The upper surface of the liquid in the vessel and also the open end of the syphon are subject to the atmospheric pressure, but this is partly balanced on the short side by the column of liquid of height h, while on the other it is opposed by the longer column H. The pressure which is effective in causing the flow is therefore that of a column of liquid of height H-h. From this it appears that the velocity of escape of liquid through a siphon

AIR

FIG. 116.-Force Pump.

B

FIG. 117.-Siphon.

would be the same as from an opening directly into the vessel at the level of the outer end of the siphon, if it were not for the loss due to friction in the pipe.

Clearly the liquid can only rise in the siphon to a height where it can be supported by the atmospheric pressure; water therefore cannot be lifted by a siphon more than 34 ft. above its level and mercury not more than 30 inches.

Problems.

1. How high would the atmosphere have to be to cause the barometer to stand 76 cm. high, if its density was the same throughout as at the earth's surface, take it as .0012 grm. per c.c.

2. How deep must a pond be that an air bubble on reaching the surface may have twice the volume that it had at the bottom? Suppose the barometric pressure at the surface to be 75 cm. of mercury. 3. A barometer on top of a tower stands at 75.20, at the bottom it

stands at 75.40.

How high is the tower if the average density of

the air there is .0012 grm. per c.c.?

4. If the tube in the apparatus shown in figure 107 contains 100 c.c. of air, and the mercury stands in the tube 15 cm. above the level in the outer vessel, while the barometer stands at 75, find what would be the volume of the enclosed air if it were at atmospheric pressure, also what will the volume of the enclosed air become when the tube is raised sufficiently to make the mercury stand 20 cm. high inside the tube?

5. A glass bottle containing 100 c.c. of air floats at the surface of a pond with its open mouth downward. The bottle weighs 130 grm. and the density of the glass is 2.6. If the barometric pressure is 75 cm. of mercury, how deep below the surface must the bottle be pushed that it may just float in equilibrium, neither tending to rise nor sink? Neglect the weight of the enclosed air. Will the equilibrium be stable or unstable and why?

6. What force must be exerted on the piston of a force pump 3 in. in diameter to raise water 100 ft.?

PART II.-FLUIDS IN MOTION

213. Steady Flow. When a fluid is in motion if the pressure, velocity and direction of flow remain unchanged at every point in a certain region, the motion there is said to be steady. A line drawn in the fluid so that at every point it is in the direction of the flow at that point is called a stream line.

214. Continuity. In case of steady flow as much fluid must flow into any region as flows out of it in the same time. Let the figure represent either an open channel or a pipe conveying water. The total volume of water crossing the section

S

B

V

S'

of A per second will be v s cubic ft. per second if the velocity is v ft. per second and the cross section of the stream at that point is s square ft. If d represents the density at A, or the number of pounds mass per cubic foot, then vsd is the mass of water crossing A per second and similarly v's'd' is the corresponding mass crossing B in the same time, and therefore vsd=v's'd'. This equation holds for the steady flow of any fluid whether gas or liquid. But for liquids since

FIG. 118.

the density does not appreciably change during the flow, we may take d=d' and so

vs=v's'

or the velocity is inversely as the cross section of the stream. If at a narrow place in a stream the velocity is not correspondingly great, we may be sure that the stream is deep at that point. The extremely small cross section of a stream at the edge of a dam is due its great velocity at that point.

M

215. Momentum of Liquid Stream.-When a liquid is in motion each moving particle has momentum and kinetic energy. When a jet escapes through an opening in the side of a vessel the pressure which gives the jet its forward momentum acts at the same time as a reaction pressing the vessel in the opposite direction. If the orifice is free to move backward it will do so, as in case of the device known as Barker's mill shown in the figure. In case of the end of a hose the rush of water around a curve will by its centrifugal force tend to straighten the hose. If the end is free it will very probably swing over too far, in consequence of its inertia, when it will be flung back again, thus thrashing to and fro.

G

FIG. 119.-Barker's mill.

216. Turbine Water Wheels.-The centrifugal force of a stream as it moves by curved guides is made use of as a means of obtaining power in turbine water wheels. Such a wheel is shown in section in the diagram. The water flows inward toward the wheel through the fixed guides, which cause it to enter in the proper direction, and then driving the wheel forward and sweeping by the wheel guides B B, it escapes at the center of the wheel. The guides A A may be made adjustable so as to regulate the flow of water. The entering water from the flume is conducted to the turbine by a pipe

which is kept constantly full, thus giving the advantage of its pressure. The turbine may be set at the lowest level so that the water escapes directly into the tail race, or it may be set higher if the water escaping from the wheel enters a closed draft pipe which leads down to the tail water.

The sinking of the water in this draft pipe produces a suction which increases the efficiency of the wheel. In the great 5000 horse-power turbines in use at Niagara the water enters the

B

wheel from below in such a way that the weight of the wheel and shaft are almost exactly balanced by the upward pressure of the water, making the friction in the bearings extremely small.

217. Efficiency of Water Wheels. -When water flows from one level down to another it loses potential energy. That proportion of the potential energy lost by the water

FIG. 120.-Turbine water wheel diagram, which is transformed into useful work in a water wheel is called its efficiency. It is clear that to be efficient a wheel must as far as possible let the water down from the higher to the lower level without dashing, and the water escaping at the bottom should have little velocity, its energy having been expended in useful work.

218. Various Water Wheels. The old-fashioned overshot wheel, taking water from the upper level and lowering it to the bottom of the fall, uses the whole energy of the fall, but its size and weight cause great frictional loss.

Where a small supply of water at high pressure is available, some form of jet wheel is often best. Here the wheel is driven at high speed by the force of a jet escaping against cups set around the periphery of the wheel.

219. Hydraulic Ram.-The hydraulic ram is an appliance by which a small quantity of water may be raised a considerable height by using a small fall in a stream. The water is conducted to the ram through a straight, smooth, inclined pipe offering little resistance to the flow. At C is a valve opening downward

through which the water at first escapes; but as its speed increases, it catches the valve in its rush and shuts it. This sudden stoppage of the stream causes a great pressure at this end of the pipe in consequence of the forward momentum of the stream, and the valve d which opens upward is forced open and some water driven into the pipe e. The valve d then closes and prevents any return of water from e. But with the sudden stoppage of the stream the valve C if properly weighted rebounds and opens again, the stream again escapes at C with increasing · velocity until the valve is again caught and closed, when water is again driven through the valve d by the hammer-like blow

of the column of water in A. The action is thus kept up indefinitely, water being gradually forced up the pipe e until it may reach many times the height through which the stream falls. The air chamber B is essential to the action of the ram as it presents an elastic cushion with but little inertia, enabling the valve d to yield instantly. At f there is a minute opening, the air sniff, through which, in the recoil of the water, air is drawn in, maintaining the supply in the air chamber. If a hydraulic ram were perfectly efficient, it would raise one-tenth of the amount of water flowing into it through ten times the height of the fall or one-half the water twice the height of the fail. But in practice the efficiency of a good ram is about 50 per cent.

Rams are now made in which the supply pipe is as much as 4 ft. in diameter. In these rams the valve which arrests the flow is moved by a piston operated by water from a small branch of the main pipe.