CHAPTER XXIV

HYDRAULIC MACHINES

A HEAD of water may be utilised by employing a machine driven by the water, and in the present chapter we shall consider some of the simpler types of these machines.

Weight Machines.-The most simple class of

h

Fig. 362.

machine which can be driven by water from an elevated reservoir is that in which the water during its descent

rests on the buckets or vanes of a wheel, so that its weight becomes the effort driving the wheel.

Overshot Wheel.-In Fig. 362 we have one example of this class, the common overshot wheel. The water from the reservoir A pours into the buckets of the wheel, and by its weight turns the wheel, the buckets emptying into the tail race B.

The total head available is h, and in descending this distance the energy exerted by gravity on a weight W of water is Wh. Let

Then

G=delivery of stream in gallons per minute.

Energy exerted per minute by gravity= 10 Gh ft. -lbs.

The whole of this energy cannot be utilised. For, in the first place, the water runs on to the wheel with a velocity v; on striking the wheel vanes a pressure is created by the sudden change of velocity to V, the speed of the vanes or buckets (compare page 486), so that some of the head 2/2g originally used in producing v is usefully employed in creating a pressure helping to drive the wheel, but we know there is a waste of head (v-V)2/2g at least. The value of V is limited, because if it become large the water will be thrown out of the buckets by centrifugal action, hence V does not exceed about 5 f.s.

For reasons which we cannot in the present book enter into v should be about twice V, so that v is 10 f.s. Hence

Again, the water being in the buckets has the velocity V, and thus a portion of the head is wasted in this way, since the velocity is of no use to us. For this loss we

have

Head wasted=V2/2g.

We may add this to the preceding, and we then obtain

Head wasted in shock and in _(- V)2 ̧ V2

=

+

giving velocity V

2g 2g

There is still another loss caused by the buckets emptying before reaching the bottom of the fall, and by spilling of water. This loss depends on practical con

B

Fig. 363.

siderations as to shape of buckets, and hence we cannot express it by a formula.

We see that the losses or wastes contain some of constant value, and hence their relative effect is greater in small falls. For this reason these wheels are not used for values of h less than 10 feet. There is a limit on the other side, because for a very high fall the wheel becomes of very great diameter and too cumbrous. limit lies probably between 60 and 70 feet. The efficiency obtained in practice varies between 65 and 75 per cent.

The

Breast Wheel. In order to avoid the loss by

spilling of water from the buckets, a wheel is used which moves in a masonry channel; the buckets are replaced by vanes which fit this channel, but not so closely as to touch the sides; so there is a leakage past the vanes, but this does not cause so much loss as the buckets do.

Fig. 363 shows the construction, CD showing the breast or channel. It will be seen that the diameter of the wheel is necessarily greater than the fall, so that these wheels cannot be used for falls exceeding about 50 ft. The average efficiency is about .75. The water enters the wheel through guide blades at A, which are arranged so as to prevent as much as possible any shock as the water enters the buckets, and the waste of head which accompanies such shocks.

Pressure Machines. In the preceding machines the water has been open to the atmosphere, and each portion contained in a bucket or between two successive vanes has acted simply by its weight. In the class of machine we are now about to consider the water is confined within a pipe which is led from the source to the working cylinder of the machine, and the pressure due to the head moves the piston; the water is then discharged just as steam is exhausted from a steam engine. Hydraulic or Bramah Press. - The simplest

A

B

machine of this class is one in which there is practically no motion, but the effort is very much magnified. The head is in this case produced not by an elevated reservoir, but by loading a piston CD with P lbs. (Fig. 364). CD fits a cylinder, area ACD, which is connected by a pipe with the larger cylinder, area Ав, in which fits the working piston AB. AB presses against the body which is to be pressed, and exerts on it a total pressure R, the reaction R of

Fig. 364.

AB,

the body being the resistance to the motion of AB, as in former examples.

Assuming for simplicity that AB and CD are on the same level, we have, since there is no motion-the body pressed being supposed now to be compressed to the full amount-equal intensity of pressure at AB and CD. Hence

or

Total pressure on AB : Total pressure on CD=AAB : Acd,

R: PAAB : ACD,

so that by making the ratio of areas very large, a small

load or effort applied to CD can exert a great pressure at AB.

In the actual press a plunger takes the place of the piston CD, as in Fig. 365, and the effort P is applied to the top of the plunger by a hand lever GHK, to the end K of which a force Q is applied. Acp is now the sectional area of the plunger.

Accumulators. In some cases natural sources of head are available to work pressure machines, but in the majority of cases the head is produced artificially, as in the case we have been considering, or as in the hydraulic engines used on board ship, in which a head is first created by means of a steam engine. In one or two cases the engine which creates the head has actually