Filed under: Water Power | Tags: earth energy, electric power plants, farm power, Impulse Water Wheel, water powered farm
The reaction turbine is best adapted to low heads, with a large supply
of water. It is not advisable, under ordinary circumstances, to use it
under heads exceeding 100 feet, as its speed is then excessive. It
may be used under falls as low as two feet. Five thousand cubic feet
of water a minute would give approximately 14 actual horsepower under
such a head. A sluggish creek that flows in large volume could thus be
utilized for power with the reaction turbine, whereas it would be
useless with an impulse wheel. Falls of from five to fifteen feet are
to be found on thousands of farm streams, and the reaction turbine is
admirably adapted to them.
Reaction turbines consist of an iron “runner” which is in effect a
rotary fan, the pressure and momentum of the column of water pressing
on the slanted blades giving it motion and power. These wheels are
manufactured in a great variety of forms and sizes; and are to be
purchased either as the runner (set in bearings) alone, or as a runner
enclosed in an iron case. In case the runner alone is purchased, the
owner must enclose it, either with iron or wood. They vary in price
according to size, and the means by which the flow of water is
controlled. A simple 12-inch reaction turbine wheel, such as would be
suitable for many power plants can be had for $75. A twelve-inch
wheel, using 18 or 20 square inches of water, would generate about
7-1/2 horsepower under a 20-foot head, with 268 cubic feet of water a
minute. Under a 30-foot head, and with 330 cubic feet of water such a
wheel will give 14 horsepower. A 36-inch wheel, under a 5-foot head,
would use 2,000 cubic feet of water, and give 14 horsepower. Under a
30-foot head, this same wheel, using 4,900 cubic feet of water a
minute, would develop over 200 horsepower. If the farmer is confronted
by the situation of a great deal of water and small head, a large
wheel would be necessary. Thus he could secure 35 horsepower with only
a 3-foot head, providing his water supply is equal to the draft of
8,300 cubic feet a minute.
From these sample figures, it will be seen that the reaction turbine
will meet the requirements of widely varying conditions up to, say a
head of 100 feet. The farmer prospector should measure first the
quantity of water to be depended on, and then the number of feet fall
to be had. The higher the fall, with certain limits, the smaller the
expense of installation, and the less water required. When he has
determined _quantity_ and _head_, the catalogue of a reputable
manufacturer will supply him with what information is necessary to
decide on the style and size wheel he should install. In the older
settled communities, especially in New England, a farmer should be
able to pick up a second-hand turbine, at half the price asked for a
new one; and since these wheels do not depreciate rapidly, it would
serve his purpose as well, in most cases, as a new one.
Reaction turbines may be either horizontal or vertical. If they are
vertical, it is necessary to connect them to the main shaft by means
of a set of bevel gears. These gears should be substantially large,
and if the teeth are of hard wood (set in such a manner that they can
be replaced when worn) they will be found more satisfactory than if of
cast or cut metal.
The horizontal turbine is keyed to its shaft, like the impulse wheel,
so that the wheel shaft itself is used for driving, without gears or a
quarter-turn belt. (The latter is to be avoided, wherever possible.)
There are many forms of horizontal turbines; they are to be had of the
duplex type, that is, two wheels on one shaft. These are arranged so
that either wheel may be run separately, or both together, thus
permitting one to take advantage of the seasonal fluctuation in water
supply. A convenient form of these wheels includes draft tubes, by
which the wheel may be set several feet above the tailrace, and the
advantage of this additional fall still be preserved. In this case the
draft tube must be airtight so as to form suction, when filled with
escaping water, and should be proportioned to the size of the wheel.
Theoretically these draft tubes might be 34 feet long, but in practice
it has been found that they should not exceed 10 or 12 feet under
ordinary circumstances. They permit the wheel to be installed on the
main floor of the power station, with the escape below, instead of
being set just above the tailrace level itself, as is the case when
draft tubes are not used.
Reaction turbines when working under a variable load require water
governors (like impulse wheels) although where the supply of water is
large, and the proportion of power between water wheel and dynamo is
liberal–say two to one, or more–this necessity is greatly reduced.
Reaction wheels as a rule govern themselves better than impulse
wheels, due both to the fact that they use more water, and that they
operate in a small airtight case. The centrifugal ball governor is the
type usually used with reaction wheels as well as with impulse wheels.
This subject will be discussed more fully later.
Filed under: Water Power | Tags: earth energy, Impulse Water Wheel, water powered farm
In recent years more efficient forms of the old-fashioned overshoot,
pitch-back breast, and undershoot wheels have been developed, by
substituting steel or other metal for wood, and altering the shape of
the buckets to make better use of the power of falling water.
In some forms of overshoot wheels, an efficiency of over 90 per cent
is claimed by manufacturers; and this type offers the additional
advantage of utilizing small quantities of water, as well as being
efficient under varying quantities of water. They utilize the falling
weight of water, although by giving the water momentum at the point of
delivery, by means of the proper fall, impulse too is utilized in some
measure. The modern steel overshoot wheel receives water in its
buckets from a spout set a few degrees back of dead center; and its
buckets are so shaped that the water is retained a full
half-revolution of the wheel. The old-style overshoot wheel was
inefficient principally because the buckets began emptying themselves
at the end of a quarter-revolution. Another advantage claimed for
these wheels over the old style is that, being made of thin metal,
their buckets attain the temperature of the water itself, thus
reducing the danger of freezing to a minimum. They are manufactured in
sizes from 6 feet in diameter to upwards of fifty feet; and with
buckets of from 6 inches to 10 feet in width. In practice it is usual
to deliver water to the buckets by means of a trough or pipe, through
a suitable spout and gate, at a point two feet above the crown of the
wheel. For this reason, the diameter of the wheel corresponds very
closely to the head in feet.
Filed under: Water Power | Tags: electric power plants, Impulse Water Wheel, measure water power, weir
The principal items of cost in installing an impulse wheel are in
connection with the pipe line, and the governor. In small heads, that
is, under 100 feet, the expense of pipe line is low. Frequently,
however, the governor will cost more than the water motor itself,
although cheaper, yet efficient, makes are now being put on the market
to meet this objection. In a later chapter, we will take up in detail
the question of governing the water wheel, and voltage regulation, and
will attempt to show how this expense may be practically eliminated by
the farmer.
To secure large heads, it is usually necessary to run a pipe line many
hundreds (and in many cases, many thousands) of feet from the flume to
the water wheel. Water flowing through pipes is subject to loss of
head, by friction, and for this reason the larger the pipe the less
the friction loss. Under no circumstances is it recommended to use a
pipe of less than two inches in diameter, even for the smallest water
motors; and with a two-inch pipe, the run should not exceed 200 feet.
Where heavy-pressure mains, such as those of municipal or commercial
water systems, are available, the problem of both water supply and
head becomes very simple. Merely ascertain the pressure of the water
in the mains _when flowing_, determine the amount of power required
(as illustrated in a succeeding chapter of this book), and install the
proper water motor with a suitably sized pipe.
Where one has his own water supply, however, and it is necessary to
lay pipe to secure the requisite fall, the problem is more difficult.
Friction in pipes acts in the same way as cutting down the head a
proportional amount; and by cutting down the head, your water motor
loses power in direct proportion to the number of feet head lost. This
head, obtained by subtracting friction and other losses from the
surveyed head, is called the _effective head_, and determines the
amount of power delivered at the nozzle.
Water Wheel for Power
In this example it is seen that a 240-foot static head is reduced by
friction to 230.1 feet effective head. By referring to the table we
find the wheel fitting these conditions has a nozzle so small that it
cuts down the rate of flow of water in the big pipe to 4.4 feet a
second, and permits the flow of only 207 cubic feet of water a minute.
The actual horsepower of this tube and nozzle, then, can be figured by
applying formula (A), Chapter III, allowing 80 per cent for the
efficiency of the wheel. Thus:
Actual horsepower =
207 x 230.1 x 62.5
—————— = 90.21 x .80 = 72.168 Hp.
33,000
To calculate what the horsepower of this tube 12 inches in diameter
and 900 feet long, would be without a nozzle, under a head of 240
feet, introduces a new element of friction losses, which is too
complicated to figure here. Such a condition would not be met with in
actual practice, in any event. The largest nozzles used, even in the
jumbo plants of the Far West, rarely exceed 10 inches in diameter; and
the pipe conveying water to such a nozzle is upwards of eight feet in
diameter.
PIPE FRICTION TABLES
INDICATING THE CALCULATED LOSS OF HEAD DUE TO FRICTION IN RIVETED
STEEL PIPE WITH VARIOUS WATER QUANTITIES AND VELOCITIES
[Courtesy of the Pelton Water Wheel Company]
Heavy-faced figures = Loss of head in feet for each one thousand
feet of pipe. Light-faced figures = Water quantity in cubic feet per
minute.
——–+——————————————————————————————-+
Pipe | Velocity in Feet per Second |
Diameter+——+——+——+——+——+——+——+——+——+——+——+——+——-+
| 2.0 | 2.2 | 2.4 | 2.6 | 2.8 | 3.0 | 3.2 | 3.4 | 3.6 | 3.8 | 4.0 | 4.2 | 4.4 |
——–+——+——+——+——+——+——+——+——+——+——+——+——+——-+
|=17.1=|=20.0=|=25.6=|=28.3=|=32.0=|=37.3=|=40.9=|=45.8=|=50.4=|=56.0=|=62.3=|=68.1=|=74.9= |
3″ | 5.9 | 6.5 | 7.1 | 7.7 | 8.3 | 8.9 | 9.4 | 10.0 | 10.6 | 11.2 | 11.8 | 12.4 | 13.0 |
|=11.0=|=13.0=|=15.0=|=17.3=|=20.2=|=23.2=|=26.2=|=29.6=|=33.0=|=36.5=|=41.0=|=45.4=|=49.2= |
4″ | 10.5 | 11.5 | 12.6 | 13.6 | 14.7 | 15.7 | 16.8 | 17.8 | 18.8 | 19.9 | 21.0 | 22.0 | 23.0 |
| =7.7=| =9.4=|=11.0=|=12.9=|=14.9=|=16.9=|=19.5=|=21.6=|=24.0=|=27.0=|=29.8=|=32.9=|=36.0= |
5″ | 16.4 | 18.0 | 19.6 | 21.2 | 22.9 | 24.5 | 26.1 | 27.8 | 29.5 | 31.0 | 32.7 | 34.3 | 36.0 |
| =6.0=| =7.2=| =8.6=| =9.9=|=11.7=|=13.0=|=14.6=|=16.6=|=19.0=|=21.5=|=23.4=|=25.5=|=27.8= |
6″ | 23.5 | 25.9 | 28.2 | 30.6 | 32.9 | 35.3 | 37.7 | 40.0 | 42.4 | 44.7 | 47.1 | 49.5 | 51.8 |
| =4.9 | =6.9=| =7.0=| =8.1=| =9.3=|=10.6=|=12.0=|=13.6=|=15.2=|=17.0=|=19.0=|=21.0=|=23.0= |
7″ | 32.0 | 35.3 | 38.5 | 41.7 | 44.9 | 48.1 | 51.3 | 54.5 | 57.7 | 60.9 | 64.1 | 67.3 | 70.5 |
| =4.0=| =4.9=| =6.0=| =6.9=| =7.8=| =9.1=|=10.0=|=10.2=|=13.0=|=14.4=|=15.9=|=17.2=|=19.2= |
8″ | 41.9 | 46.1 | 50.2 | 54.4 | 58.6 | 62.8 | 67.0 | 71.2 | 75.4 | 79.6 | 83.7 | 87.9 | 92.1 |
| =3.4=| =4.2=| =5.1=| =5.9=| =6.7=| =7.7=| =8.9=| =9.8=|=11.0=|=12.2=|=13.8=|=15.0=|=16.0= |
9″ | 53.0 | 58.3 | 63.6 | 68.9 | 74.2 | 79.5 | 84.8 | 90.1 | 95.4 |101 |106 |111 |116 |
| =2.9=| =3.7=| =4.4=| =5.1=| =5.9=| =6.7=| =7.5=| =8.6=| =9.5=|=10.6=|=12.1=|=13.1=|=14.1= |
10″ | 65.4 | 72.0 | 78.5 | 85.1 | 91.6 | 98.2 |105 |111 |118 |124 |131 |137 |144 |
| =2.6=| =3.2=| =3.8=| =4.4=| =5.1=| =5.9=| =6.6=| =7.5=| =8.4=| =9.5=|=10.3=|=10.1=|=12.5= |
11″ | 79 | 87 | 95 |103 |111 |119 |127 |134 |142 |150 |158 |166 |174 |
|=2.36=| =2.9=| =3.4=| =3.9=| =4.5=| =5.2=| =5.9=| =6.7=| =7.5=| =8.5=| =9.4=|=10.0=|=11.0= |
12″ |94 |103 |113 |122 |132 |141 |151 |160 |169 |179 |188 |198 |207 |
——–+——+——+——+——+——+——+——+——+——+——+——+——+——-+
——–+——+——+——+——+——-+——-+——-+——-+——-+——-+——-+——-+
| 4.6 | 4.8 | 5.0 | 5.2 | 5.4 | 5.6 | 5.8 | 6.0 | 7.0 | 8.0 | 9.0 | 10.0 |
——–+——+——+——+——+——-+——-+——-+——-+——-+——-+——-+——-+
|=78.1=|=82.0=|=89.5=|=98.9=|=105.0=|=113.2=|=120.8=|=130.0=|=162.8=|=216.0=|=270.= |=323.= |
3″ | 13.6 | 14.2 | 14.8 | 15.3 | 15.9 | 16.5 | 17.1 | 17.7 | 20.6 | 23.5 | 26.5 | 29.5 |
|=52.3=|=57.0=|=61.5=|=68.0=| =72.5=| =78.2=| =83.1=| =89.5=|=121.= |=155.= |=198.= |=242.= |
4″ | 24.1 | 25.1 | 26.2 | 27.2 | 28.3 | 29.3 | 30.4 | 31.5 | 36.6 | 41.9 | 47.2 | 52.4 |
|=39.2=|=42.3=|=46.0=|=49.8=| =53.5=| =58.0=| =62.0=| =67.0=| =89.= |=118.= |=148.= |=182.= |
5″ | 37.6 | 39.2 | 40.9 | 42.5 | 44.1 | 45.8 | 47.5 | 49.1 | 57.1 | 65.4 | 73.7 | 82.0 |
|=30.6=|=33.1=|=35.6=|=39.0=| =41.6=| =44.6=| =48.0=| =51.6=| =69.0=| =89.0=|=114.= |=140.= |
6″ | 54.1 | 56.5 | 58.9 | 61.2 | 63.6 | 65.9 | 68.3 | 70.7 | 82.4 | 94.3 | 106 | 118 |
|=25.1=|=27.3=|=29.5=|=32.0=| =34.5=| =37.1=| =40.0=| =43.0=| =58.0=| =75.0=| =95.0=|=116.= |
7″ | 73.7 | 76.9 | 80.2 | 83.3 | 86.6 | 89.8 | 93.0 | 96.2 | 112 | 128 | 145 | 161 |
|=20.0=|=22.5=|=24.9=|=27.0=| =28.8=| =30.6=| =32.8=| =35.5=| =47.5=| =61.2=| =78.6=| =95.1=|
8″ | 96.3 |101 |105 |109 | 113 | 117 | 121 | 125 | 146 | 168 | 189 | 210 |
|=17.1=|=19.2=|=21.0=|=22.9=| =24.6=| =26.2=| =28.0=| =30.1=| =40.1=| =52.1=| =66.6=| =82.0=|
9″ |122 |127 |132 |138 | 143 | 148 | 154 | 159 | 185 | 212 | 238 | 265 |
|=14.8=|=16.7=|=17.9=|=19.9=| =21.0=| =22.7=| =24.3=| =25.9=| =34.8=| =45.9=| =58.0=| =70.1=|
10″ |150 |157 |163 |170 | 177 | 183 | 190 | 196 | 229 | 261 | 295 | 327 |
|=13.0=|=14.7=|=15.9=|=17.1=| =18.2=| =20.1=| =21.3=| =22.6=| =30.7=| =40.0=| =50.8=| =62.0=|
11″ |182 |190 |198 |206 | 214 | 222 | 229 | 237 | 277 | 316 | 356 | 396 |
|=11.6=|=13.0=|=14.0=|=15.1=| =16.1=| =17.8=| =19.1=| =20.2=| =27.1=| =35.9=| =45.4=| =55.9=|
12″ |217 |226 |235 |245 | 254 | 264 | 273 | 283 | 330 | 377 | 425 | 472 |
——–+———+———-+——+——-+——-+——-+——-+——-+——-+——-+——-+
EXAMPLE
Assume the surveyed head as 240 feet, the water quantity as 207
cubic feet per minute and a pipe line 12 inches in diameter 900 feet
long. To ascertain the friction loss, refer to column of pipe
diameter and follow across the column for 12 inches diameter to the
quantity, 207 cubic feet per minute. The heavy-faced figures above
207 indicate that the loss per 1000 feet of pipe length is 11 feet.
Therefore, since the pipe in the example is 900 feet long, the loss
will be
11.’ x 900/1000 or 9.9 feet, and the effective head will be
240′ – 9.9′ = 230.1′
Steel tubing for supply pipes, from 3 to 12 inches in diameter is
listed at from 20 cents to $1.50 a foot, according to the diameter and
thickness of the material. Discounts on these prices will vary from 25
to 50 per cent. The farmer can cut down the cost of this pipe by
conveying his supply water from its natural source to a pond, by means
of an open race, or a wooden flume. An ingenious mechanic can even
The Efficient Water Wheel
construct his own pipe out of wood, though figuring labor and
materials, it is doubtful if anything would be saved over a riveted
steel pipe, purchased at the regular price. This pipe, leading from
the pond, or forebay, to the water wheel, should be kept as short as
possible; at the same time, the fall should not be too sharp. An angle
of 30 deg. will be found very satisfactory, although pipe is frequently
laid at angles up to 50 deg.
Filed under: Water Power | Tags: Impulse Water Wheel, Tangential Water Wheel, Water Power
The modern impulse, or tangential wheel (so called because the driving
stream of water strikes the wheel at a tangent) is best adapted to
situations where the amount of water is limited, and the head is
large. Thus, a mountain brook supplying only seven cubic feet of water
a minute–a stream less than two-and-a-half inches deep flowing over a
weir with an opening three inches wide–would develop two actual
horsepower, under a head of 200 feet–not an unusual head to be found
in the hill country. Under a head of one thousand feet, a stream
furnishing 352.6 cubic feet of water a minute would develop 534.01
horsepower at the nozzle.
Ordinarily these wheels are not used under heads of less than 20 feet.
The Efficient Water Wheel
A wheel of this type, six feet in diameter, would develop six
horsepower, with 188 cubic feet of water a minute and 20-foot head.
The great majority of impulse wheels are used under heads of 100 feet
and over. In this country the greatest head in use is slightly over
2,100 feet, although in Switzerland there is one plant utilizing a
head of over 5,000 feet.
Efficient Modern Adaptations of the Archaic Undershot and Overshot Water Wheels
The old-fashioned impulse wheels were inefficient because of the fact
that their buckets were not constructed scientifically, and much of
the force of the water was lost at the moment of impact. The impulse
wheel of to-day, however, has buckets which so completely absorb the
momentum of water issuing from a nozzle, that the water falls into the
tailrace with practically no velocity. When it is remembered that the
nozzle pressure under a 2,250-foot head is nearly 1,000 pounds to the
square inch, and that water issues from this nozzle with a velocity of
23,000 feet a minute, the scientific precision of this type of bucket
can be appreciated.
A typical bucket for such a wheel is shaped like an open clam shell,
the central line which cuts the stream of water into halves being
ground to a sharp edge. The curves which absorb the momentum of the
water are figured mathematically and in practice become polished like
mirrors. So great is the eroding action of water, under great
heads–especially when it contains sand or silt–that it is
occasionally necessary to replace these buckets. For this reason the
larger wheels consist merely of a spider of iron or steel, with each
bucket bolted separately to its circumference, so that it can be
removed and replaced easily. Usually only one nozzle is provided; but
in order to use this wheel under low heads–down to 10 feet–a number
of nozzles are used, sometimes five, where the water supply is
plentiful.
The wheel is keyed to a horizontal shaft running in babbited bearings,
and this same shaft is used for driving the generator, either by
direct connection, or by means of pulleys and a belt. The wheel may be
mounted on a home-made timber base, or on an iron frame. It takes up
very little room, especially when it is so set that the nozzle can be
mounted under the flooring. The wheel itself is enclosed, above the
floor, in a wooden box, or a casing made of cast or sheet iron, which
should be water-tight.
Since these wheels are usually operated under great heads, the problem
of regulating their water supply requires special consideration. A
gate is always provided at the upper, or intake end, where the water
pipe leaves the flume. Since the pressure reaches 1,000 pounds the
square inch and more, there would be danger of bursting the pipe if
the water were suddenly shut off at the nozzle itself. For this reason
it is necessary to use a needle valve, similar to that in an ordinary
garden hose nozzle; and by such a valve the amount of water may be
regulated to a nicety. Where the head is so great that even such a
valve could not be used safely, provision is made to deflect the
nozzle. These wheels have a speed variation amounting to as much as 25
per cent from no-load to full load, in generating electricity, and
since the speed of the prime mover–the water wheel–is reflected
directly in the voltage or pressure of electricity delivered, the
wheel must be provided with some form of automatic governor. This
consists usually of two centrifugal balls, similar to those used in
governing steam engines; these are connected by means of gears to the
needle valve or the deflector.
As the demand for farm water-powers in our hill sections becomes more
general, the tangential type of water wheel will come into common use
for small plants. At present it is most familiar in the great
commercial installations of the Far West, working under enormous
heads. These wheels are to be had in the market ranging in size from
six inches to six feet and over. Wheels ranging in size from six
inches to twenty-four inches are called water motors, and are to be
had in the market, new, for $300 for the smallest size, and $2750 for
the largest. Above three feet in diameter, the list prices will run
from $2000 for a 3-foot wheel to $8000 for a 6-foot wheel. Where one has
a surplus of water, it is possible to install a multiple nozzle wheel,
under heads of from 10 to 100 feet, the cost for 18-inch wheels of
this pattern running from $1500 to $1800 list, and for 24-inch wheels
from $2000 to $2500. A 24-inch wheel, with a 10-foot head would give
1.19 horsepower, enough for lighting the home, and using an electric
iron. Under a 100-foot head this same wheel would provide 25.9
horsepower, to meet the requirements of a bigger-than-average farm
plant.
Filed under: Water Power | Tags: Water Power, water powered farm, water wheels
In general, there are two types of water wheels, the _impulse_ wheel
and the _reaction_ wheel. Both are called turbines, although the name
belongs, more properly, to the reaction wheel alone.
Impulse wheels derive their power from the _momentum_ of falling
water. Reaction wheels derive their power from the _momentum and
pressure_ of falling water. The old-fashioned _undershot_, _overshot_,
and _breast_ wheels are familiar to all as examples of impulse
wheels. Water wheels of this class revolve in the air, with the energy
of the water exerted on one face of their buckets. On the other hand,
reaction wheels are enclosed in water-tight cases, either of metal or
of wood, and the buckets are entirely surrounded by water.
The old-fashioned undershot, overshot, and breast wheels were not very
efficient; they wasted about 75 per cent of the power applied to them.
A modern impulse wheel, on the other hand, operates at an efficiency
of 80 per cent and over. The loss is mainly through friction and
leakage, and cannot be eliminated altogether. The modern reaction
wheel, called the _turbine_, attains an equal efficiency. Individual
conditions govern the type of wheel to be selected.
The Topics we will cover in the upcoming days include:
Different types of water wheels–The impulse and reaction
wheels–The impulse wheel adapted to high heads and small amount of
water–Pipe lines–Table of resistance in pipes–Advantages and
disadvantages of the impulse wheel–Other forms of impulse
wheels–The reaction turbine, suited to low heads and large
quantity of water–Its advantages and limitations–Developing a
water-power project: the dam; the race; the flume; the penstock;
and the tailrace–Water rights for the farmer.
Filed under: Water Power | Tags: measure water power, water, water powered farm, water wheels
Let us take still another problem which the prospector may be called
on to solve: _A man finds that he can conveniently get a fall of 27
feet. He desires 20 actual horsepower. What quantity of water will be
necessary, and what capacity wheel?_
Twenty actual horsepower will be 20 x 4/3 = 26.67 theoretical
horsepower. Formula:
33,000 x Hp. required
(D) Cubic feet per minute = ———————
(Head in feet x 62.5)
Substituting values, then, we have:
Cu. ft. per minute =
33,000 x 26.67
————– = 521.5 cubic feet a minute.
27 x 62.5
A head of 27 feet would give this stream a velocity of 41.7 feet a
second, and, from formula (B) we find that the capacity of the wheel
The Efficient Water Wheel
should be 30 square inches.
It is well to remember that the square inches of wheel capacity does
not refer to the size of pipe conveying water from the head to the
wheel, but merely to the actual nozzle capacity provided by the wheel
itself. In small installations of low head, such as above a penstock
at least six times the nozzle capacity should be used, to avoid losing
effective head from friction. Thus, with a nozzle of 30 square inches,
the penstock or pipe should be 180 square inches, or nearly 14 inches
square inside measurement. A larger penstock would be still better.
Tommorrow THE WATER WHEEL AND HOW TO INSTALL IT
Filed under: Water Power | Tags: measure water power, water head, water wheels
Let us attack the problem of water-power in another way. _A farmer
wishes to install a water wheel that will deliver 10 horsepower on the
shaft, and he finds his stream delivers 400 cubic feet of water a
minute. How many feet fall is required?_ Formula:
33,000 x horsepower required
(C) Head in feet = ——————————
Cu. Ft. per minute x 62.5
Since a theoretical horsepower is only 75 per cent efficient, he would
require 10 x 4/3 = 13.33 theoretical horsepower of water, in this
instance. Substituting the values of the problem in the formula, we
have:
33,000 x 13.33
Answer: Head = —————- = 17.6 feet fall required.
400 x 62.5
_What capacity of wheel would this prospect (400 cubic feet of water a
minute falling 17.6 feet, and developing 13.33 horsepower) require?_
By referring to the table of velocities, we find that the velocity for
17.5 feet head (nearly) is 33.6 feet a second. Four hundred feet of
water a minute is 400/60 = 6.67 cu. ft. a second. Substituting these
values, in formula (B) then, we have:
Answer: Capacity of wheel =
144 x 6.67
———- = 28.6 square inches of water.
33.6
Filed under: Water Power | Tags: measure water power, water powered farm, water wheels
Water wheels are not rated by horsepower by manufacturers, because the
same wheel might develop one horsepower or one hundred horsepower, or
even a thousand horsepower, according to the conditions under which
it is used. With a given supply of water, the head, in feet,
determines the size of wheel necessary. The farther a stream of water
falls, the smaller the pipe necessary to carry a given number of
gallons past a given point in a given time.
A small wheel, under 10 x 13.5 ft. head, would give the same power
Small Water Wheel
with the above 376 cubic feet of water a minute, as a large wheel
would with 10 x 376 cubic feet, under a 13.5 foot head.
This is due to the _acceleration of gravity_ on falling bodies. A
rifle bullet shot into the air with a muzzle velocity of 3,000 feet a
second begins to diminish its speed instantly on leaving the muzzle,
and continues to diminish in speed at the fixed rate of 32.16 feet a
second, until it finally comes to a stop, and starts to descend. Then,
again, its speed accelerates at the rate of 32.16 feet a second, until
on striking the earth it has attained the velocity at which it left
the muzzle of the rifle, less loss due to friction.
The acceleration of gravity affects falling water in the same manner
as it affects a falling bullet. At any one second, during its course
of fall, it is traveling at a rate 32.16 feet a second in excess of
its speed the previous second.
In figuring the size wheel necessary under given conditions or to
determine the power of water with a given nozzle opening, it is
necessary to take this into account. The table on page 51 gives
velocity per second of falling water, ignoring the friction of the
pipe, in heads from 5 to 1000 feet.
The scientific formula from which the table is computed is expressed
as follows, for those of a mathematical turn of mind:
Velocity (ft. per sec.) = sqrt(2gh); or, velocity is equal to the
square root of the product (g = 32.16,–times head in feet, multiplied
by 2).
SPOUTING VELOCITY OF WATER, IN FEET PER SECOND, IN HEADS
OF FROM 5 TO 1,000 FEET
Head Velocity
5 17.9
The Efficient Water Wheel
6 19.7
7 21.2
8 22.7
9 24.1
10 25.4
11 26.6
11.5 27.2
12 27.8
12.5 28.4
13 28.9
13.5 29.5
14 30.0
14.5 30.5
15 31.3
15.5 31.6
16 32.1
16.5 32.6
17 33.1
17.5 33.6
18 34.0
18.5 34.5
19 35.0
19.5 35.4
20 35.9
20.5 36.3
21 36.8
21.5 37.2
22 37.6
22.5 38.1
23 38.5
23.5 38.9
24 39.3
24.5 39.7
25 40.1
26 40.9
27 41.7
28 42.5
29 43.2
30 43.9
31 44.7
32 45.4
33 46.1
34 46.7
35 47.4
36 48.1
37 48.8
38 49.5
39 50.1
40 50.7
41 51.3
42 52.0
43 52.6
44 53.2
45 53.8
46 54.4
47 55.0
48 55.6
49 56.2
50 56.7
55 59.5
60 62.1
65 64.7
70 67.1
75 69.5
80 71.8
85 74.0
90 76.1
95 78.2
100 80.3
200 114.0
300 139.0
400 160.0
500 179.0
1000 254.0
_In the above example, we found that 376 cubic feet of water a minute,
under 13.5 feet head, would deliver 7.2 actual horsepower. Question:
What size wheel would it be necessary to install under such
conditions?_
By referring to the table of velocity above, (or by using the
formula), we find that water under a head of 13.5 feet, has a spouting
velocity of 29.5 feet a second. This means that a solid stream of
water 29.5 feet long would pass through the wheel in one second. _What
should be the diameter of such a stream, to make its cubical contents
376 cubic feet a minute or 376/60 = 6.27 cubic feet a second?_ The
following formula should be used to determine this:
144 x cu. ft. per second
(B) Sq. Inches of wheel = ————————–
Velocity in ft. per sec.
Substituting values, in the above instance, we have:
Answer: Sq. Inches of wheel =
144 x 6.27 (Cu. Ft. Sec.)
————————— = 30.6 sq. in.
29.5 (Vel. in feet.)
That is, a wheel capable of using 30.6 square inches of water would
meet these conditions.
By one of the above simple methods, the problem of _Quantity_ can
easily be determined. The next problem is to determine what _Head_ can
be obtained. _Head_ is the distance in feet the water may be made to
fall, from the Source of Supply, to the water wheel itself. The power
of water is directly proportional to _head_, just as it is directly
proportional to _quantity_. Thus the typical weir measured above was
30 inches wide and 6-1/4 deep, giving 189 cubic feet of water a
minute–_Quantity._ Since such a stream is of common occurrence on
thousands of farms, let us analyze briefly its possibilities for
power: One hundred and eighty-nine cubic feet of water weighs 189 x
62.5 pounds = 11,812.5 pounds. Drop this weight one foot, and we have
11,812.5 foot-pounds. Drop it 3 feet and we have 11,812 x 3 =
35,437.5 foot-pounds. Since 33,000 foot-pounds exerted in one minute
is one horsepower, we have here a little more than one horsepower. For
simplicity let us call it a horsepower.
Now, since the work to be had from this water varies directly with
_quantity_ and _head_, it is obvious that a stream _one-half_ as big
Water Wheel for Power
falling _twice_ as far, would still give one horsepower at the wheel;
or, a stream of 189 cubic feet a minute falling _ten times_ as far, 30
feet, would give _ten times_ the power, or _ten_ horsepower; a stream
falling _one hundred times_ as far would give _one hundred_
horsepower. Thus small quantities of water falling great distances, or
large quantities of water falling small distances may accomplish the
same results. From this it will be seen, that the simple formula for
determining the theoretical horsepower of any stream, in which
Quantity and Head are known, is as follows:
Cu. Ft.
per Feet
minute x head x 62.5
(A) Theoretical Horsepower = ———————-
33,000
_As an example, let us say that we have a stream whose weir
measurement shows it capable of delivering 376 cubic feet a minute,
with a head (determined by survey) of 13 feet 6 inches. What is the
horsepower of this stream?_
Answer:
Cu. ft. p. m. head pounds
376 x 13.5 x 62.5
H.P. = —————————– = 9.614 horsepower
33,000
This is _theoretical horsepower_. To determine the _actual_ horsepower
that can be counted on, in practice, it is customary, with small water
wheels, to figure 25 per cent loss through friction, etc. In this
instance, the actual horsepower would then be 7.2.
Filed under: Water Power | Tags: measure a stream, measure water power, water wheels
Weirs are for use in small streams. For larger streams, where the
construction of a weir would be difficult, the U. S. Geological Survey
engineers recommend the following simple method:
Measuring Larger Streams
Choose a place where the channel is straight for 100 or 200 feet, and
has a nearly constant depth and width; lay off on the bank a line 50
or 100 feet in length. Throw small chips into the stream, and measure
the time in seconds they take to travel the distance laid off on the
bank. This gives the surface velocity of the water. Multiply the
average of several such tests by 0.80, which will give very nearly the
mean velocity. Then it is necessary to find the cross-section of the
flowing water (its average depth multiplied by width), and this
number, in square feet, multiplied by the velocity in feet per second,
will give the number of cubic feet the stream is delivering each
second. Multiplied by 60 gives cubic feet a minute.
