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CHAPTER 76
1962 Guide And Data Boole ^1 "
The sensible beat, q,, to raise the temperature of the snow to 32 F is
q, - 2.6 (32 - O
(3)
when
t rate of snowfall, inches of water equivalent per hour, t, *= air temperature, Fahrenheit.
The heat of fusion, qm , to melt the snow is
. - 746s
(4)
The heat of evaporation, q,, (mass transfer) is q. = hf/flJOZaio + 0.055)(0.185 - p,,)
where
(5)
h/, = heat of evaporation at the film temperature, Btu per pound.
w " wind speed, miles per hour. " vapor pressure of moist air, inches of mercury.
The heat transfer, 9ft , (convection and radiation) is
F - Depth of Finish Cost--Assumed ss X in. tf eunaete. Finish Cast b ssphsit but then com Aib should be reduced tram S in..Depth .Uk should mhnyi keep therms! resistance equsl to S in. af concrete.
8 - Depth required by structure! design (should be s mininmm dt ^
Fig. 1 .... Detail of Snow Melting Panel
9ft - U.4(0.0201p + 0.055)(</ - L)
(6)
where 1/ " water film temperature, Fahrenheit. (Usually taken as 33 F.)
In addHion to determining the four heating requirements,
it is necessary to make allowance for back and edge losses.
These losses vary from 30 to 50 percent, depending upon the
slab construction and fluid temperature.
The equation for the required fluid temperature to provide
an output 9 has been derived in Reference 2. For construc
tion
to Fig. 1, the equation is
t_ - 0.59. + t,
(7)
where tm --
fluid temperature (antifreeze solution), Fahrenheit.
Equation 7 will apply to 1 in. as well as in. IPS pipe-- see fig. 1.
Equations 2 to 7 permit the designer to determine the heating requirement of a snow-melting system. The solutions of these equations, however, require the simullaneous con sideration of the four climatic factors: (1) wind speed, (2) air temperature, (3) relative humidity, and (4) rate of snowfall. It is not satisfactory to use annual averages or maximums for the climatic factors. If averages or maximums are used there is no assurance that they will ever occur simultaneously. It is necessary, therefore, to make a frequency analysis of the solutions to Equation 2 for all the occurrences of snowfall for a period of several years. Such an analysis for 33 cities appears in Table 1 which contains the operating information for a snow-melting system. For freezing temperatures (32 F and bdow) without snowfall the system may be idling which means that some heat is supplied to the slab so that there will be immediate melting when snow starts to faD. Column 4 of Table 1 gives the average temperature during freezing periods. This temperature is used in calculating the idling load. The other term needed to calculate idling load is the wind speed during the period of freezing temperatures.
The column, Hours of Snowfall, indicates the number of hours that snow b falling at. rates equal to.or greater than 0.01 in. of water equivalent per hour. There are snowfalls of
trace quantities about twice as often as there are for measur- able quantities of 0.01 in. or more. It b assumed that these light falls can be handled by the idling load.
The remaining columns of Table 1 represent the frequency distribution of required heat output. This distribution is' based on the solution to the baric equation for two values of the free area ratio, A^ This distribution represents the basis of the analysis and b also the basis for Tables 2 and 3.
For specific conditions, or for cities other than those given in Table 1, the designer will have to use Equations 2 and 7. Solutions to these equations are given in Table 4 for relative humidities of 80 percent. For other values of relative humid ity, Equations 8 and 9 can be used to determine the correc tions.
^SL. - - X,(0.0201. + 0.055),, dp~
(8)
Op., - --2 (0.0201. + 0.085)8/*
()
It will be necessary for the designer to determine values for
the appropriate climatic variables before solving Equation 2. Probably the best procedure b to contact the local weather
bureau office and examine the Local Climatological Summary. An approximation can be made by using Tahle 5 for values
- of , and solutions for Equation 2 taken from Table 4, with
the following qualifications:
1. When A-ggning a Class I system use: Ar " 1.0, f, = 30 F, and p = IS mph
2. When designing a Class II system use: Ar = 1.0, ! 20 F, and v -- 15 mph
3. When designing a Class III system use: A, -- 1.0,1, a 0 F, and v 15 mph
Snow-melting installations are classified in Table 2 ac cording to types as Class I, II, or III. These classes have been dtarnssad thoroughly in Reference 3, and are defined in the footnotes to Table 2. Briefly, snow-melting systems art classified as to the urgency for melting as follows:
Class I (minimum): Residential walks or driveways and inteiplant areaways.
Class II (moderate): Commercial (stores and offices) side walks and driveways, and steps of hospitals.
?Snow Melting
Class ni (maximum): Toll plazas of highways and bridges, and aprons and loading areas of airports.
classifications depend upon the allowable rate of
gnow melting. For example, a residential system does not
^ve to melt snow as rapidly as a commercial system. In
fact, a depth of snow of an inch for an hour or so during a
Heavy storm might not be objectionable with a residential
^stem. On the other hand, a store manager would consider
gg system inadequate if half an inch of snow accumulated
on the sidewalk in front of the store. The difference, then,
between a Class I system and a Class II system b in the
jequiied ability of each system to melt snow. The one feature
b yirnmnn to all
b that the systems must be
adequate for some combination of weather factors. The
^gner may select equipment having capacity to melt show
trhenever conditions are milder than some critical values, but
be willing to have an inadequate system for a given fraction
of the time. In other words, the designer will take a calculated
risk providing he knows the odds of that risk. For a residential
system, where initial cost must be at a minimum, the designer
must accept more frequent snow accumulations.
Table 2 contains the design beat requirements for the 3
rliLgwi of snow-melting systems. Under Class I systems, the
values in parentheses are idling rates and, since they exceed
the Gass I design rates, should be taken as design output for
this classification. Design rates may be altered by the de
signer if he feels that a particular job should have different
design criteria from those given in the footnotes of Table 2.
Any change in design conditions used should be based on the
frequency distribution given in Table 1.
Use of Tables 1, 2 and 3 b illustrated by Example 1.
'. Example l: An engineer has been retained to design snow-
melting systems for the service areas of a turnpike running from the eastern edge of the Wisconsin-Illinois border north west to the Wiseonsw-Mizmesota border just east of St. Paul.
He decides that Chicago data will be adequate for the southern terminus and that Minneapoiis-St. Paul data will be adequate
for the northern terminus. His problem is to determine the heat and hydraulic requirements of the systems for service
areas between Chicago and St. Paul.
Solution: Assume, for this example, that the city in question is Madison, Wis. Weather bureau records indicate that the annual average number of days with snow cover of an inch or more would be 100, and that the engineer can assume an aver age snowfall of 40 inches. In addition, he can estimate about 11 days per year with a snowfall of an inch or more (see Refer ence 3).
For the walkways to the restaurant from the parking area a Gaia .I design rate could be used. This rate could be taken as 90 Btuh per sq ft. Thu is in good agreement with data in Tables 2 and 3, which give the rate at 89 (design rate) for Chicago and 95 (idling rate) for Minneapolis.
The lanes k--dir>g from the turnpike to the gasoline pumps and parking areas should be rated as Class II areas. A check of Tables 1 and 2 would indicate that 160 Btuh per sq ft would
be adequate.
If an emergency area were included, for a wrecking truck, ambulance, or police garage, it would be wise to consider a Class III rate for such areas. An inspection of Table 1 for Chicago shows that a rate of 275 Btuh per sq ft would be ade quate for A, -- 1 for 99.4 percent of the time. Similarly, 275 would be adequate 99.4 percent of the time in St. Paul. There fore, 275 Btuh per sq ft seems sufficient for the emergency *reaa. Table 2 in Gass III column lists 350 Btub per sq ft for Chicago and 254 for St. Paul but for uses similar to the areas u> this example, 275 should be adequate.
Hydraulic Requirement
After determining the bating requirements, it is necessary to determine the hydraulic requirements of the system. This
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Table 2 .... Design Data for Three Gasses of Snow-Melfing System*
cay
Albuquerque, N. M. Amarillo, Tex. Boston, Mass. Buffalo-Niagara Falls, N. T. Burlington, Vt.
Dwffen Ou^xrf, fife p*r (Hr) (Sq R)
Qcra 1 xyxtem1
Oats fl Oats ED tyttets1 lyrten*
7! 82 167 98 143 241 107 231 255 80 192 307 90 142 244
Caribou-limestone, Me. Cheyenne, Wyo. Chicago, HI. Colorado Springs, Colo. Columbus, Ohio
Detroit, Mich. Duluth, Minn. Falmouth, Mass. Great Falls, Mont. Hartford, Conn.
Lincoln, Neb. Memphis, Term. Minneapoiis-St. Paul, Minn. Mt. Home, Idaho New York, N. Y.
Ogden, Utah Oklahoma City, Qkla. Philadelphia, Pa. Pittsburgh, Pa. Portland, Ore.
Rapid City, S. D. Reno, Nev. St. Louis, Mo. Salina, Kan. Sault Ste. Marie, Mich.
Seattle-Tacoma, Wash. Spokane, Wash. Washington, D. C.
89 (93) 83 89 49 (63) 52
138 129 165 63 72
69 S3 (114) 93 84 (112) 115
140 206 144 138 254
64 (67) 134
63 (95) SO 121
202 144 155 90 298
98 66 97
89 v 86
216 81 229 157 97
58 (86) 98 122 85 52 (78)
102 154 152 120 144
92 12S 87 127 117 121
307 425 350 293 253
255 374 165 372 260
246 212 254 140 342
217 350 263 275 111
447 155 198 228 213
133 189 144
From Air Conditioning, Beating and Ventilating, August 1957, p. 92.
Where idling rate is greater than Class I design rate, idling rate is given in parentheses and should be used as Class I design output.
1 For Clese I (residential) Systems, the design output b eet st that required best mitput (see Tsble !) when At -- 0 st the 98th percentile at tbs hequouu distribution; tbst is where S8% of the boure base this output cr less.
* For Clsm II (fxxmmetmsl) Systems, tbs doexa output is tbs maximum out put when Ar ~ 0 in Tsble 1 (last column).
1 For Class HI (industrial) Systems the
output is iiirnni< byJbe-
EoHowing (our requirements: (1) Output Is never exceeded (or two rnneririitiTn
boon; (3) Output (or A, = 1. Tsble I, is st least 1 Btu per hour per sq (t greater
thaa maximum output (or A, -- 0; (1} Ar b greater than or equal to 04 maxi
mum requirement shown in Table 1 (or A, -- 1. That b,g -- , + +04
Ifc + Ok) lor the onftditinos where ), + + m +
maximum; (4)
The free ares ratio A, b unity lor st least 08% rf the boon listed in Table I.