0,6

= 0,8

1,86

1,21

0,64

0,20

Sudden enlargement

= 0,1

= 0,3

= 0,6

= 0,9

0,81

0,49

0,16

0,01

Gradual enlargement

= 5°

= 10°

= 20°

= 30°

= 40°

0,17

0,28

0,45

0,59

0,73

Sudden exit

≅ 0 1,0

Square-edged orifice

at exit

= 0,2

= 0,4

= 0,6

= 0,8

2,44

2,26

1,96

1,54

Bar in duct

= 0,10

= 0,25

= 0,50

0,7

1,4

4,0

Pipe or rod in duct

= 0,10

= 0,25

= 0,50

0,2

0,55

2,0

Streamlined object

in duct

= 0,10

= 0,25

= 0,50

0,07

0,23

0,90

This value is for a two-piece mitre. For three-, four- or five-piece mitres, see Figure F.8.

For permanent loss in venturis, use a loss coefficient of 0,05 based on throat area.

A and D represent the cross-sectional area and the diameter, respectively, of the relevant section of the fitting.

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Key

X radius ratio, R/D

Y equivalent length, L/D

1 3-piece elbow

2 4-piece elbow

3 5-(or more) piece elbow

Figure F.8 — Equivalent lengths for mitred elbows of round cross-section

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F.8.4.5 Pressure drop in branch connections

Velocity head, H

v,i

at location i, expressed in millimetres of water column (mm H

O), and the corresponding

pressure-drop values for the flow-through manifold branch and run connections can be calculated in SI units as

given in Equations (F.18) and F.19):

(5,102 10 )

−

=× ⋅

(F.18)

v, m,a,

(5,102 10 ) /

−

=×

(F.19)

where

is the linear velocity at location i, expressed in metres per second;

is the flowing bulk density, in kilograms per cubic metre (kg/m

)

;

m,a,i

is the linear velocity at location i, expressed in kilograms per square metre per second;

i equals 1 for an upstream location, 2 for a downstream location and 3 for a branch location; see

Figures F.9 and F.10.

Velocity head, H

v,i

at location i, expressed in inches of water column (in H

O), and the corresponding pressure-

drop values for the flow-through manifold branch and run connections can be calculated in USC units as given in

Equations (F.20) and F.21):

(2,989 10 )

−

=× ⋅

(F.20)

v, m,a,

(2,989 10 ) /

−

=× (F.21)

where

is the linear velocity at location i, expressed in feet per second;

is the flowing bulk density, expressed in pounds-mass per cubic foot;

m,a,i

is the linear velocity at location i, expressed in pounds per square foot per second;

i equals 1 for an upstream location, 2 for a downstream location and 3 for a branch location; see

Figures F.9 and F.10.

Upon obtaining the velocity-head figures at the necessary locations, the run- or branch-connection pressure drop

can then be calculated, respectively, with Equations (F.22) and (F.23).

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