Flow of Water in When the flow ing stream of water is completely enclosed, as in a pipe, it is evident that no attention need be paid to the grade. The pipe may stand vertical if so desired. The difference in level vertically between the intake of water at the upper end of the pipe and the point of discharge is called the ahead)) It is expressed in feet, but in prac tice it is translated into pressure — the pressure equivalent to the weight of a column of water having the area of the pipe and a height equal to the head.
The friction set up by the perimeter of a pipe filled with running water is very consider able, and as soon as the lower end.of the pipe is opened and the water is allowed to flow the pressure corresponding to the head disappears by a large percentage. This is called technically °loss of Its effect is to cut down the velocity of the stream in the pipe, and hence, to reduce the theoretical discharge very materially. Several ((laws° have been deduced from a num ber of experiments made under these conditions. They are: (1) The loss of head from friction is di rectly proportional to the length of the pipe. (2) It is inversely proportional to the diameter of the pipe. (3) It increases nearly as the square of the actual velocity of the stream in the pipe. (4) It increases with the interior roughness of the pipe. Another source of loss of head is to be found in every bend of the pipe. This is greater as the velocity is large, and is very small when the current is very slow.
From the first two laws above quoted it is seen that the discharge of water from a pipe must depend upon the proportion of the length to the diameter. Hydraulic engineers are ac customed to classify pipes as *short* and gong.* A short pipe is one whose length is less than 500 times its diameter; a long pipe is one whose length is more than 500 times its diameter: In a short pipe the loss of velocity due to friction is so small as to be negligible in practical work. In a long pipe, on the contrary, particularly if of small pro portional diameter, the friction is sometimes great enough practically to nullify the velocity and reduce the discharge to a mere trickle. As an example it may be stated that experiment has proved that one pipe of 24 inches diameter (452 square inches in area) will dis charge as much water as 32 pipes of 6 inches in diameter (904 square inches in combined area). That is, the advantage of half of the
area of the smaller pipes was lost by the fric tion of the larger perimeter surface. This mat ter assumes great importance in designing water-supply systems for cities, where the ap portionment of the large mains and the small supply pipes must be directed to conserving the *head° or force of the flow against its too great diminution by friction., Hydraulic Gradient.--Another phenomenon which presents itself in the problem of the engineer is what is known as the "hydraulic gradient.* This is a grade line as sumed under the influence of 'the varying pres sure by a body of water flowing in a pipe toward a lower level. It is ascertained experimentally by inserting in such a pipe a series of vertical tubes freely open to the atmosphere, and reach ing upward to the level of the water in the supply reservoir. If the water in the pipe were not flowing, it is evident that in all the tubes the water would stand at the same level—that of the water in the reservoir. Upon allowing the water to flow, however, the water in the up right tubes falls, not to a uniform level, but to a graded line. In the tube nearest the reservoir it falls least; in the tube farthest from the res ervoir it falls most. A line connecting the points at which the water stands in all of the tubes is the hydraulic gradient for that partic ular pipe.
The hydraulic gradient will vary according to the diameter of the pipe, its length, the grades on which it is laid, the roughnesses of its in terior, its expansions or contractions in diameter and the distances from the reservoir at which they occur, and the number and sharpness of the bends placed in the system. The application of the principle of the hydraulic gradient in water-supply work appears when it becomes nec essary or desirable to carry a supply pipe over a hill, which, though it be on a lower level than the water in the reservoir, may be above the line of the hydraulic gradient. In this case a siphon must be formed, otherwise the water supply will be cut off from the hill and the pipe line beyond it. See SIPHON.