consistent with the nature of this work. The method which we shall give is simple, and will be found to answer all the purposes of the practical man.

In a river, the greatest velocity is at the surface and in the middle of the stream; from which it diminishes toward the bottom and sides, where it is least.

The velocity at the middle of the stream may be ascer tained, by observing how many inches a body floating with ́ the current passes over in a second of time. Gooseberries will fit this purpose exceedingly well; if they are not at hand, a cork may be employed.

Take the number of inches that the floating body passes over in one second, and extract its square root; double this square root, subtract it from the velocity at top, and add one, the result will be the velocity of the stream at the bottom.

And these velocities being ascertained, the mean velocity, or that with which if the stream moved in every part, it would produce the same discharge, may be found = the velocity at top - ✓velocity at top + ·5. Exam. If the velocity at the top and in the middle of the stream, be 36 inches per second, then, 36 (2 × √36) +1 36 12 + 1 = 25 the least velocity, or the velocity at bottom. And the mean velocity will be

36

= 36

- 6 + 5

30.5.

36 +5 When the water in a river receives a permanent increase from the junction of some other river, the velocity of the water is increased. This increase in velocity causes an increase of the action of the water on the sides and bottom, from which circumstance the width of the river will always be increased, and sometimes, though not so frequently, the depth also. By the reason of this increased action of the water on the bottom, the velocity is diminished until the tenacity of the soil or the hardness of the rock afford a sufficient resistance to the force of the water. The bed of the river then changes only by very slow degrees, but the bed of no river is stationary.

It is of the greatest use to know the amount of the action of any stream on its bed, and for this purpose a knowledge of the nature of the bed and of the velocity at bottom, are absolutely necessary.

Every kind of soil has a certain velocity which will insure the stability of the bed. A less velocity would allow the

waters to deposit more of the matter which is carried with the current, and a greater velocity would tear up the channel. From extensive experiments it has been found, that a velocity of 3 inches per second at the bottom, will just begin to work upon the fine clay used for pottery, and, however firm and compact it may be, it will tear it up. A velocity of 6 inches will lift fine sand-8 inches, will lift coarse sand (the size of linseed)-12 inches, will sweep along gravel-24, will roll along pebbles an inch diameter -and 3 feet at bottom, will sweep along shivery stones the size of an egg.

When water issues through a hole in the bottom or side of a vessel, its velocity is the same as that acquired by a body falling through free space from a height equal to that of the surface of the water above the hole.

The most correct rule for ascertaining the velocity of water running through pipes and canals is this:

57 x height of head x diam. of pipe)

length of pipe × 57 × diam. of pipe

23} =

the velocity in inches with which the water will issue from the orifice. All the measures are understood to be taken in inches.

Exam.—If there be a reservoir of water whose depth is 6 feet, having a tube 1 foot long and 24 inches bore, open so as to let the water escape at a distance of 18 inches from the bottom, then we have, 6 × 12 = 72 whole depth of water on the reservoir, and 72 - 18 of the head of the fluid above the orifice, wherefore by the

rule,

57 × 54 X 2.5

=

=

54, the height

7695 2.5) × 231

12 × 57 X 2.5

=

=

X 23 =

✓ (4·5) × 23 = 2.121 × 23 49.49 inches per second, the velocity of the water. And, by multiplying this result by the area of the orifice, we get the quantity discharged in one second-hence, if the pipe be circular, we have,

2.5

2

1.25 radius, and

2.5 x 3.1416
2

== half

circumference

-

1.9635 = area of orifice, hence, 49.49 × 1.963597·173 cubic inches.

The quantity of water that flows out of a vertical rectan gular aperture, that reaches as high as the surface, is of

3

the quantity that would flow out of the same aperture placed horizontally at the depth of the base.

When water issues out of a circular aperture in a thin plate placed on the bottom or side of a reservoir, the stream is contracted into a smaller diameter, to a certain distance from the orifice. The vein is smaller at the distance of half the diameter of the orifice where the area of the section of the vein is of that of the orifice, and at the above point the stream has the velocity given by theory, so that to obtain the quantity of water discharged, we multiply the velocity by the area of the orifice, and 18 of this will be the true result. When the water issues through a short tube, the vein of the stream will be less contracted than in the former case, in the proportion of 16 to 13. But when the water issues through an aperture which is the frustum of a cone, whose greater base is the aperture, the height of the conic frustum one half the diameter of the aperture and the area of the small end to that of the large end, as 10:16; then, in this case, there will be no contraction of the vein; and from this it may be inferred, that, when a supply of water is required, the greatest possible from a given orifice, this form should be employed.

To determine the quantity of water discharged by a small vertical or horizontal orifice, the time of discharge, and the height of the fluid in the vessel, when any two of these quantities are known.

Let A represent the area of the small orifice, W the quantity of water discharged; T the time of discharge, H the height of fluid in the vessel, and g 16.087 feet, the space described by gravity in a second.

Then we have,

W

A

H

=

= 2 × Axt✔g × H

By means of these formulæ we may determine the quan. tity of water W' which is discharged in the same time T, from any other vessel in which A' is the area of the orifice

and H the altitude of the fluid; for since t and g are con stant, we shall have

W: W'AH: A' H'.

Table showing the quantity of Water discharged in one Minute by Orifices differing in form and position.

From these results we may conclude,

1. That the quantities of water discharged in equal times by the same orifice from the same head of water, are very nearly as the areas of the orifices; and,

2. That the quantities of water discharged in equal times by the same orifices under different heads of water, are nearly as the square roots of the corresponding heights of the water in the reservoir above the centres of the orifices.

3. The quantities of water discharged during the same time by different apertures under different heights of water in the reservoir, are to one another in the compound ratio of the areas of the apertures, and of the square roots of the heights in the reservoirs.

This general rule may be considered as sufficiently correct for ordinary purposes; but, in order to obtain a great degree of accuracy, Bossut recommends an attention to the three following rules.

1. Friction is the cause, that, of several similar orifices

the smallest discharges less water in proportion than those which are greater, under the same altitudes of water in the

reservoir.

2. Of several orifices of equal surface, that which has the smallest perimeter ought, on account of the friction, to give more water than the rest, under the same altitude of water in the reservoir.

3. That, in consequence of a slight augmentation which the contraction of the fluid vein undergoes, in proportion as the height of fluid in the reservoir increases, the expense ought to be a little diminished.

Table of Comparison of the Theoretic with the Real dis charges from an orifice one inch in diameter.

It appears from this table, that the real as well as the theoretical discharges are nearly proportional to the square roots of the heights of the fluid in the reservoir. Thus for the heights 1 and 4, whose square roots are as 1 to 2 feet, the real discharges are 2722 and 5436, which are to one another as 1 to 1.997, very nearly as 1 to 2.