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714 CHAPTER 32 For uninsulated non-meta!lic ducts,
/ 1953 Guide
V= 1 x
J_
/i + k + 7.
(21)
where
U = overall coefficient of heat transfer, Btu per (hour) (square foot) (Fahren heit degree).
J\ -- surface conductance (inside) Btu per (hour) (square foot) (Fahrenheit degree).
/<> = surface conductance (outside) Btu per (hour) (square foot) (Fahrenheit degree).
x = thickness, inches.
k = unit conductivity of material, Btu per (hour) (square foot) (Fahrenheit degree per inch thickness).
Table 11.. Weights and Thicknesses . of Standard Copper Sheets* Rolled lo Weight
Weight per Square Foot
Thickness. Inches
- Ounces
10 12 14 16 18 20 24 28 32 36 40 44 48. 66 64
Pounds
0.626 0.750 0.875 1.000 1.125 1.250 1.500 1.750 2.000 2.250 2.500 2.750 3.000 3.500 4.000
Decimal Equivalent
0.0135 0.0162 0.0189 0.0216 0.0243 0.0270 0.0324 0.0378 0.0432 0.0486 0.0540 0.0594 0.0648 0.0756 0.0864
Nearest. Fraction
Ut % % %
xAx % 4 Mt '%
'/ % % %
'`Variations from these weights must be expected in practice.
Nearest Gage No.
B. & S.
27 26 25 23 22 21 20 19 .17 * 16
15, 15 14 13
11
.
Stubs ` ' U. S. Sto.
29 27
26 24
23 22
21 20
19
18 17 17
; 16 15
14
.
29
28 26
25 24
23 22
20 19
18 ' 17
17
16 14 . 13 '
Where x is small and k is large, however, the factor ~ is of little impor tance and may be neglected.
Film conductance /i for air flowing in ducts apparently depends only on the velocity of the air and the diameter of the duct. A fairly reliable inside coefficient can be calculated from Schultz's modified equation:
0.32 8 /i =
(22)
where
v -- velocity of air in duct, feet per second. D = inside diameter of duct, feet.
Film conductance fo depends on a number of variables including tem perature, diameter, and emissivity of the outer surface, and can be calcu lated from data in Chapter 5. From this explanation, it is seen that it is unwise to recommend a given value of U for all uninsulated metal ducts.
AirDuct.Design
715
'The heatloss from a given length of duct can be expressed by:, ' -s-r-rl
<2. = UPl
' : "i (23)
where ~
<2 = heat loss through duct walls, Btu per hour. P = perimeter of duct, feet. 2 = length of duct, feet. ti .= temperature of air entering duct, Fahrenheit degrees. 2j = temperature of air leaving duct, Fahrenheit degrees. t, = temperature of air surrounding duct, Fahrenheit degrees.
The heat given up by,the air in the duct is:
. Q, = O.iiwit, - tt) = 14.4A7mPv(2, -- (:)
'' '
(24)
where
w = weight of air through duct, pounds per hour. A = cross-sectional area of duct, square feet. F,, = mean velocity of fluid, feet per minute. pv = density of air at specified temperature at which velocity Vm, is measured
pounds per cubic foot.
Equating (23) and (24):
2i -}- ti -- 2li ti tt
28.8.4 Vinpv TJ PI
Let y = ^
fr rectangular ducts, and
jpor roun(j ducts
and solve for U and t?:
lily + 1) - 2ti 2i = ------;----------r------
Ay - l)
,,,r, (25)
. h(y - 1) +22,
U = -----
-----
(y + l)
;oj^ (26)
For low velocities and long ducts of small cross-section, a somewhat more accurate formula may be used as follows:
ti = ---- + t,
(27)
where
UPL Z 14.4ApvFm'
e = Naperian base of logarithms = 2.718.
In using Equations 25, 26, and 27, one of the duct air temperatures will be unknown and will be obtained by substitution of the other known or assumed values.
Heat loss coefficients for insulated ducts with various conductivities are given in Fig. 16. The conductivities of various materials, which are based on mean temperatures, ranging from about 70 to 90 F, will be found in Table 2 of Chapter 9. For cases where the mean temperature is other