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TABLE showing the Head necessary to overcome the Friction of Water in Horizontal Pipes,

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Feet. Inches. Feet. Inches. Feet. Inches.

Feet. Inches.

Feet. Inches. Feet. Inches. Feet. Inches. Feet. Inches. Feet. Inches.

Feet. Inches.

0

6

1

0

6

2

0

2

6

3

0

3

6

4

0

4

6

5

0

Bore of the
Pipes.

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Look for the velocity of water in the pipe in the upper line, and in the column beneath it, and opposite to the given diameter, is the height of the column or head requisite to overcome the friction of such pipe for 100 feet in length, and obtain the required velocity.

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GENERAL RULES.

Discharge by Horizontal Pipes.

1. THE less the diameter of the pipe, the less is the proportional discharge of the fluid.

2. The greater the length of the discharging pipe, the greater the diminution of the discharge. Hence, the discharges made in equal times by pipes of different lengths, of the same diameter, and under the same altitude of water, are to one another in the inverse ratio of the square roots of their lengths. *See note, p. 175. 3. The friction of a fluid is proportionally greater in small than in large pipes. 4. The velocity of water flowing out of an aperture is as the square root of the height of the head of the water.

Theoretically the velocity would be height ×8. ✔height 5.4 velocity in feet per second.

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Discharge by Vertical Pipes.

In practice it is

The discharge of fluids by vertical pipes is augmented, on the principle of the gravitation of falling bodies; consequently, the greater the length of the pipe, the greater the discharge of the fluid.

Discharge by Inclined Pipes.

A pipe which is inclined will discharge in a given time a greater quantity of water than a horizontal pipe of the same dimensions.

Deductions from various Experiments.

1. The areas of orifices being equal, that which has the smallest perimeter will discharge the most water under equal heads; hence circular apertures are the most advantageous.

2. That in consequence of the additional contraction of the fluid vein, as the head of the fluid increases the discharge is a little diminished.

3. That the discharge of a fluid through a cylindrical horizontal tube, the diameter and length of which are equal to one another, is the same as through a simple orifice.

4. That the above tube may be increased to four times the diameter of the orifice with advantage.

8.

5. The velocity of motion that would result from the direct, unretarded action of the column of a fluid which produces it, being a constant, or The velocity through an aperture in a thin plate, with the same pressure, is 5. Through a tube from two to three diameters in length, projecting outward, 6.5 Through a tube of the same length, projecting inward. Through a conical tube of the form of the contracted vein

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5.45

7.9

Curvilineal and rectangular pipes discharge less of a fluid than rectilineal pipes.

Discharge from Reservoirs receiving no Supply of Water.

For prismatic vessels the general law applies, that twice as much would be discharged from the same orifice if the vessel were kept full during the time which is required for emptying itself.

Discharges from Compound or Divided Reservoirs.

The velocity in each may be considered as generated by the difference of the heights in the two contiguous reservoirs; consequently, the square root of the difference will represent the velocity, which, if there are several orifices, must be inyersely as their respective areas.

Discharge by Weirs and Rectangular Notches.

The quantity of water discharged is found by taking of the velocity due to the mean height, using 5.1 for the coefficient of the velocity.

EXAMPLE. What quantity of water will flow from a pond, over a weir 102 inches in length by 12 inches deep?

1 foot X 5.1X 8.5 area of weir=28.9 cubic feet in one second.

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TABLE of the Rise of Water in Rivers, occasioned by the erection of Piers, &c.

Velocity of
current in
feet per sec.

Amount of obstruction compared with area of section of the river.

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Velocity of Water in Pipes or Sewers.

The time occupied in an equal quantity of water through a pipe or sewer of equal lengths, and with equal falls, is proportionally as follows:

In a right line as 90, in a true curve as 100, and in passing a right angle as 140. The resistance that a body sustains in moving through a fluid is in proportion to the square of the velocity.

The resistance that any plane surface encounters in moving through a fluid with any velocity is equal to the weight of a column whose height is the space a body would have to fall through in free space to acquire that velocity, and whose base is the surface of the plane.

EXAMPLE. If a plané, 10 inches square, move through water at the rate of 8 feet per second, then 82÷64-1. the space a body would require to fall to acquire a velocity of 8 feet per second; and as 1 foot 12 inches, then 10×12 = 120 cubic inches, the column of water whose height and base are required.

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As 1728 120 1000 69.4, or 4.3 lbs., which is the amount of resistance met with by the plane at the above velocity.

And it is the same, whether the plane moves against the fluid or the fluid against the plane.

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The following Table shows the results of experiments with a plane one foot square, at an immersion of 3 feet below the surface, and at different velocities per second.

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*NOTE.

This is a deduction of M. Bossut.

A formula handed me by Mr. J. Findlay is here given, and, from its apparent truth in comparison with the preceding rule, I would recommend its application. Let d represent diameter of pipe, h the height of it, and 7 the length.

Then,

2500 dXh
150 d

= v.

WATER WHEELS.

THIS subject belongs properly to Hydrodynamics, but a separate classification is here deemed preferable.

WATER WHEELS are of three kinds, viz., the Overshot, Undershot, and Breast.

The Overshot Wheel is the most advantageous, as it gives the greatest power with the least quantity of water. The next in order, in point of efficiency, is the Breast Wheel, which may be considered a mean between the Overshot and the Undershot. For a small supply of water with a high fall, the first should be employed; where the quantity of water and height of fall are both moderate, the second form should be used. For a large supply of water with a low fall, the third form must be resorted to.

Before proceeding to erect a water wheel, the area of the stream and the head that can be used must be measured.

Find the velocity acquired by the water in falling through that height by the rule, viz.: Extract the square root of the height of the head of the water (from the surface to the middle of the gate), and multiply it by 8.

NOTE.-Where the opening is small, and the head of water is great, or propor tionally so, use from 5.5 to 8 for the multiplier.

EXAMPLE. The dimensions of a stream are 2 by 80 inches, from a head of 2 feet to the upper surface of the stream; what is the velocity of the water per minute, and what is its weight?

2 feet and of 2 inches

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25 inches 2.08 feet, √2.08×*6.5× 60561.60 feet velocity per minute.

And 80×2×561.6 feet 12 inches, ÷1728624 cubic feet, X 62 lbs. 39000 lbs. of water discharged in one minute.

To find the Power of an Overshot Wheel.

RULE.-Multiply the weight of water in lbs. discharged upon the wheel in one minute by the height or distance in feet from the lower edge of the wheel to the centre of the opening in the gate; divide the product by 50000, and the quotient is the number of horses' power.

EXAMPLE. In the preceding example, the weight of the water discharged per minute is 39000 lbs. If the height of the fall is 23 feet, the diameter of the wheel being 22, what is the power of the wheel?

23 feet 8 inches clearance below 22.4 22.33.
39000×22.33 50000 17.41 horses' power, Ans.

To find the Power of a Stream.

RULE.-Multiply the weight of the water in lbs. discharged in one minute by the height of the fall in feet; divide by 33000, and the quotient is the answer.

* Estimate of velocity.

EXAMPLE.-What power is a stream of water equal to of the following dimensions, viz.: 1 foot deep by 22 inches broad, velocity 350 feet per minute, and fall 60 feet; and what should be the size of the wheel applied to it?

12×22×350×12÷1728×621×60 feet

33000=72.9, Ans.

Height of fall 60 feet, from which deduct for admission of water, and clearance below, 15 inches, which gives 58.9 feet for the diarneter of the wheel.

Clearance above 3 15 inches.

below 12

The power of a stream, applied to an overshot wheel, produces effect as 10 to 6.6.

Then, as 10: 6.6 :: 72.9: 48 horses' power equal that of an overshot wheel of 60 feet applied to this stream.

When the fall exceeds 10 feet, the overshot wheel should be applied.

The higher the wheel is in proportion to the whole descent, the greater will be the effect.

The effect is as the quantity of water and its perpendicular height multiplied together.

The weight of the arch of loaded buckets in pounds, is found by multiplying of their number, X the number of cubic feet in each, and that product by 40.

To find the Power of an Undershot Wheel when the Stream is confined to the Wheel.

RULE.-Ascertain the weight of the water discharged against the floats of the wheel in one minute by the preceding rules, and divide it by 100000; the quotient is the number of horses' power.

NOTE.-The 100000 is obtained thus: The power of a stream, applied to an undershot wheel, produces effect as 10 to 3.3; then 3.3: 10 :: 33000: 100000.

When the opening is above the centre of the floats, multiply the weight of the water by the height, as in the rule for an overshot wheel.

EXAMPLE. What is the power of an undershot wheel, applied to a stream 2 by 80 inches, from a head of 25 feet!

√25×6.5×60 1950 feet velocity of water per minute, and 2X80 160 inches 1950×12÷17282166.6 cubic feet 62.5=

*135412 lbs. of water discharged in one minute; thien 135412÷ 100000 1.35 horses' power.

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NOTE. The maximum work is always obtained when the velocity of the wheel is half that of the stream. Let V represent velocity of float boards, and v velocity of water; then X force of the water, will be the force of the effective stroke.

The effect of an undershot wheel to the power expended is, at a medium, one half that of an overshot wheel.

The virtual or effective head being the same, the effect will be very nearly as the quantity of water expended.

When the fall is below 4 feet, an undershot wheel should be applied.

To find the Power of a Breast Wheel.

RULE.Find the effect of an undershot wheel, the head of water Jof which is the difference of level between the surface and where it strikes the wheel (breast), and add to it the effect of that of an overshot wheel, the height of the head of which is equal to the differ

* Equal 160x12÷1728×62.5X1950 momentum of water and its velocity.

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