On p. 611 we give some diagrams to show how the velocity of the water in the main varies as the valve is closed; in all cases we have neglected the frictional resistance of the valve itself, which will vary with the type employed. In the case of a long pipe it will be noticed that the velocity of flow in the pipe, and consequently the quantity of water flowing, is but very slightly affected by a considerable closing of the valve, e.g. by closing a fully opened valve on a pipe 1000 feet long to 03 of its full opening, the quantity of water has only been reduced to o'g of its full flow. But in the case of very short pipes the quantity passing varies very nearly in the same proportion as the opening of the valve. Resistance of Knees, Bends, etc.-We have already shown that if the direction of a stream of water be abruptly changed through a right angle, the whole of its energy of motion is destroyed; a similar action occurs in a right-angled knee or elbow in a pipe, hence its resistance is at least equivalent to the friction in a length of pipe about 37 diameters long. In addition to this loss, the water overshoots the corner, as shown FIG. 548. in Fig. 548, and causes a sudden contraction and enlargement of section with a further loss of head. The losses in sockets, sudden enlargements, etc., can be readily calculated; others have been obtained by experiment, and their values are given in the following table. When calculating the friction of systems of piping, the equivalent lengths as given should be added, and the friction calculated as though it were a length of straight pipe. Velocity of Water in Pipes.-Water is allowed to flow at about the velocities given below for the various purposes named :— Pressure pipes for hydraulic purposes for long mains 3 to 4 feet per sec. Ditto for short lengths 1 1 ... ... Up to 25 1 Such velocities are unfortunately common, but they should be avoided if possible. CHAPTER XVII. HYDRAULIC MOTORS AND MACHINES. THE work done by raising water from a given datum to a receiver at a higher level is recoverable by utilizing it in one of three distinct types of motor. 1. Gravity machines, in which the weight of the water is utilized. 2. Pressure machines, in which the pressure of the water is utilized. 3. Velocity machines, in which the velocity of the water is utilized. Gravity Machines. In this type of machine the weightenergy of the water is utilized by causing the water to flow into the receivers of the machine at the higher level, then to descend with the receivers in either a straight or curved path to the lower level at which it is discharged. If W lbs. of water have descended through a height H feet, the work done = WH foot-lbs. Only a part, however, of this will be utilized by the motor, for reasons which we will now consider. The illustrations, Figs. 549, 550, show various methods of utilizing the weight-energy of water. Those shown in Fig. 549 are very rarely used, but they serve well to illustrate the principle involved. The ordinary overshot wheel shown in Fig. 550 will perhaps be the most instructive example to investigate as regards efficiency. Although we have termed all of these machines gravity machines, they are not purely such, for they all derive a small portion of their power from the water striking the buckets on entry. Later on we shall show that, for motors which utilize the velocity of the water, the maximum efficiency occurs when the velocity of the jet is twice the velocity of the buckets or vanes. In the case of an overshot water-wheel, it is necessary to keep down the linear velocity of the buckets, otherwise the centrifugal force acting on the water will cause much of it to be wasted by spilling over the buckets. If we decide that the inclination of the surface of the water in the buckets to the horizontal shall not exceed 1 in 8, we get the peripheral velocity of the wheel V, 2R, where R is the radius of the wheel in feet. = Take, for example, a wheel required for a fall of 15 feet. The diameter of the wheel may be taken as a first approximation as 12 feet. Then the velocity of the rim should not exceed 2/6 = say 5 feet per second. Then the velocity of the water issuing from the sluice should be 10 feet per second; the head h required to produce this velocity will be V2 or, introducing a coefficient to h = 2g' allow for the friction in the sluice, we may = 16 foot. One-half of this head, we shall show later, is lost by shock. The depth of the shroud is usually from 0'75 to 1 foot; the distance from the middle of the stream to the c. of g. of the water in the bucket may be taken at about 1 foot, which is also a source of loss. 0.15 D FIG. 551. The next source of waste is due to the water leaving the wheel before it reaches the bottom. The exact position at which it leaves varies with the form of buckets adopted, but for our present purpose it may be taken that the mean discharge occurs at an angle of 45° as shown. Then by measurement from the diagram, or by a simple calculation, we see that this loss is o'15D. A clearance of about 0'5 foot is usually allowed between the wheel and the tail water. We can now find the diameter of the wheel, remembering that H = 15 feet, and taking the height from the surface of the water to the wheel as 2 feet. This together with the 0'5 foot clearance at the bottom gives us D = 12'5 feet. Thus the losses with this wheel are Half the sluice head = o'8 foot Drop from centre of stream to buckets = 1'0 Water leaving wheel too early, = 1'9 O'15 X 12'5 feet Clearance at bottom = 0.5 Hydraulic efficiency of wheel = 4'2 feet 15-42 15 = 72 per cent. The mechanical efficiency of the axle and one toothed wheel will be about 90 per cent., thus giving a total efficiency of the wheel of 65 per cent. With greater falls this efficiency can be raised to 80 per cent. The above calculations do not profess to be a complete treatment of the overshot wheel, but they fairly indicate the sort of losses such wheels are liable to. Pressure Machines.-In these machines the water at the FIG. 552. higher level descends by a pipe to the lower level, from whence it passes to a closed vessel or a cylinder, and acts on a movable |