of Arthur Pennell, of Kansas City. The general plan adopted is to first dis. solve the chemicals in a closed tank, and then connect this to the supply main so that its contents will be forced into the main tank, the supply-pipe being so arranged that thorough mixture of the solution with the water is obtained. A waste-pipe from the bottom of the tank is opened from time to time to draw off the precipitate. The pipe leading to the tender is arranged to draw the water from near the surface. A water-tank 24 feet in diameter and 16 feet high will contain about 46,600 gallons of water. About three hours should be allowed for this amount of water to pass through the tank to insure thorough precipitation, giving a permissible consumption of about 15,000 gallons per hour. Should more than this be required, auxiliary settling-tanks should be provided. The chemicals added to precipitate the scale-forming impurities are sodium carbonate and quicklime, varying in proportions according to the relative proportions of sulphates and carbonates in the water to be treated. Sufficient sodium carbonate is added to produce just enough sodium sulphate to combine with the remaining lime and magnesia sulphate and produce glauberite or its corresponding magnesia salt, thereby to get rid of the sodium sulphate, which produces foaming, if allowed to accumulate. For a description of a purifying plant established by the Southern Pacific R. R. Co. at Port Los Angeles, Cal.. see a paper by Howard Stillmann in Trans. A. S. M. E., vol. xix, Dec. 1897. HYDRAULICS-FLOW OF WATER. Formulæ for Discharge of Water though Orifices and Weirs. For rectangular or circular orifices, with the head measured from centre of the orifice to the surface of the still water in the feeding reservoir. Q = = C √2gH Y. a. (1) For weirs with no allowance for increased head due to velocity of approach: Q = = C% V2gHX LH, (2) For rectangular and circular or other shaped vertical or inclined orifices; formula based on the proposition that each successive horizontal layer of water passing through the orifice has a velocity due to its respective head: Q = cL% √2g X (WH3 - WHt3). (3) Q = quantity of water discharged in cubic feet per second; C = approximate coefficient for formulas (1) and (2); c = correct coefficient for (3) and (4). Values of the coefficients c and Care given below. g= 32.16; 1/2g= 8.02; H= head in feet measured from centre of orifice to level of still water; Ho head measured from bottom of orifice; Ht = head measured from top of orifice; h = H, corrected for velocity of ap4 Va2 proach, Va, = H+ -; a = area in square feet; L = length in feet. 32g Flow of Water from Orifices.-The theoretical velocity of water flowing from an orifice is the same as the velocity of a falling body which has fallen from a height equal to the head of water, = W2gH. The actual velocity at the smaller section of the vena contracta is substantially the same as the theoretical, but the velocity at the plane of the orifice is CV2gH, in which the coefficient C has the nearly constant value of .62. The smallest diameter of the vena contracta is therefore about .79 of that of the orifice. If C be the approximate coefficient = .62, and c the correct coeffi cient, the ratio varies with different ratios of the head to the diameter с For vertical rectangular orifices of ratio of head to width W: For = .5 .6 .8 1 1.5 2. 3. 4. 5. 8. W C с = .9428 .9657 .9823 .9890 .9953 .9974 .9988 .9993 .9996 9998 For HD or H÷W over 8, C = c, practically. Weisbach gives the following values of c for circular orifices in a thin wall. H measured head from centre of orifice. For an orifice of D = .033 ft. and a well-rounded mouthpiece, H being the effective head in feet, Hamilton Smith, Jr., found that for great heads, 312 ft. to 336 ft., with con. verging mouthpieces, c has a value of about one, and for small circular orifices in thin plates, with full contraction, c = about .60. Some of Mr. Smith's experimental values of c for orifices in thin plates discharging into air are as follows. All dimensions in feet. Circular, in steel, D = Circular, in brass, D = .100, Circular, in iron, D == .100, C = 3.19 .6298 .6264 .536 1.74 .6265 2.73 3.57 4.63 .6113 .6070 .6060 .6051 .457 2.05 3.18 .6155 .6041 Square, in brass, .05 .05, H = .313 C.6410 .6157 .6127 .6113 .6097 1.71 2.75 3.74 4.59 .6084 .6076 .6060 .6065 1.82 2.83 3.75 4.70 .6203 .6180 .6176 6168 For the rectangular orifice, L, the length, is horizontal. Mr. Smith, as the result of the collation of much experimental data of others as well as his own, gives tables of the value of c for vertical orifices, with full contraction, with a free discharge into the air, with the inner face of the plate, in which the orifice is pierced, plane, and with sharp inner corners, so that the escaping vein only touches these inner edges. These tables are abridged below. The coefficient c is to be used in the formulæ (3) and (4) above. For formulæ (1) and (2) use the coefficient C found from the C C values of the ratios above. 3.70 4.63 .6238 .939 .6139 .917 C = .6476 .6280 Values of Coefficient c for Vertical Orifices with Sharp Edges, Full Contraction, and Free Discharge into Air. (Hamilton Smith, Jr.) Square Orifices. Length of the Side of the Square, in feet. .03 .04 .05 .07 .10 .12 .15 .20 .40 .60 .80 1.0 .6 1.0 3.0 6.0 10. 20. 100.(?) .660 .645 .636 .630 .623 .617 .613 .610 .605 .601 .598 .596 .605 .603 .601 .600 .599 .605 .605 .6041 .603 603 .605 .604 .604 .603 .602 .602 598 .15 .20 .40 .60 .637 .628 .618 .612 .606 .6 .655 .640 .630.624 .618 .613 .609 .605 .601 .596 .593 .590 1.0 .644 .631 .623 .617 .612 .608 .605 .603 .600 .598 .595 .593 .591 .632 .621 .614 .610 .607 .601 .601 .600 .599 .599 .597 .596 .595 .623 .614 .609 .605 603 .602 .600 .599 .599 .598 .597 .597 .596 .618 .611 .607 .604 .602 .600 .599 .599 .598 .598 .597 .596 .596 .611 .606 .603 .601 .599 .598 .598 .597 .597 .597 .596 .596 .595 .601 .600 .599 .598 .597 .596 .596 .596 .596 .596 .596 .595 .594 50.(?) .596 .596 .595 .595 .594 .594 .594 .594 .594 .594 .594 .593 .593 100.(?) .593 .593' 592 .592 .592 .592 .592.592 .592 .592 .592 .592 .592 2. 4. 6. 10. 20. HYDRAULIC FORMULE.-FLOW OF WATER IN OPEN AND CLOSED CHANNELS. Flow of Water in Pipes.-The quantity of water discharged through a pipe depends on the "head;" that is, the vertical distance be tween the level surface of still water in the chamber at the entrance end of the pipe and the level of the centre of the discharge end of the pipe; also upon the length of the pipe, upon the character of its interior surface as to smoothness, and upon the number and sharpness of the bends: but it is independent of the position of the pipe, as horizontal, or inclined upwards or downwards. The head, instead of being an actual distance between levels, may be caused by pressure, as by a pump, in which case the head is calculated as a vertical distance corresponding to the pressure 1 lb. per sq. in. = 2.309 ft. head, or 1 ft. head = .433 lb. per sq. in. = The total head operating to cause flow is divided into three parts: 1. The velocity-head, which is the height through which a body must fall in vacuo to acquire the velocity with which the water flows into the pipe = v2÷2g, in which v is the velocity in ft. per sec. and 2g 64.32; 2. the entry-head, that required to overcome the resistance to entrance to the pipe. With sharpedged entrance the entry-head about the velocity-head; with smooth rounded entrance the entry-head is inappreciable; 3. the friction-head, due to the frictional resistance to flow within the pipe. In ordinary cases of pipes of considerable length the sum of the entry and velocity heads required scarcely exceeds 1 foot. In the case of long pipes with low heads the sum of the velocity and entry heads is generally so small that it may be neglected. General Formula for Flow of Water in Pipes or Conduits. Meau velocity in ft. per sec. mean hydraulic radius X slope diameter c Do. for pipes running full = c1 -X slope, in which c is a coefficient determined by experiment. (See pages 559-564.) The mean hydraulic radius = area of wet cross-section In pipes running full, or exactly half full, and in semicircular open chan nels running full it is equal to 4 diameter. The slope = the head (or pressure expressed as a head, in feet) length of pipe measured in a straight line from end to end. In open channels the slope is the actual slope of the surface, or its fall per unit of length, or the sine of the angle of the slope with the horizon. Chezy's Formula: v = c =cVTVs = cvrs; r = mean hydraulic radius, S= slope head length, v = velocity in feet per second, all dimensions in feet. с Quantity of Water Discharged. -If Q = discharge in cubic feet per second and a = area of channel, Q = av = ac Vrs. a Vr is approximately proportional to the discharge. It is a maximum at 308°, corresponding to 19/20 of the diameter, and the flow of a conduit 19/20 full is about 5 per cent greater than that of one completely filled. Table giving Fall in Feet per Mile, the Distance on Slope corresponding to a Fall of 1 Ft., and also the Values of s and Vs for Use in the Formula v = c √rs. Values of √r for Circular Pipes, Sewers, and Conduits of different Diameters. .088 .125 .161 .177 *191 .204 .228 .251 .290 2 - ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ CO CO CO 20 20 20 20 20 20 20 20 20 20 20 19 area = 14 diam. for circular pipes run. perimeter Diam., 1.061 9 1.500 1.070 9 3 1.521 1.080 9 6 1.541 .750 4 9 1.089 9 1.561 Values of the Coefficient c. (Chiefly condensed from P. J. Flynn on Flow of Water.)-Almost all the old hydraulic formulæ for finding the mean velocity in open and closed channels have constant coefficients, and are therefore correct for only a small range of channels. They have often been found to give incorrect results with disastrous effects. Ganguillet and Kutter thoroughly investigated the American, French, and other experiments, and they gave as the result of their labors the formula now generally known as Kutter's formula. There are so many varying conditions affecting the flow of water, that all hydraulic formulæ are only approximations to the correct result. When the surface-slope measurement is good, Kutter's formula will give results seldom exceeding 7% error, provided the rugosity coefficient of the formula is known for the site. For small open channels D'Arcy's and Bazin's formulæ, and for cast-iron pipes D'Arcy's formulæ, are generally accepted as being approximately correct. Kutter's Formula for measures in feet is in which v = mean velocity in feet per second; r = X |