it, and escaping parallel to the plate, equals twice the product of the area of the jet into the pressure calculated from the "head due to the velocity," and for this case H = 2 × · V2 2 g V2 instead of 2 g but as found in White's experiments the maximum pressure at the point on the plate exactly opposite the jet corresponds to h = V2 2 g Experiments made with four different shapes of nozzles placed under the center of a falling stream of water showed that the pressure produced was capable of sustaining a column of water almost exactly equal to the height of the falling water. Tests by J. A. Knesche (Indust. Eng'g, Nov., 1909), in which a Pitot tube was inserted in a 4-inch water pipe, gave C = about 0.77 for velocities of 2.5 to 8 feet per second, and smaller values for lower velocities. He holds that the coefficient of a tube should be determined by experiment before its readings can be considered accurate. Maximum and Mean Velocities in Pipes. Williams, Hubbell and Fenkel (Trans. A. S. C. E., 1901) found a ratio of 0.84 between the mean and the maximum velocities of water flowing in closed circular conduits, under normal conditions, at ordinary velocities; whereby observations of velocity taken at the center under such conditions, with a properly rated Pitot tube, may be relied on to give results within 3% of correctness. The Venturi Meter, invented by Clemens Herschel, and described in a pamphlet issued by the Builders' Iron Foundry of Providence, R. I., is named for Venturi, who first called attention, in 1796, to the relation between the velocities and pressures of fluids when flowing through converging and diverging tubes. It consists of two parts, the tube, through which the water flows, and the recorder, which registers the quantity of water that passes through the tube. The tube takes the shape of two truncated cones joined in their smallest diameters by a short throat-piece. At the up-stream end and at the throat there are pressure-chambers, at which points the pressures are taken. The action of the tube is based on that property which causes the small section of a gently expanding frustum of a cone to receive, without material resultant loss of head, as much water at the smallest diameter as is discharged at the large end, and on that further property which causes the pressure of the water flowing through the throat to be less, by virtue of its greater velocity, than the pressure at the up-stream end of the tube, each pressure being at the same time a function of the velocity at that point and of the hydrostatic pressure which would obtain were the water motionless within the pipe. The recorder is connected with the tube by pressure-pipes which lead to it from the chambers surrounding the up-stream end and the throat of the tube. It may be placed in any convenient position within 1000 feet of the meter. It is operated by a weight and clockwork. The meter is balanced in the recorder by the difference of level in two columns of mercury in cylindrical receivers, one within the other. The inner carries a float, the position of which is indicative of the quantity of water flowing through the tube. By its rise and fall the float varies the time of contact between an integrating drum and the counters by which the successive readings are registered. There is no limit to the sizes of the meters nor the quantity of water that may be measured. Meters with 24-inch, 36-inch, 48-inch, and even 20-foot tubes can be readily made. Measurement by Venturi Tubes (Trans. A. S. C. E., Nov., 1887, and Jan., 1888). Mr. Herschel recommends the use of a Venturi tube, inserted in the force main of the pumping engine, for determining the quantity of water discharged. Such a tube applied to a 24-inch main has a total length of about 20 feet. At a distance of 4 feet from the end nearest the engine the inside diameter of the tube is contracted to a throat having a diameter of about 8 inches. A pressure gage is attached to each of two chambers, the one surrounding and communicating with the entrance or main pipe, the other with the throat. According to experiments made upon two tubes of this kind, one inches in diameter at the throat and 12 inches at the entrance, and the other about 36 inches in diameter at the throat and 9 feet at its entrance, the quantity of water which passes through the tube is very nearly the theoretical discharge through an opening having an area equal to that of the throat, and a velocity which is that due to the difference in head shown by the two gages. Mr. Herschel states that the coefficient for these two widely varying sizes of tubes, and for a wide range of velocity through the pipe, was found to be within 2%, either way, of 98%. In other words, the quantity of water flowing through the tube per second is expressed within two per cent by the formula W 0.98 A V2 gh, in which A is the area of the throat of the tube, h the head, in feet, corresponding to the difference in the pressure of the water entering the tube and that found at the throat, and g 32.16. = Measurement of Discharge of Pumping Engines by Means of Nozzles (Trans. A. S. M. E., Vol. XII, 575). The measurement of water by computation from its discharge through orifices, or through the nozzles of fire hose, furnishes a means of determining the quantity of water delivered by a pumping engine, which can be applied without much difficulty. John R. Freeman (Trans. A. S. C. E., Nov., 1889) describes a series of experiments covering a wide range of pressures and sizes, and the results show that the coefficient of discharge for a smooth nozzle of ordinary good form was within one-half of 1%, either way, of .977; the diameter of the nozzle being accurately calipered, and the pressures being determined by means of an accurate gage attached to a suitable piezometer at the base of the play-pipe. In order to use this method for determining the quantity of water discharged by a pumping engine, it would be necessary to provide a box as many nozzles as would be required to carry off the water. According to Mr. Freeman's estimate, four 14-inch nozzles, thus connected, with a pressure of 80 pounds per square inch, would discharge the full capacity of a 22-million engine. He also suggests the use of a portable apparatus with a single opening for discharge, consisting essentially of a Siamese nozzle, so-called, the water being carried to it by three or more lines of fire hose. To insure reliability for these measurements, it is necessary that the shut-off valve in the force-main, or the several shut-off valves, should be tight, so that all the water discharged by the engine may pass through the nozzles. THE MINER'S INCH (From Merriman's Treatise on Hydraulics.) The miner's inch may be roughly defined to be the quantity of water which will flow from a vertical standard orifice one inch square, when the head on the center of the orifice is 61⁄2 inches. The coefficient of discharge is about 0.623, and accordingly the actual discharge from the orifice in cubic feet per second is = and the discharge in one minute is 60 X 0.0255 1.53 cubic feet. The mean value of one miner's inch is therefore about 1.5 cubic feet per minute. The actual value of the miner's inch, however, differs considerably in different localities. Bowie states that in different counties of California it ranges from 1.20 to 1.76 cubic feet per minute. The reason for these variations is due to the fact that when water is bought for mining or irrigating purposes, a much larger quantity than one miner's inch is required, and hence larger orifices than one square inch are needed. Thus at Smartsville, a vertical orifice or module, 4 inches deep and 250 inches long, with a head of 7 inches above the top edge, is said to furnish 1000 miner's inches. Again at Columbia Hill, a module 12 inches deep and 1234 inches wide, with a head of 6 inches above the upper edge, is said to furnish 200 miner's inches. In Montana the customary method of measurement is through a vertical rectangle, one inch deep, with a head on the center of the orifice of 4 inches, and the number of miner's inches is said to be the same as the number of linear inches in the rectangle; thus under the given head an orifice one inch deep and 60 inches long would furnish 60 miner's inches. The discharge of this is said to be about 1.25 cubic feet per minute, or 75 cubic feet per hour. The following are the values of the miner's inch in different parts of the Unites States. In California and Montana it is established by law that 40 miner's inches shall be the equivalent of one cubic foot per other States and Territories there is no legal value, but by common agreement 50 miner's inches is the equivalent of one cubic foot per second in Arizona, Idaho, Nevada, and Utah; this makes the miner's inch equal to 1.2 cubic feet per minute. A module is an orifice which is used in selling water, and which under a constant head is to furnish a given number of miner's inches, or a given quantity per second. The size and proportions of modules vary greatly in different localities, but in all cases the important feature to be observed is that the head should be maintained nearly constant in order that the consumer may receive the amount of water for which he bargains and no more. The simplest method of maintaining a constant head is by placing the module in a chamber which is provided with a gate that regulates the entrance of water from the main reservoir or canal. This gate is raised or lowered by an inspector once or twice a day so as to keep the surface of the water in the chamber at a given mark. This plan is a costly one, on account of the wages of the inspector, except in works where many modules are used and where a daily inspection is necessary in any event, and it is not well adapted to cases where there are frequent and considerable fluctuations in the surface of the water in the feeding canal. Numerous methods have been devised to secure a constant head by automatic appliances; for instance, the gate which admits water into the chamber may be made to rise and fall by means of a float upon the surface; the module itself may be made to decrease in size when the water rises, and to increase when it falls, by a gate or by a tapering plug which moves in and out and whose motion is controlled by a float. These self-acting contrivances, however, are liable to get out of order, and require to be inspected more or less frequently. Another method is to have the water flow over the crest of a weir as soon as it reaches a certain height. The use of the miner's inch, or of a module, as a standard for selling water, is awkward and confusing, and for the sake of uniformity it is greatly to be desired that water should always be bought and sold by the cubic foot per second. Only in this way can comparison readily be made, and the consumer be sure of obtaining exact value for his money. The cut, Fig. 129, shows the form of measuring-box ordinarily used, and the following table gives the discharge in cubic feet per minute of a miner's inch of water, as measured under the various heads and |