Flow of Water in Circular Pipes from 3⁄4% inch to 12 inches Diameter. Based on D'Arcy's formula for clean cast-iron pipes. Q = ac √r Vs. .00403 .00914 .02855 .06334 .11659 114 .19115 11% .28936 13 2 00028 Quantity in cubic feet per second. .00127 .00090 .00064 .00052 .00045.00040 .00033] .00289 .00204 .00145 .00118 .00102 .00091 .00075 .00065 00903 .00638 .00451 .00369 .00319 .00286 00233 .00202 .02003 .01416 .01001 .00818 .00708 .00633 .00517 .00448 03687 .02607 .01843 .01505 .01303 .01166 .00952 .00824 .06044 .04274 .03022 .02468 .02137 .01912 .01561 .01352 .09140 .06470 .04575 .03736 .03235 .02894 .02363 .02046 .13077 .09247 .06539 .05339 .04624 .04136 .03377 .02927 .23647.16722 .11824 .09655 .08361 .07479 .06106 .05288 .38225 .27031 .19113 .15607 .13515 .12089 .09871 .08548 .81042 .57309 .40521 .33088 28654 .25630.20927 .18123 1.4422 1.0198 .72109 .58882 .50992 .45610 .37241 .32251 2.3104 1.6338 1.1552 .94331 .81690 .73068 .59660 .51666 3.4314 2.4265 1.7157 1.4110 1.2132 1.0852 .88607 .76734 4.8284 3.4143 2.4141 1.9713 1.7072 1.5270 1.2468 1.0797 6.5302 4.6178 3.2651 2.6662 2.3089 2.0652 1.6862 1.4603 8.5222 6.0265 4.2611 3.4795 3.0132 2.6952 2.2006 1.9058 11 10.886 7.6981 5.4431 4.4447 3.8491 3.4428 2.8110 2 4344 12 13.571 9.5965 6.7853 5.5407 4.7982 4.2918 3.5043 3.0347 .41357 .74786 212 1.2089 3 2.5630 4 4.5610 5 7.3068 6 .00403 .00914 .02855 .06334 .41357 2 .74786 21% 1.2089 3 2.5630 00025 .00023 00022 00020 .00019 .00018 .00017 .00016 .00058 .00053 .00049 .00046 .00043 .00041 .00039 .00037 .00181 .00165 .00153 .00143 .00134 .00128 .00122 .00117 .00400 .00366 .00339 .00317 .00298 .00283 .00270 .00259 .11659 114 .00737 .00673) .00623 .00583 .00549 .00521 .00497 .00476 .19115 11% .01209 .01104 .01022 .00956 .00901 .00855 .00815 .00780 .28936 134 .01830 .01671 .01547.01447 .01363 .01294 .01234 .01181 .02615 .02388 .02211 .02068 .01948 .01849 .01763 .01688 .04730 .04318 .03997 .03739 .03523 .03344 .03189 .03053 .07645 .06980 .06462 .06045 .05695 .05406 .05155 .04935 .16208 .14799 .13699 .12815 .12074 .11461 .10929 .10463 .28843 .26335 .24379 .22805 .21487 .20397 .19448 .19620 .46208 .42189 .39055 .36534 .34422 .32676 .31156 .29830 .68628 .62660 .58005 .54260 .51124 .48530 .46273 .44303 .96567 .88158 .81617 .76350 .71936 .68286 .65111 .62340 1.3060 1.1924 1.1038 1.0326 .97292 .92356 .88060 .84310 1.7044 1.5562 1.4405 1.3476 1.2697 1.2053 1.1492 1.1003 2.1772 1.9878 1.8402 1.7214 1.6219 1.5396 1.4680 1.4055 2.7141 2.4781 2.2940 2.1459 2.0219 1.9193 1.8300 1.7521 4.5610 5 7.3068 6 10.852 15.270 8 Value of √s= .06324 05774 .05345 .05 .04711 .04472 .04264 .04082 For U. S. gals. per sec., multiply the figures in the table by....... 7.4805 For any other slope the flow is proportional to the square root of the slope; thus, flow in slope of 1 in 100 is double that in slope of 1 in 400. Flow of Water in Pipes from % Inch to 12 Inches Diameter for a Uniform Velocity of 100 Ft. per Min. Given the diameter of a pipe, to find the quantity in gallons it will deliver, the velocity of flow being 100 ft. per minute. Square the diameter in inches and multiply by 4.08. If Q = quantity in gallons per minute and d diameter in inches, then Q= = 4.08d. 100 For any other velocity. V', in feet per minute, Q': = 4.082 = .0408da V'. Given diameter of pipe in inches and velocity in feet per second, to find discharge in cubic feet and in gallons per minute. d2 X.7854 X v X 60 Q' = = 0.32725d2v cubic feet per minute. 144 =.32725 7,4805 or 2.448d2v U. S. gallons per minute. To find the capacity of a pipe or cylinder in gallons, multiply the square of the diameter in inches by the length in inches and by .0034. Or multiply the square of the diameter in inches by the length in feet and by .0408. The loss of head due to friction when water, steam, air, or gas of any kind flows through a straight tube is represented by the formula in which the length and d = the diameter of the tube, both in feet; v = velocity in feet per second, and ƒ is a coefficient to be determined by experiment. According to Weisbach, f= .00644, in which case which is one of the older formulæ for flow of water (Downing's). Prof. Unwin says that the value of f is possibly too small for tubes of small bore, and he would put f = .006 to .01 for 4-inch tubes, and ƒ = .0084 to .012 for 2inch tubes. Another formula by Weisbach is From the general equation for velocity of flow of water v = c √r Vs, = for round pipes CA we have v2 = and h = 41v2 in which c is the coefficient c of D'Arcy's, Bazin's, Kutter's, or other formula, as found by experiment. Since this coefficient varies with the condition of the inner surface of the tube, as well as with the velocity, it is to be expected that values of the loss of head given by different writers will vary as much as those of quantity of flow. Two tables for loss of head per 100 ft. in length in pipes of different diameters with different velocities are given below. The first is given by Clark, based on Ellis' and Howland's experiments; the second is from the Pelton Water-wheel Co.'s catalogue, authority not stated. The loss of head as given in these two tables for any given diameter and velocity differs considerably. Either table should be used with caution and the results compared with the quantity of flow for the given diameter and head as given in the tables of flow based on Kutter's and D'Arcy's formulæ. Relative Loss of Head by Friction for each 100 Feet Length of Clean Cast-iron Pipe. (Based on Ellis and Howland's experiments.) Feet Feet Feet Feet Feet Feet | Feet Feet Feet Feet of of of of of of of of of of Head Head Head Head Head Head Head Head Head Head Feet 2 .97 .55 .41 32 .27 .23 .19 .18 15 .12 .095 .075 33 36 15 | 18 | 21 | 24 | 2 | 80| 3 |「 86 「 40 「 4 48 .147 .117 .109 .065 055 .052 .049 .047 .036 .030 .088 .085 .076 .067 .056 .046 Loss of Head in Pipe by Friction.-Loss of head by friction in each 100 feet in length of different diameters of pipe when discharging the following quantities of water per minute (Pelton Water-wheel Co.): 1 Inside Diameter of Pipe in Inches. 2 8 5 6 Flow of Water in Riveted Steel Pipes. The laps and rivets tend to decrease the carrying capacity of the pipe. See paper on "New Formulas for Calculating the Flow of Water in Pipes and Channels," by W. E. Foss, Jour. Assoc. Eng. Soc., xiii, 295. Also Clemens Herschel's book on "115 Experiments on the Carrying Capacity of Large Riveted Metal Conduits," John Wiley & Sons, 1897. |