Electricity for the farm Part 3

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 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 pa.s.s 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 cu. ft. per second (B) Sq. Inches of wheel = -------------------------- Velocity in ft. per sec.

Subst.i.tuting values, in the above instance, we have:

Answer: Sq. Inches of wheel =

144 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.

_What Head is Required_

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 horsepower required (C) Head in feet = ------------------------------ Cu. Ft. per minute 62.5

Since a theoretical horsepower is only 75 per cent efficient, he would require 10 4/3 = 13.33 theoretical horsepower of water, in this instance. Subst.i.tuting the values of the problem in the formula, we have:

33,000 13.33 Answer: Head = ---------------- = 17.6 feet fall required.

400 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. Subst.i.tuting these values, in formula (B) then, we have:

Answer: Capacity of wheel =

144 6.67 ---------- = 28.6 square inches of water.

33.6

_Quant.i.ty of Water_

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 quant.i.ty of water will be necessary, and what capacity wheel?_

Twenty actual horsepower will be 20 4/3 = 26.67 theoretical horsepower. Formula:

33,000 Hp. required (D) Cubic feet per minute = --------------------- (Head in feet 62.5)

Subst.i.tuting values, then, we have:

Cu. ft. per minute =

33,000 26.67 -------------- = 521.5 cubic feet a minute.

27 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 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.

CHAPTER IV

THE WATER WHEEL AND HOW TO INSTALL IT

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 quant.i.ty 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.

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-fas.h.i.+oned _undershot_, _overshot_, and _breast_ wheels are familiar to all as examples of impulse wheels. Water wheels of this cla.s.s 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-fas.h.i.+oned 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 Impulse, or Tangential Water Wheel_

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 furnis.h.i.+ng 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.

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.