LECTURE XXXV.—QUESTIONS.

1. Prove the law for changing p, r, and h along a stream line in a frictionless fluid. Apply the law to find the funnel shape of the surface of water in a basin from which the water is flowing by a central hole. (S. & A. Hons. Exam., Part I., 1898.)

2. Prove the law for changing p, r, and h along the stream lines in a frictionless fluid. Apply, neglecting change of level, to the case of adiabatic flow of air from one vessel to another through a small orifice, and deduce the rule for maximum quantity flowing. (S. & A. Hons. Exam., Part. II., 1898.)

3. Describe the action of a jet pump, or of a good form of injector.

4. Water flows through a round sharp edged orifice 3 inches in diameter in a flat plate, at about 12 inches below still-water level. Show by a sketch your notion of the shapes of the stream lines. If we wish to know the pressure at any point, why is it not sufficient to know only the depth? (S. & A. Adv. Exam., 1898.)

5. Deduce a formula giving the velocity with which water issues from an orifice, and show how to apply it to water under pressure.

6. Discuss briefly the relative advantages under various circumstances of the different methods of measuring a stream of water.

7. Find the horse-power of a waterfall 70 feet high, when the stream is such that it passes over a gauge notch 6 feet long with a head of 15 inches. If it is employed to drive a turbine of 80 per cent. efficiency, what B.H.P. would you expect to obtain?

8. Investigate the form of the surface of water which flows out of a hole in the bottom of a basin with a vortex motion.

9. What is meant by a constrained vortex, and why will such a vortex rapidly disappear when left to itself? Find the form taken by the surface and show how to apply this to finding the pressure in a centrifugal pump.

10. The wheel of a centrifugal pump 2 feet outside diameter has a very large case and rotates at 100 revolutions per minute about a vertical axis, and almost no water is being delivered. Calculate and show in a curve the pressure at points in a horizontal plane, at various distances from the axis. The vanes are bent backwards at an angle of 30° with the radius at the outer part; if the radial flow becomes 2 feet per second and the cir cumferential openings are 200 sq. inches in area, what is the kinetic energy of the water leaving the wheel? What is the pressure in excess of that at the inner rim of the wheel where the water enters without shock? If there is no frictional loss to what height will the water be lifted above the well? In an actual pump with small wheel case what is the probable lift? (S. & A. Hons. Exam., Part II., 1898.)

11. "

Barker's mill consists of a horizontal pipe with a nozzle at right angles to it at each end thus Water enters it by a vertical pipe

at the centre, and the whole is so mounted that it can rotate about the axis of this pipe. Find the torque when the water is issuing under a head h, and the mill is revolving n times per minute. Show that the power is greatest when the velocity of the nozzles is half that due to the head, and that the efficiency then cannot be over 50 per cent.

12. What are the chief conclusions to be drawn from Reynold's experiments on the flow of water through pipes?

13. What is meant by the Hydraulic Mean Depth of a pipe or channel, and show how we use it in calculating the resistance to the flow of water?

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LECTURE XXXVI.

WATER-WHEELS AND TURBINES.

CONTENTS.-Hydraulic Motors-Overshot Water-wheel-Breast-wheelsUndershot Water-wheel-Fairbairn's Improvements-Clack MillPelton Wheel-Turbines-Girard Turbine-Jonval Turbine-Günther's Governor Thomson's Vortex Turbine-Little Giant TurbineCentrifugal Pumps and Fans-Questions.

Hydraulic Motors.*-In connection with hydrostatics we have already described some machines for obtaining motion by hydraulic

Head Race

Tail Race

OVERSHOT WATER-WHEEL.

means, but in all these cases the water acts solely by its pressure,

Students should refer to Hydraulic Motors by G. R. Bodmer (London, Whittaker & Co.), and to Hydraulic Machinery by R. Gordon Blaine (London, E. & F. N. Spon, Limited) for further information on the design of water-wheels and turbines.

We now come to the consideration of other water motors in which the weight and momentum of the water are also employed. These may be divided roughly into two classes-Water-wheels, in which the water acts for the most part directly by its weight; and turbines, in which it acts by its momentum. We cannot, however, draw a very sharp line between them, as they gradually merge into one another, and the power of both ultimately depends on gravity.

Overshot Waterwheel. -- This consists of a wooden or iron frame to which is fixed a number of blades, so as to form with the inner circumference a series of buckets for holding water. The water is led along an aqueduct termed the head race to the top of the wheel, and there enters the buckets. Its weight forces them downwards and thus makes the wheel revolve. As each bucket in turn approaches its lowest position the water gradually drops out of it into the tail race. The motion of

the water as it enters the wheel also assists

to some extent in producing rotation. The buckets are so shaped and fixed to the wheel, that as little as possible of the available power shall be lost by the water spilling from them before they reach the tail race. The sectional view shows one form of bucket for this purpose whilst the outside view shows another with curved blades. One disadvantage of this wheel is, that the water leaves

it with a velocity opposite in direction to that of the tail race, if this flows the same way as the head race. The water therefore does not get away so freely from the tail race, and more clearance is necessary at the bottom of the wheel which thereby involves a loss of head.

Breast-wheels. This last consideration, coupled with the difficulty of supporting the head race for large overshot wheels, has brought about the introduction of breast-wheels, in which the water is introduced between the top and middle of the wheel as shown by the next illustration. The breast-wheel is also frequently made with curved blades into which the water drops almost vertically, and then acts chiefly by its weight. The motion of the

Head Race

Tail Race

FAIRBAIRN'S BREAST-WHEEL.

wheel in this case assists the escape of the tail water instead of hindering it as in the previous one. The curved ventilated form of bucket with closed breast, as shown in the above figure, was first introduced by Sir William Fairbairn and greatly increased the efficiency of the motor. But, for small wheels, such as are used for farms, where first cost is more important than efficiency, hey are usually made radial as shown by the following figure.

Here, the water is allowed to attain a certain amount of motion before reaching the wheel, and therefore acts partly by momentum and partly by its weight. The buckets have no ends, but the wooden breast serves to keep the water from escaping by the sides and circumference of the wheel before it reaches the bottom.