water weighs 621 lb.; therefore, the volume of water displaced weighs 625 lb.; and this is the weight of the whole body b r k m.

SECTION II.

HYDRAULICS.

WE proceed now to fluids in motion, or Hydraulics.

If water flow in a canal or river, or through a pipe of variable diameter, always filling it, the velocity of the fluid in different parts of the canal, river, or pipe, will be reciprocally as the areas of the transverse sections in those parts.

Thus, in a cast-iron pipe (a b, in fig. 55.) 7 feet long tapering from 6 inches at one end to 3 at the other, the velocity of discharge at the

narrow end is thus found. Supposing it to enter at the wider end with a velocity of

2 feet per second, what will Z

Fig. 55.

be its velocity at 3 and 6 feet respectively after entering into the tube? Here the diameters, estimated in order at 0, 3, 6, and 9 feet, are respectively 6, 5·16, 4·3, and 31⁄2 inches; hence

670

therefore the series of velocities with which the water enters, moves in at fixed points, and leaves the pipe, are 2, 27, 31, 5 inches respectively.

43

When vessels are filled with water, and apertures are made in their bottoms or sides, the fluid issues with a velocity equal to that due to the depth of the orifice beneath the surface of the fluid, or that which a heavy body would acquire by falling

from the level of the surface to the level of the orifice. If the vessel be kept constantly full, the quantity of water that issues in one second is equivalent to a column whose base is the area of the orifice, and whose altitude is expressed by the velocity with which the fluid issues.

Many curious problems might be related here about the spouting of fluids, but we must omit these, to notice the phenomena exhibited by the motion of water in pipes, open canals, and rivers. Now for measuring the velocity of rivers,

Multiply the mean depth of the stream in inches by the declivity in 2 miles in inches; then multiply the square root of the product by 10, and divide by 11 for the velocity in inches per second; or,

Multiply the mean depth of the river in feet by the declivity in one mile in inches; then multiply the square root of the product by the constant number 11.268, and the result will give the velocity in feet per minute.

When the transverse section is rectangular, multiply the breadth of the section by its depth; then divide the product · by the breadth plus twice the depth.

Thus, if the breadth be 100 feet, the depth 8 feet, the declivity 3 inches a mile, the velocity will be determined thus:

800

800

100+(2 × 8)=116=6·8965 feet=82·758 inches; therefore by the foregoing rule the velocity is

10/82-758×6=20.25 inches per second, or to 101-25 feet

11

a minute,= 20.25 × 5, where 560"÷12 inches.

In considering the velocity of water flowing through close pipes, of a given diameter and length, with a given head of water, Eytelwein conceives the whole head of water above the point of discharge to be separated into two portions, one of which he supposes to be employed in overcoming the friction and other resistances in the pipe; and the other portion employed in producing the velocity, and forcing the water through the orifice.

The height which is employed in counterbalancing the resistances, he considers to be directly proportional to the diameter of the pipe compounded with its length, and inversely as the area of the transverse section, or the square of the diameter, and consequently, on the whole, it varies inversely as the diameter. But the friction varies as the square of the velocity, hence the height equivalent to the friction must vary also as the square of the velocity.

The effect of atmospheric pressure on running liquids is, that, in a tube of considerable length, descending from a reservoir, it quickens greatly the discharge; in fact, it much resembles the operation of a piston. Hence we see in a vessel of water discharging itself by means of a tube in its bottom, a depression of the water surface in the vessel, over the tube; and as the volume of water lessens, this hollow extends itself like a large funnel. In fact, the force of the effluent water diminishes the pressure beneath; on which account the incumbent air, following the stream, finds, as it were, an easier passage, the velocity of the effluent water being always greater in the middle than towards the sides of the aperture, where it is retarded by tenacity and friction.

As regards the friction or resistance of fluids in pipes, an inch tube 200 feet long, placed horizontally, discharges only one-fourth part of the water which escapes by a simple aperture of the same diameter.

The cohesion of the fluid particles is diminished by heat, which, when increased 100 degrees, nearly doubles in certain cases the discharge.

Pumps raise water by the pressure of the atmosphere, and not by suction, as some suppose: they combine both pneumatic and hydraulic principles. By the common pump, water is raised 33 feet above its surface; but practically, we should limit the ascent to 28 feet, at which height the pump will freely act. In the lifting pump a column of water is raised whose base is always equal to the top of the piston, and its height equal to the distance from the piston to the head. The forcing-pump is used to convey water further from its bed than either of the other two, which it does by

means of a lateral pipe and valve. Fire-engines are two of these pumps in action, to produce a continued stream. The chain-pump consists of two square or cylindrical barrels, through which a chain passes, having a great many flat pistons or valves fixed, but moving free of the barrel. There are many forms of pumps, of which a large volume would scarcely suffice to contain the necessary descriptions.

We might have noticed fire-engines, garden-engines, and some other hydraulic machines, but their introduction would swell this article beyond the space it should occupy in this volume.

The ancient water-clock of the famous Ctesibius measured time by reason of the uniform discharge of the fluid, in the form of tears, from the eyes of a figure deploring the rapid speed of time; and these tears being received into a suitable vessel, gradually filled it up, and thereby floated another figure that pointed to the hours sketched on a perpendicular scale. This vessel was daily emptied by a siphon, when filled to a certain height, and its discharge, worked by machinery, told the month and the day.

In the sand hour-glass, the depth of the volume of this dry fluid does not accelerate the discharge a remarkable differ- in a simple modification of the same law.

ence

154

CHAP. VIII.

LAND-SURVEYING.

SECTION I.

DESCRIPTION AND USE OF THE INSTRU

MENTS.

Subsect. I. OF THE CHAIN.

LAND is measured with a chain, called Gunter's chain, from its inventor, of 4 poles or 22 yards or 66 feet in length. It consists of 100 equal links; and the length of each link is, therefore, of a yard, or of a foot, or 7.92 inches.

22

66 100

Land is estimated in acres, roods, and perches. An acre is equal to 10 square chains, that is, 10 chains in length, and 1 chain in breadth. Or, it is 220 x 22-4840 square yards. Or, it is 40 x 4=160 square poles. Or, it is 1000 x 100= 100,000 square links; these being all the same quantity. Also, an acre is divided into 4 parts, called roods, and a rood into 40 parts, called perches, which are square poles, or the square of a pole of 5 yards long, or the square of a quarter of a chain, or of 25 links, which is 625 square links.

So that the divisions of land measure will be thus:

The length of lines, measured with a chain, are best set down in links as integers, every chain in length being 100