Chapter IV: Part 4

NOTE.—_Theoretical and actual flow._—_The actual flow from an
orifice_, is the volume of liquid which escapes from it in a given
time. _The theoretical flow_, is a volume equal to that of a cylinder
which has for its base the orifice, and for its height the velocity,
furnished by the discovery of Torricelli. That is, the theoretical
flow is the product of the area of the orifice multiplied by the
theoretical velocity. It is observed that the vein escaping from an
orifice, contracts quite rapidly, so that its diameter is soon only
about two-thirds of the diameter of the orifice. If there was no
contraction of the vein after leaving the orifice, and its velocity
was the theoretical velocity, the actual flow would be the same
as that indicated by theory. But its section is much less than at
the orifice, and its velocity is not so great as the theoretical
velocity, so that the actual flow is much less than the theoretical
flow; and in order to reduce this to the first, it is necessary to
multiply it by a fraction.

2.—In the lower part of the vein, the liquid is not continuous; for if we employ an opaque liquid, as mercury, we can see through the vein, Fig. 98. The apparent continuity in a vein of water is owing to the fact that the globules which constitute it succeed each other at a distance inappreciable to the eye.

_The time it takes by a vessel to empty itself_ is to the time required, when it is kept constantly full, to discharge the same quantity of water, as 2 to 1, and the spaces described by the surface in its descent in a column of equal size throughout, are as the odd numbers, 9, 7, 5, 3, 1. Thus these spaces measure equal times. Since liquids are not perfectly mobile, and their exit at an orifice must be retarded by cohesion and friction, the results thus far given are much modified in practice.

When a liquid flows through an orifice in a vessel, eddies are formed about the sides of the orifice, preventing the escape of a jet equivalent to its full size; and owing to these, and to acceleration of velocity, _if the jet be downward_, it rapidly contracts in its diameter. At a distance outside about equal to diameter of the opening, it is contracted to 2/3 or 5/7 its original area; and this part has been called the “contracted vein.” It has been shown, that below this the stream still contracts, though less rapidly.

These swellings separate more widely as they descend with increased rapidity; but falling through great heights, the whole may finally be dissipated in a mist.

NOTE.—The annular swellings contain air and arise from a periodical
succession of pulsations near the orifice, which must be produced by
very small oscillations of the entire mass of the liquid, so that the
velocity of the flow is periodically variable. The sucking, whistling
noise which is often heard in the descent of water through an orifice
is caused by air drawn in by the whirling motion. See Fig. 103.

If an orifice in a vessel looks downward, and the column of liquid over it be short, this will simply drop out by its own weight, starting at a velocity of o. But if a considerable depth of liquid be above, its gravity produces a corresponding pressure on its base, or on that liquid which is near it; so that, if a plug be removed from an orifice in or close to the base, the liquid starts at once into rapid motion.

Each particle of a jet A issuing from the side of a vessel moves horizontally with the velocity above mentioned, _but it is at once drawn downward by the force of gravity_ in the same manner as a bullet fired from a gun, with its axis horizontal. It is well known that the bullet describes _a parabola with a vertical axis_, the vertex being the muzzle of the gun. Now, since each particle of the jet moves in the same curve, this jet C takes the parabolic form. In every parabola there is a certain point called the focus, and the distance from the vertex to the focus fixes the magnitude of a parabola in much the same manner as the distance from the center to the circumference fixes the magnitude of a circle.

Now it can be proved that the focus B is as much below as the surface of the water is above the orifice. Accordingly, if water issues through orifices which are small in comparison with the contents of the vessel, the jets from orifices at different depths below the surface take different forms, as shown at D. If these curves are traced on paper held behind the jet, then, knowing the horizontal distance and the vertical height, it is easy to demonstrate that the jet forms a parabola.

_Quantity of Efflux._—If we suppose the bottom of a vessel containing water to be thin, and the orifice to be a small circle whose area is A (see Fig. 100) where A B represents an orifice in the bottom of a vessel.

Every particle above A B tries to pass out of the vessel, at once and in so doing exerts a pressure on those nearest. Those that issue near A and B exert pressures in the directions M M and N N; those near the center of the orifice in the direction R Q, those in the intermediate parts in the directions P Q, P Q. In consequence, the water within the space P Q P is unable to escape, and that which does escape, instead of assuming a cylindrical form, at first contracts, and takes the form of a truncated cone.

It is found that the escaping jet continues to contract until at a distance from the orifice about equal to the diameter of the orifice; this part of the jet is called the _vena contracta_ or contracted vein, as explained on a previous page.

_Influence of tubes on the quantity of efflux._—The result before given has reference to an aperture in a thin wall. If a cylindrical or conical efflux tube is fitted to the aperture, the amount of the flow is considerably increased. A short tube, whose length is from two to three times its diameter, has been found to increase the actual efflux per second to about 82 per cent. of the theoretical. In this case the water on entering the tube forms a contracted vein, Fig. 101. just as it would do on issuing freely into the air; but afterwards it expands, and, in consequence of the adhesion of the water to the interior surface of the tube, has, on leaving the tube, a section greater than that of the contracted vein. The contraction of the jet within the tube causes a partial vacuum shown in black in the figure.

Now, if an aperture is made in the tube, near the point of greatest contraction, and is carefully fitted with a vertical tube, the lower end of which dips into water, Fig. 101, it is found that water rises in the vertical tube, thereby proving conclusively the formation of a partial vacuum.

If the nozzle has the form of a conic frustum whose larger end is at the aperture, the efflux in a second may be raised to 92 per cent., provided the dimensions are properly chosen. If the smaller end of a frustum of a cone of suitable dimensions be fitted to the orifice, the efflux may be still further increased, which will fall very little short of the theoretical amount.

_Velocities of streams._—The velocity of streams varies greatly. The slower flow of rivers has a velocity of less than three feet per second, and the more rapid, as much as six feet per second, which gives respectively about two and four miles per hour. The velocities vary in different parts of the same transverse section of a stream, for the air upon the surface of the water, as well also as the solid bottom of the stream, has a certain effect in retarding the current. The velocity is found to be greatest in the middle, where the water is deepest, Fig. 102, somewhere in _m_, below the surface; then it decreases with the depth towards the sides, being least at _a_ and _b_.

_Appearance of the surface during a discharge._—A vessel containing a liquid, discharging itself through an orifice, does not always preserve a horizontal surface. When the vein issues from an orifice in the bottom of a vessel, and the level of the liquid is near the orifice, the liquid forms a whirlpool, Fig. 103. If the liquid has a rotary movement, the funnel is formed sooner; if the orifice is at the side of the vessel, there is a depression of the surface upon that side, above the orifice, Fig. 104. These movements depend upon the form of the vessel, the height of the liquid in it, and the dimensions and form of the orifice.

In order to verify many of the laws of hydraulics in an accurate manner, it is necessary to maintain a uniform pressure on the escaping liquid, thereby obtaining a constant velocity at the orifice. This may be done in various ways, as by allowing the water to flow into the vessel in a little larger quantity than can escape from the orifice, the excess being discharged over the upper edge of the vessel; also by means of the syphon.

_By suspending solid particles_, such as charred paper, pulverized in the water, we render the currents that are formed visible. These solid particles arrange themselves, in curved lines, towards and into the orifice, as a center of attraction, Fig. 105. The particles in immediate contact with the orifice, not moving so easily as those within, must cause contraction; so, also, _we can see that gravity in accelerating the velocity, must cause continual decrease in the section of the jet_.

_Upward jets of water._—As the velocity of a liquid escaping from an orifice is the same as that which a body acquires, falling from a height equal to the distance from the level of the liquid to the orifice, a jet of water escaping from a horizontal opening upwards, should theoretically reach the level of the liquid in the vessel. But this never takes place, Fig. 106, because of—1st, the friction in the conducting tubes destroying the velocity. 2nd, the resistance of the air. 3rd, the returning water falling upon that which is rising. The height of the jet is increased by having the orifices very small, in comparison with the conducting tube; piercing them in a very thin wall, and inclining the jet a little, thus avoiding the effect of the returning water.

_Height of the jet._—If a jet issuing from an orifice in a vertical direction has the same velocity as a body would have which fell from the surface of the liquid to that orifice, the jet ought to rise to the level of the liquid. It does not, however, reach this; for the particles which fall hinder it. But by inclining the jet at a small angle with the vertical it reaches about 9/10 of the theoretical height, the difference being due to friction and to the resistance of the air.

_The quantities of water which issue from orifices of different areas are very nearly proportional to the size of the orifice_, provided the level remains constant, and this is true irrespective of the form of the opening which may be round, square, or any other shape.

_Escape of liquids through short tubes._—We often place in an orifice, to increase the flow, a short tube (called an adjutage) either cylindrical or conical. If the vein pass through the tube without adhering to it, the flow is not modified; if the vein adhere (the liquid wetting the interior walls) the contracted part is dilated, and the flow is increased.

In the last case, and with a cylindrical adjutage, its length not being more than four times its diameter, the flow is augmented about one-third. Conical pipes, converging towards the exterior, increase the flow still more than the preceding, the flow and velocity of the vein varying with the angle.

_Escape of liquids through long tubes._—When a liquid passes through a long straight tube, the flow soon diminishes greatly in velocity, because of the friction which takes place between the liquid particles and the walls. If there be any bends or curves in the tube, it is still further diminished by the same cause. The discharge is then much less than it would be from an orifice in a thin wall, and therefore the tube is generally inclined; the liquid then passes down this inclined plane, or it is forced through by pressure, applied at the opposite end.

_Direction of the jet from lateral orifices._—From the principle of the equal transmission of pressure, water issues from an orifice _in the side of a vessel_ with the same velocity as from an aperture in the bottom of a vessel at the same depth.

MEASUREMENT OF WATER PRESSURE.

_In reference to the table on the next page_, it may be well to say that it has two uses; by it when the “_head_” is known the _pressure_ can be ascertained to a fraction, thus, _Ex. 1_, If the head is 140 feet, then the pressure is 60·64 pounds per square inch. Again, _Ex. 2_, If the pressure is 15·16 per square inch, then the head is 35 feet.

PRESSURE OF WATER.

The pressure of water in pounds per square inch for every foot in height to 300 feet; and then by intervals, to 1000 feet head· By this table, from the pounds pressure per square inch, the feet head is readily obtained; and _vice versa_.

------+----------
Feet | Pressure
Head. |per square
| inch.
------+----------
1 | 0·43
2 | 0·86
3 | 1·30
4 | 1·73
5 | 2·16
6 | 2·59
7 | 3·03
8 | 3·46
9 | 3·89
10 | 4·33
11 | 4·76
12 | 5·20
13 | 5·63
14 | 6·06
15 | 6·49
16 | 6·93
17 | 7·36
18 | 7·79
19 | 8·22
20 | 8·66
21 | 9·09
22 | 9·53
23 | 9·96
24 | 10·39
25 | 10·82
26 | 11·26
27 | 11·69
28 | 12·12
29 | 12·55
30 | 12·99
31 | 13·42
32 | 13·86
33 | 14·29
34 | 14·72
35 | 15·16
36 | 15·59
37 | 16·02
38 | 16·45
39 | 16·89
40 | 17·32
41 | 17·75
42 | 18·19
43 | 18·62
44 | 19·05
45 | 19·49
46 | 19·92
47 | 20·35
48 | 20·79
49 | 21·22
50 | 21·65
51 | 22·09
52 | 22·52
53 | 22·95
54 | 23·39
55 | 23·82
56 | 24·26
57 | 24·69
58 | 25·12
59 | 25·55
60 | 25·99
61 | 26·42
62 | 26·85
63 | 27·29
64 | 27·72
65 | 28·15
66 | 28·58
67 | 29·02
68 | 29·45
69 | 29·88
70 | 30·32
71 | 30·75
72 | 31·18
73 | 31·62
74 | 32·05
75 | 32·48
76 | 32·92
77 | 33·35
78 | 33·78
79 | 34·21
80 | 34·65
81 | 35·08
82 | 35·52
83 | 35·95
84 | 36·39
85 | 36·82
86 | 37·25
87 | 37·68
88 | 38·12
89 | 38·55
90 | 38·98
91 | 39·42
92 | 39·85
93 | 40·28
94 | 40·72
95 | 41·15
96 | 41·58
97 | 42·01
98 | 42·45
99 | 42·88
100 | 43·31
101 | 43·75
102 | 44·18
103 | 44·61
104 | 45·05
105 | 45·48
106 | 45·91
107 | 46·34
108 | 46·78
109 | 47·21
110 | 47·64
111 | 48·08
112 | 48·51
113 | 48·94
114 | 49·38
115 | 49·81
116 | 50·24
117 | 50·68
118 | 51·11
119 | 51·54
120 | 51·98
121 | 52·41
122 | 52·84
123 | 53·28
124 | 53·71
125 | 54·15
126 | 54·58
127 | 55·01
128 | 55·44
129 | 55·88
130 | 56·31
131 | 56·74
132 | 57·18
133 | 57·61
134 | 58·04
135 | 58·48
136 | 58·91
137 | 59·34
138 | 59·77
139 | 60·21
140 | 60·64
141 | 61·07
142 | 61·51
143 | 61·94
144 | 62·37
145 | 62·81
146 | 63·24
147 | 63·67
148 | 64·10
149 | 64·54
150 | 64·97
151 | 65·40
152 | 65·84
153 | 66·27
154 | 66·70
155 | 67·14
156 | 67·57
157 | 68·00
158 | 68·43
159 | 68·87
160 | 69·31
161 | 69·74
162 | 70·17
163 | 70·61
164 | 71·04
165 | 71·47
166 | 71·91
167 | 72·34
168 | 72·77
169 | 73·20
170 | 73·64
171 | 74·07
172 | 74·50
173 | 74·94
174 | 75·37
175 | 75·80
176 | 76·23
177 | 76·67
178 | 77·10
179 | 77·53
180 | 77·97
181 | 78·40
182 | 78·84
183 | 79·27
184 | 79·70
185 | 80·14
186 | 80·57
187 | 81·00
188 | 81·43
189 | 81·87
190 | 82·30
191 | 82·73
192 | 83·17
193 | 83·60
194 | 84·03
195 | 84·47
196 | 84·90
197 | 85·33
198 | 85·76
199 | 86·20
200 | 86·63
201 | 87·07
202 | 87·50
203 | 87·93
204 | 88·36
205 | 88·80
206 | 89·23
207 | 89·66
208 | 90·10
209 | 90·53
210 | 90·96
211 | 91·39
212 | 91·83
213 | 92·26
214 | 92·69
215 | 93·13
216 | 93·56
217 | 93·99
218 | 94·43
219 | 94·86
220 | 95·30
221 | 95·73
222 | 96·16
223 | 96·60
224 | 97·03
225 | 97·46
226 | 97·90
227 | 98·33
228 | 98·76
229 | 99·20
230 | 99·63
231 | 100·06
232 | 100·49
233 | 100·93
234 | 101·36
235 | 101·79
236 | 102·23
237 | 102·66
238 | 103·09
239 | 103·53
240 | 103·96
241 | 104·39
242 | 104·83
243 | 105·26
244 | 105·69
245 | 106·13
246 | 106·56
247 | 106·99
248 | 107·43
249 | 107·86
250 | 108·29
251 | 108·73
252 | 109·16
253 | 109·59
254 | 110·03
255 | 110·46
256 | 110·89
257 | 111·32
258 | 111·76
259 | 112·19
260 | 112·62
261 | 113·06
262 | 113·49
263 | 113·92
264 | 114·36
265 | 114·79
266 | 115·22
267 | 115·66
268 | 116·09
269 | 116·52
270 | 116·96
271 | 117·39
272 | 117·82
273 | 118·26
274 | 118·69
275 | 119·12
276 | 119·56
277 | 119·99
278 | 120·42
279 | 120·85
280 | 121·29
281 | 121·72
282 | 122·15
283 | 122·59
284 | 123·02
285 | 123·45
286 | 123·89
287 | 124·32
288 | 124·75
289 | 125·18
290 | 125·62
291 | 126·05
292 | 126·48
293 | 126·92
294 | 127·35
295 | 127·78
296 | 128·22
297 | 128·65
298 | 129·08
299 | 129·51
300 | 129·95
310 | 134·28
320 | 138·62
330 | 142·95
340 | 147·28
350 | 151·61
360 | 155·94
370 | 160·27
380 | 164·61
390 | 168·94
400 | 173·27
500 | 216·58
600 | 259·90
700 | 303·22
800 | 346·54
900 | 389·86
1000 | 433·18

HYDRAULIC GAUGES.

_The Piezometer, or pressure gauge, is an instrument for measuring the pressure of water in a pipe._

It may be broadly stated that all pressures and weights relating to water, steam, gases, etc., are now recorded by gauges.

The principle of construction of the dial gauge is that the pressure may be indicated by means of a spring and pointer upon a divided dial similar to a clock face, but marked in divisions, indicating pounds, hundreds, etc., _pressure_ instead of hours and minutes. The more approved forms of gauges are now constructed upon the principle of the _Bourdon_ spring or metallic barometer invented in 1849. (See page 113 for illus.)

The essential principle—or discovery—is this: that a metal curved tube—oval cross section, _under pressure, tends to straighten itself_ according to the force exerted by the pressure inside. Figs. 107 and 108 show the ordinary style of gauge which consists of an elliptical tube, connected at one end to a pipe in communication with the pressure, and at the other end with toothed arc and pinion to a pointer spindle as shown in cuts.

NOTE.—Hydraulic gauges are indispensable as it is often necessary to
stop the pressure at points below that at which the safety valve has
been set.

Within the gauges—or cases, is a small coiled tube closed at one end, while the other end is attached to the socket through which the water is admitted; this tube has a tendency to straighten when under pressure, and thus its free closed end moves, and this motion is communicated to the pointer; when the pressure is relieved the tube assumes its original position and the pointer returns to zero. There are many modifications and special adaptations of the Bourdon discovery, but the principle remains, and the same useful results are obtained with both single and double tubes, the latter being the most resensitive.

Fig. 107 shows the dial of a hydraulic gauge which is graduated to suit the work to which it is related. These gauges are made for pressures from 1,000 to 20,000 pounds per square inch. The springs are formed of heavy solid bar steel turned and bored to size and are of the Bourdon style. They are in use in large railroad shops, sugar refineries and cotton-seed oil mills. These gauges are also made with connections through the back of the case.

The gauge illustrated in Fig. 108 is used in connection with hot water heaters, denoting the height of column of water in the tank or reservoir, one hand being painted red and the other black. As it is necessary to have at all times in the tank or reservoir a certain height of water, the red hand is set at the point on the dial which denotes this height. The black hand is connected with the working parts of the gauge and indicates on the dial the actual height of water in the tank or reservoir.

The dial of this gauge is graduated in feet, instead of pounds.

A check valve is almost indispensable in using a hydraulic gauge, as the pressure is often suddenly removed and the momentum of the hand will throw the pinion out of gear with the toothed arc, and is liable to break the hair-spring. A check valve prevents any trouble of this kind and should always be used.

WATER PRESSURE MACHINES

WATER WHEELS.

_Hydraulic machinery_ may be broadly divided into

1. Motor machines, and,
2. Pumps.

_Water motors_ may be divided into

1. Water wheels,
2. Turbines, and,
3. Water pressure engines.

_In hydraulic motor machines_ a quantity of water descending from a higher to a lower level, or _from a higher to a lower pressure_, drives a machine which receives energy from the water and applies it to overcoming the resistances of other machines doing work.

_In the next general class_, work done on the machine by a steam engine or other source of energy is employed in lifting water _from a lower to a higher level_. A few machines such as the ram and jet pump _combine the functions of both motors and pumps_.

_The subject of water wheels is but a continuation of much that has been illustrated and defined in the historical introduction_ to which is now added the following summary.

In every system of machinery _deriving energy from a natural water-fall there exist the following parts_:

(1) _A supply channel_, leading the water from the highest accessible level, _to the site of the machine_; this may be an open channel of earth, masonry, or wood, or it may be a closed cast or wrought-iron pipe; in some cases part of the head race is an open channel, part a closed pipe.

(2) _Leading from the motor_ there is a tail race, culvert, or discharge pipe delivering the water after it has done its work.

(3) _A waste channel_ placed on or at the origin of the head race by which surplus water, in floods, escapes.

(4) _The motor itself_, which either overcomes a useful resistance directly, as in the case of a ram acting on a lift or crane chain, or indirectly by actuating transmissive machinery, as when a turbine drives the shafting, belting, and gearing of a mill. With the motor is usually combined regulating machinery for adjusting the power and speed, to the work done.

The great convenience and simplicity of water motors has led to their adoption in certain cases, where no natural source of water power is available. In these cases, an artificial source of water power is created by using a steam engine to pump water to a reservoir at a great elevation, or to pump water into a closed reservoir in which there is great pressure.

Water flowing from the reservoir through hydraulic engines gives back the energy expended, less so much as has been wasted in friction. Where a continuously acting steam engine stores up energy by pumping the water, while the work done by the hydraulic engines is done intermittently,—this arrangement is considered the most useful.

NOTE.—“Wherever a stream flows from a higher to a lower level it
is possible to erect a water motor. The amount of power obtainable
depends on the available head and the supply of water. In choosing
a site the engineer will select a portion of the stream where there
is an abrupt natural fall, or at least a considerable slope of the
bed. He will have regard to the facility of constructing the channels
which are to convey the water, and will take advantage of any bend in
the river which enables him to shorten them. He will have accurate
measurements made of the quantity of water flowing in the stream,
and he will endeavor to ascertain the average quantity available
throughout the year, the minimum quantity in dry seasons, and the
maximum for which bye-wash channels must be provided. In many cases
the natural fall can be increased by a dam or weir thrown across the
stream. The engineer will also examine to what extent the head may
vary in different seasons, and whether it is necessary to sacrifice
part of the fall and give a steep slope to the tail race to prevent
the motor being flooded by backwater in freshet time.

In designing or selecting a water motor it is sufficient to consider
only its efficiency in normal working conditions. It is generally
quite as important to know how it will act with a scanty water supply
or a diminished head. The greatest difference in water motors is in
their adaptability to varying working conditions.”—ENCYC. BRIT.

_Water wheels_ are large vertical wheels driven by water falling from a higher to a lower level: they are motors on which the water acts, partly by weight, partly by impulse. _Turbines_ are wheels, generally of small size compared with water wheels, driven chiefly by the impulse of the water. Before entering the moving part of the turbine, the water is allowed to acquire a considerable velocity; during its action on the wheel this velocity is diminished, and the impulse due to the change of momentum drives the turbine. Roughly speaking, the fluid acts in a water-pressure engine directly by its pressure, _in a water wheel chiefly by its weight causing a pressure_.

_A flutter-wheel_ is shown in Fig. 110. This is a water wheel of moderate diameter placed at the bottom of a chute so as to receive the impact of the head of water in the chute and penstock. Its name is derived from its rapid motion, the effect of which is to cause a commotion of the water like “the fluttering” of a fowl.

_Impact Wheels._—The simplest and most imperfect of the horizontal wheels are the so-called impact wheels or impact turbines, such as shown in Fig. 111.

They consist of 16 or 20 rectangular blades fastened to the wheel at an inclination of 50° to 70° with the horizon. The water is brought on through a race of 40° to 20° inclination, so that it strikes at about right angles upon the blades.

These wheels are used in falls from 10 to 20 ft., where a large number of revolutions is necessary, as in grain mills, where the moving millstone is hung on the vertical shaft of the wheel, hence intermediate gearing is unnecessary. These crude machines are found in Southern Europe, North Africa, in the Alps, Pyrenees, and in Algiers. They are about 5 ft. in diameter, and the blades are 15 inches high and 8 to 10 inches long (measured radially).

Fig. 112 shows an “_undershot water wheel_.” In this style of wheel, the work is done by impact alone, as the running water acts only on a few immersed buckets on the under side of the wheel.

In the _breast wheel_, Fig. 113, the water is admitted on a level or slightly above the center of the shaft, so that the water acts by impact and weight.

NOTE.—“_A weir_ is a dam erected across a river to stop and raise the
water, as for the purpose of taking fish, of conveying a stream to a
mill, of maintaining the water at a level required for navigating it,
or for the purposes of irrigation.”

For facilitating the computation of the quantity of water flowing
over weirs, Weir Tables, are used, based upon approved formulas, of
which “Francis’ Formula” is perhaps the most reliable. These tables
are applicable to the subject of water wheels but cannot be printed
in this work.

Fig 114 represents an _over-shot water wheel_ (F G H L, with axis at O) in which the water flows upon the top of the wheel at _h_, in the same direction in which it revolves, therefore the impact of the water is utilized upon the upper buckets H, a, b, after which the weight of the water acts in the buckets c, d, e, F, e´, d´ and c´. At b´ the buckets begin to overflow and empty themselves as shown at a´. It will be seen that the water acts upon almost one-half the circumference of this wheel, thus realizing the greatest mechanical effect with the smallest quantity of water.

_The current-wheel_ is perhaps the first application of the force of water in motion, to drive machinery. In the first century B. C., water-wheels for driving mills were used in Asia Minor and on the Tiber. In the former case we suppose, but in the latter case we know, that these were current-wheels.

_The tide or current wheel_, (Fig. 115) erected in the vicinity of the north end of London Bridge, and subsequently under its northern arch, was erected by Peter Morice, a Dutchman, in 1582, and operated force-pumps which supplied a part of London with water. The stand-pipe from the pump was 120 feet high, and conducted the water to a cistern at that height. The amount raised was about 216 gallons per minute. The wheel worked sixteen pumps, each 7 inches in diameter, and having a uniform stroke of 30 inches.

During the seventeenth and eighteenth centuries the works were extended from time to time, and occupied one after another of the arches. In the first arch of the bridge was one wheel working sixteen force-pumps. In the third arch were three wheels, working fifty-two pumps. The united effect was 2,052 gallons per minute, raised 120 feet high.

In 1767 Smeaton added wheels in the fifth arch. Steam-engines were added about this time to assist at low water and at neap-tides. Thus the matter remained till 1821. Stow, the antiquarian and historian, describes the works in 1600; and Beighton in 1731 gives an account of them at that date.

The water-wheels at that time were placed under several of the arches. The axis of these wheels was 19 feet long 3 feet diameter. The radial arms supported the rings and twenty-six floats, 14 feet long by 18 inches wide. The axis turned on brass gudgeons supported by counterpoised levers, which permitted the vertical adjustment of the wheel as the tide rose and fell. On the axis of the wheel was a cog-wheel 8 feet in diameter and having forty-four cogs; meshing into a trundle-wheel 4-1/2 feet in diameter and having 20 rounds, or pins and whose iron axle revolved in brasses.

The axis of the trundle was prolonged at each end, and had quadruple cranks which connected by rods to the ends of four walking beams 24 feet long, whose other ends worked the piston-rods of the pumps. The axis of oscillation of the lever supporting the wheel, and by which it was adjusted to the height of the tide, was coincident with the axis of the trundle, so that the latter engaged the 8-feet cog-wheel in all conditions of vertical adjustment. Cranks operated one end of the beams while pumps were attached to the other end.

Fig. 116 exhibits an _overshot water wheel_ employed at Laxey, Isle of Man, for driving the pumps which drain the mines at that village; these have an extreme depth of 1,380 feet. The wheel is 72 feet 6 inches in diameter, 6 feet in breadth, exerts a force of about 200 horse-power and is capable of pumping 250 gallons per min. from a depth of 1,200 feet. Its crank-stroke is 10 feet. The water for driving it is conducted by pipes from a reservoir on a neighboring hill, and ascends in the column of masonry shown to the left of the wheel. (Knight Vol. III.) An extra crank appears to be shown in the foreground of this reproduction of an old drawing.

TURBINE WATER WHEELS.

The word turbine is derived from the Latin, “_turbo_”—that which spins or whirls around—a whirlwind.

The _turbine_ is a horizontal water wheel, and is similar to the _hydraulic tourniquet_ or reaction wheel shown in Fig. 117. This consists of a glass vessel, M, containing water and capable of moving about its vertical axis. At the lower part there is a tube, C, bent horizontally in opposite direction at the two ends. If the vessel were full of water and the tubes closed, the pressure of the sides of C would balance each other, being equal and acting in contrary direction: but, being open, the water runs out and the pressure is not exerted on the open part but only on the opposite side, as shown in the figure A.

And this pressure, not being neutralized by an opposite pressure, imparts a rotary motion in the direction of the arrow, the velocity of which increases with the height of the liquid and the size of the aperture. This description and the illustration gives an idea of the crude _reaction wheel_ invented by Barker about 1740; again a turbine is simply a centrifugal pump reversed, but the turbine is usually furnished with curved _guide vanes_ to guide the water as it enters the wheel.

NOTE.—The _steam turbine_ has come into common use and competes in
its economical performance with the simpler and less economical
types of the steam engine; it is impelled by steam jets, the steam
impinging upon vanes or buckets on the circumference of a rotating
disc or cylinder.

_In those turbines which are without guide blades_—i. e., which have a high fall—the discharged water still possesses a great velocity and the wheel is thereby deprived of a considerable part of mechanical power. This loss can, however, be obviated or lessened by using the energy of this discharged water to drive a second wheel.

A construction of this sort has been carried out by Ober-Bergrath Althaus in the tanning mill at Vallendar near Ehrenbreitstein. The essential parts of the arrangement can be seen in Fig. 118. A E A is an ordinary reaction wheel with four curved revolving pipes and a fall of 124 ft., and B B is a larger wheel with floats which is set in rotation by the water issuing from A. A. _Since the two wheels turn in opposite directions, they must be connected together by a special form of wheel-work._ The outer wheel affords the additional advantage of serving at the same time as a fly-wheel, thereby giving a more uniform rate of motion to the whole machinery.

Turbines are variously constructed, but all have curved floats or buckets against which the water acts by its impulse or reaction in flowing either _outward_ from a 1 central chamber, 2 _inward_ from an external casing, 3 _from above downward_, and, 4 from _below_; these constructions are either divided into _outward, vertical or central discharge wheels_.

Turbines may also be divided into _reaction turbines_, or those actuated substantially by the water passing through them (their buckets moving in a direction opposite to that of the flow); _impulse turbines_ or those principally driven by impact against their blades or buckets (the buckets moving with the flow); and _combined reaction and impulse wheels_ which include the best modern types of turbines. In reaction turbines the wheel passages are designed to be always full and therefore the water under pressure; in the impulse turbine the passages are not usually full.

Turbines in which the water flows in a direction parallel to the axis are called _parallel flow turbines_—or _journal turbines_.

The _turbine-dynamometer_ is a device used for measurings or testing the power delivered by turbines (whence its name).

_Fourneyron’s Turbine._ This is, in its latest form, when properly constructed, the nearest perfect of the horizontal water-wheels. It revolves either in the air or under water, and may be either high or low pressure. For the low-pressure wheel, the water enters the flume from the open reservoir, with free surface, as in Fig. 119. For high pressure, the reservoir is boxed up and the water brought in at the side through a pipe, as shown in Fig. 124, page 136. The first is for low and the second for high falls.

NOTE.—The early history of the turbine is one of considerable
interest _especially in view of the development of the steam, from
the water turbine_.

“M. Fourneyron, who began his experiments in 1823, erected his
first turbine in 1827, at Pont sur l’Ognon, in France. The result
far exceeded his expectations, but he had much prejudice to contend
with, and it was not until 1834 that he constructed another, in
Franche Comté at the iron-works of M. Caron, to blow a furnace. It
was of 7 or 8 horse-power, and worked at times with a fall of only 9
inches. Its performance was so satisfactory that the same proprietor
had afterwards another of 50 horse-power erected, to replace 2
water-wheels, which together, were equal to 30 horse-power. The fall
of water was 4 feet 3 inches, and the useful effect, varied with the
head and the immersion of the turbine, 65 to 80 per cent. Several
others were now erected: 2 for falls of seven feet; 1 at Inval,
near Gisors, for a fall of 6 feet 6 inches, the power being nearly
40-horse, on the river Epté, expending 35 cubic feet of water per
second, the useful effect being 71 per cent. of the force employed.”

_The Leffel-Samson turbine_ wheel is shown in the engraving, Fig. 120, page 129, where _N.N._ represents the bottom casting of the case flanged to support the wheel by resting upon the bottom of the penstock.

The draft tube _I_ is of conical shape as represented at _J. J._ to reduce the friction of discharge water which after performing its work in the wheel escapes at the bottom of the draft tube. _This tube must always project into the tail water at least two or three inches._ The gates _H.H.H._ are pivoted at the center so that they are balanced and are opened and closed with the least possible friction. These gates are operated by rods _L. L._, connecting with a rack and pinion which are manipulated by the operator as occasion requires, by an extension shaft from the coupling _K_, having a hand-wheel on top.

Power is transmitted from the wheel shaft _F_ to the gears and pulleys connected with the coupling above; the manner of setting turbine wheels in openstocks is shown a few pages further on.

From the construction of gates and guides upon turbine wheels one may readily see the absolute necessity of carefully guarding the flume against the admission of sticks and other solid materials that might wreck the wheel or jam the gates so that they could not be operated; this is best accomplished by placing a water rack in front of the head gate at the entrance to the flume.

These water racks are best made of flat bars of wrought iron placed edgewise in a vertical position, or what is better, let the top incline say one foot or two (depending upon the size of flume) towards the head gates. When placed in an inclined position it is very much easier to clean the rack from drift wood and the like than when placed in a vertical position as by means of a hoe or scraper these obstructions may be hauled up over the top of the inclined rack.

The racks should be made very strong and substantial to guard against being broken by ice in the winter, for should the rack give way at any inopportune time the admission of sticks and other rubbish might wreck the wheel.

The “runner” which is the revolving part, as shown in Fig. 121, is composed of two separate and distinct types of wheels, and has two diameters, as shown. Each wheel or set of buckets receives its separate quantity of water from one and the same set of guides but each set acts only once and independently upon the water used, hence the water does not act twice upon the combined wheel as might be supposed, as in the compound steam engine.

The upper wheel _G_ receives the water as shown by the arrows at _A_, and has _a central and downward discharge_, while the lower wheel _C_ receives the water as shown by the arrows at _B_ and has an _inward, downward and outward_ discharge as shown by the arrows at _D_.

These two sets of buckets need to be exceedingly strong. The lower set _B_ are made of heavy flanged steel plate and are cast into their places by being placed in the sand mould, and the cast iron flows around them forming the heavy ring _C_, surrounding the outer and lower edges. This ring is a part of the diaphragm which separates the two wheels. The upper edge of the ring _C_ is beveled to form a neat joint which prevents any unnecessary loss of water.

This runner is balanced and secured to a hammered iron or steel shaft _F_. It is supported usually by a step of the best specially selected hard wood thoroughly soaked in oil for months before use. The lower end of the shaft is dished out at _E_, forming a true arc of a circle—concave—while the wooden step is made spherical—convex—to fit into the end of the shaft. The step is formed in this way so that no sand can lodge between the bearing surfaces, and cut them out. The resident oil in the wood combined with the water make a most durable means of lubrication, and these steps last for many months where the water is clear.

To get at the exact quantity of water consumed by a turbine wheel, one cannot make an accurate calculation from the openings through the wheels but the water is measured after it has passed through the wheel, as it flows away into the tail race. Any slight variation in the form of buckets or admission apertures will make an appreciable variation in the quantity of water discharged by a turbine wheel.

These wheels are made either for vertical or horizontal shafts and are also made single or double. The engraving, Fig. 122, shows a _Hercules turbine within the case and gate ready to set in the penstock_.

Up to the year 1876 this make of wheel tested at the flume of the Holyoke Water Works showed the highest efficiency at all stages of gate, namely 87 per cent. (page 97, Emerson’s tests).

The design of case will naturally lead the reader to conclude that this wheel has, 1, an inward, 2, downward and, 3, an outward discharge which is correct. _The gate is simply a curb_ or hollow cylinder which forms a sleeve outside the case and is raised and lowered by the gearing and rack shewn in the engraving. As this sleeve rises it gradually uncovers the openings shown which admits water into the wheel.

_Horizontal Turbine_—The turbine of 10,500 horse power installed in the Shawinigan plant, Canada, see IV Pt. 2. is of _the horizontal type_, the water entering at, A, the lowest part of the turbine and flows around and fills the outer special tube, passes through an annular gate, flows radially through the wheel thence out through two draft tubes, B, one on each side. The weight of the water wheel is 182 tons, the shaft weighing 10 tons and the bronze runner 5 tons. It is 30 feet from base to top and 32 feet 2-1/2 inches wide over all. The shaft, C, is of solid forged steel, 22 inches diameter in the middle, tapering down to 10 inches diameter on one end and 16 inches diameter on the other, the distance between bearings being 27 feet. The intake is 10 feet in diameter and the quantity of water going through the turbine when developing full power is 395,000 gallons a minute. The speed of the wheel is 180 revolutions per minute with a head of water acting on the turbine of 125 to 135 feet.

Fig 123 is designed to show _The Setting of a turbine wheel in a wooden penstock_.

The principal and most essential dimensions necessary to be considered in setting turbines are indicated by letters, each size having its own particular dimensions.

_In setting the wheel_ in the ordinary penstock it is necessary in the first place, to have the floor exactly level, and it is generally more convenient to lay down a ring of soft wood around the hole in the floor, as it will be much easier to dress off with a plane than the plank floor. The floor should be supported by posts under the timbers around the hole, so that there will be no settling of the floor after being once made level. As the flange on which the wheel rests is turned true, the wheel will, when placed on this level floor, stand in the exact position required, _i. e._, the shaft will be exactly vertical.

If the wheel is a large one and was taken apart for shipment, the draft tube is first erected in position, then the wheel is placed on its step, the other parts being put on in their order. The step and other bearings are adjusted before leaving the shop, but it will sometimes happen that they will in some way get shifted, and as the wheel is being put together, they should be inspected and readjusted, if necessary. The only change that can occur in the step is its vertical adjustment, which is regulated by screws. When the right height is found, the broad flange around the lower part of the wheel should stand about one-sixteenth of an inch below the under side of the base of the guide rim where it rests upon the draft tube. The adjustable bearing on the top of the cover plate should be fitted up closely around the shaft, but not screwed so tightly as to bind it.

All these wheels above fifteen inches in diameter are provided with chains and weights to counterbalance the weight of the gate, so that it will move easily. It is best, when it can be done without much trouble, to carry the weights outside of the flume, but they can be used inside where the height is sufficient, although it will require a little more weight to be as effective. When the wheel is not likely to be started up at once, it is a good plan, when putting it together, to smear the step and the shaft at the bearing with tallow, as a protection against rust while it remains idle.

It is sometimes necessary to use a draft tube longer than is ordinarily attached to the wheel. If properly constructed and applied there will be no sensible loss of power, but it must be air tight, and when of considerable length it is better enlarged gradually toward the lower end, especially in cases where it may be necessary to carry this tube near the pit bottom.

_Iron cases for Turbines._ Fig. 124 shows the setting of a Hercules wheel within an iron case.

Although the expense of iron is as a rule considerably greater than wood, the results obtained by the use of iron cases and penstocks are much better than could be possible with wood, on account of their durability and freedom from leakage.

It is generally conceded that there is a great risk of the step becoming heated and burning out when placed in a draft tube above the tail-water, and a jet of water is required to counteract this tendency to overheat. As all such fixtures are liable to derangement and often fail to operate, we are in favor of setting the wheel with the step immersed, whenever it can be done without too great expense.

This case consists of two cast iron heads with boiler iron sides and is provided with a cover, so that the wheel may be taken out entire. This cover is fitted with stuffing boxes for both wheel and gate shafts, and a manhole affords easy access to the wheel. The bearing surfaces of the heads are nicely turned, insuring tight joints, and all holes for rivets are accurately spaced and drilled. The heads of the larger cases are made to clamp, the two halves being planed together; the cases are fitted with mouthpieces having cast iron flanges for feeder connections, to secure by bolts to either iron or wooden feeders.

Where two wheels of the same or different diameters are to be used, corresponding cases connected in the centre with one common feeder connection, or are placed in cases provided with separate feeders. In connection with these cases an _iron draft tube of any desired length may be used_. The wheel is usually fitted to the case before leaving the works, and in erecting the smaller wheels, all that remains to be done is to set the case on the foundations provided for it and make the necessary connections as stated in explanation previously made for Figs. 122 and 123.

The general arrangements required for the proper erection of turbines are well understood by competent millwrights and do not in ordinary cases present any serious difficulties. It may be of interest to many, and to the advantage of some who may consider the use of water power, if a few general remarks on this subject are added.

In practice there is almost always a little loss of head due to the velocity with which the water passes through the channels leading to and away from the wheel, and it should be the aim in constructing flumes to bring the loss to a minimum. When the size of the wheel and the quantity of water to be used have been determined, 1, the size of the conduit for carrying the water to the wheel, 2, the width and depth of the wheel-pit and tail-race, and 3, the dimensions and location of the flume for the wheel are to be considered and properly arranged.

All of these should be of such dimensions as to insure the flow of water through them at a moderate velocity, and with as little change of direction as may be practicable.

The larger the pipe or canal the better, but there must be a limit in practice, and it may be laid down as a general rule that a velocity of _three feet per second_ is good practice in short tubes of uniform section of not more than fifty feet in length; but _the velocity should be reduced as the distance increases_, until in a length of 200 feet, it should not exceed two feet per second.

The same rule applies to the tail-race, except that the velocity should be somewhat lower in ditches cut through rock or earth and having the naturally resulting roughness of sides and bottom.