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632 CHAPTER 23 .1958 Guide i complete discussion of free area ratio and its effect on system performance, see Reference 14. The equations: for the heating requirements of a snow-melting system have been derived and thoroughly explained, in-Reference 15. The general equation for slab output, 3o, is " -' 9o = 9 + im + Ka (? + ?h) . . ' (15) where q, = sensible heat transferred to snow, Btu per (hour) (square foot). qm = heat of fusion, Btu per (hour) (square foot). . liA -- ratio of snow-free area to total area, dimensionless. 9. = heat of vaporization, Btu per (hour) (square foot). 9h = heat transfer by convection and radiation, Btu per (hour) (square foot). The sensible heat, to raise the.; temperature of the snow.to 32 F is where ' 9. = 2.6s (32 - !,,) ... - (16) s = rate of snowfall, see Table 5; inches of water equivalent per hour. ( = air temperature, Fahrenheit. The heat of fusion, qm, to melt the snow, is 9m = 746s The heat of vaporization, qe, (mass transfer) is (17) g,, = 1074(0.0201s + 0.055)(0.185 - p,,)ftA (18) where p,v = vapor pressure of moist air, inches of mercury. The heat transfer, qi,, (convection and radiation) is r 9,, = 11.4(0.0201c +. 0.055)(if - 1,,)Ba (19) where v = wind velocity, miles per hour. ([ = water film temperature, Fahrenheit. . , In addition 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. iv' The equation for the required fluid temperature to provide an output qi has been derived in Reference 15. For construction similar to Fig. 19; the equation is . where = 0.59o + (i ... ia = mean fluid temperature (antifreeze solution), Fahrenheit. (20)^5; . r< : Equation 20 will suffice for 1 in. IPS as well as % in. -- see Fig. 19. Values for s for certain cities are given in Table 5. Using the values;--,; for s given in Table. 5, the appropriate values for ta and v, the values fof>^-_. ?o may be found in Table 6. In preparing Table 6, only values of pav f relative humidities of 80 percent were; used. The variation in q,, and trafc j Panel Heating 633 Table 5. Snowfall DatX ^or Various Cities* City Coll Number or Readings with Maximum Temperature in OtHoub- Period below Freezing at Various Snowfall Rates Snowfall Rate in Equivalent inches of Water per Six Hours. Total Readings .Taken .Assumed . Design, Rate op Snowfall11 0.00 to 0.24 0.25 to 0.49 0.50 to 0.74 0.75 to 0.99 s Col. 2 Col. 3 Col. 4 Col.5' Col. 6 Col. 7 Albany, N. Y......... .............. ........ ......... Asheville; .N. C....`......................'............ Billings, Mont................................. ........ .2052 463 1640: Boise, Idaho...................................... ...... . rioo Buffalo, N.`Y................................. ........ Burlington, Vt.......................................... Caribou, Maine......................................... Chicago, III........................................ 1323 1871 2390 1363 1498 Cincinnati, Ohio.................. Cleveland, Ohio............ Columbus, Ohio............ Denver. Col.............................. Detroit. Mich.......... 1045 1569 1351 1207 .1830 Evansville. Ind........ Hartford, Onnn. , . Kansas City, Mo....... Madison. Wise......... Minneapolis. Minn. Oklahoma City, Okla. Omaha. Neb............ Philadelphia, Pa. Pittsburgh, Pa.. Portland. Maine. St. Louis, Mo.!.......... Salt Lake City. Utah Spokane, Wash............ Washington. D. C. New York, N. Y*................ . 916 1514 1189 2370 2703 613 1795 891 1365 2054 1088 1482 .1545 533 29 5 4 3 - Ill :-23 . .9 .19 3 3 2 4 4 5 .. 5 44 12 .5 7 *8 8' 10 6 33 5 5 11 . 7 5 1 3720 0.16 1 0 3538 0.08 0 .0 . 3532 0.08 . .0 . 0i 4 - - - 2 ; 1 3.-. 1 . 0 0. 'i 0 01 3720 , , 0.08 ;. 3720:' 3720 3720. , 1672 2976 0.16 0.16 : 0.08 . o.ie 0.03 0 0 1 0\ 2;r 0 0 0 6- .0 3720 3720 3720 3720 3720 0.08 0.08 0.08 0.08 0.08 1. . 1 93 21 20 00 3720 3720 3720 3720 3720 0.08 0.25 0.16 0.08 0.08 4 0 3720 * 0.16 1 0 3720 0.16 2 1 3720 0.16 2 0' 3720' 0.08 4 1 3720 0.16 0^ 1 3720 : 0.08 ' 0 0 . 3720, ,0.08. / 1 0 * 3720 ; 0.16 2 1 3348 6.18 0.16 * US. Weather Bureau. - Based on readings taken 1:30a.m., 7:30a.m., 1:30 p.m., and 7:30 p.m. il0j^m,ber 15 *o February 15 from 1940 to 1949. (Where the total readings are less than 3720 the 4 and ss/fS0TM 13 8 t^an ^ years.) The difference between Col. 6 and the sum of readings in Cols. 2; 3, ' b 13 number of readings with a maximum temperature (in the 6-hr period) above freezing, coinis found as follows: Proceed to left (on line from any city) from Column 5 until the column mng tenth reading is found. Assume that the larger value in the beading of the selected Period. TK* averaQe maximum value, and should be multiplied by 2 to obtain the maximum rate for a 6-hour laraer ***um rate divided by 6 is the design rate per hour. This is equivalent to dividing the ""aw value in the heading of tL 1 x ' -* ** * Ne Y iuvuw jaw uuui ivuuu, as uswu ui uwuum * DaraKU City record was not used in this tabulation since the records for that station were not com- with those of the other stations. ml kunudities of 75, 80, 85 and 90 percent are given in Reference 14, and y be calculated by solving Equations 21 and 22.: = -537 (0.0201!) + 0.055) A, dp,, (21)