PART II. Source of fresh water. Natural drainage. Catchment basins. CHAPTER I. ON DRAINAGE AND THE STORAGE AND § I. ON THE SOURCE OF FRESH WATER AND NATURAL WATER emits vapour at all temperatures with which we are acquainted. The density of the vapour at emission is the maximum consistent with the gaseous condition at the temperature. As the vapour ascends and diffuses in the air, the density diminishes. A stratum of air at the temperature for which the density of the suspended vapour is the maximum is said to be saturated, and any lowering of the temperature below this point causes condensation till saturation is restored. The condensed vapour collects in globules, which either fall directly as rain, or descend into a denser stratum of air, assume the nebulous condition, and float, forming clouds and mist, and are re-evaporated or precipitated according to the subsequent changes in the state of the atmosphere. All supplies of fresh water are derived from the condensation of aqueous vapour, and the discharge of springs and rivers from the land into the sea is the excess within the coast lines of the water of condensation above the water evaporated and permanently absorbed in animals, vegetables, and minerals. The rain which falls on surfaces above the sea-level, and escapes evaporation and permanent absorption, gravitates to the sea; and flows thither through and beneath the soil, directly on the surface, and through the pores and fissures of rocks. The water flowing on the surface collects according to the configuration of the ground, and forms streams, lakes, and rivers. The water flowing underground either oozes to the surface at imperceptible points, or drains into and flows in the fissures and escapes in springs. Lines drawn on the map of a country through the sources of the tributaries of each of the rivers that flow directly into the (1) This chapter has been contributed by Mr. P. B. Cunningham, Civil Engineer, late of the Indian Government Service.-W. C. G. sea, enclose a number of areas of the shape of the letter U, more or less distorted. These areas are approximately what are called the catchment basins of the great rivers,—that is, the areas upon which the rainfall is gathered that supplies their waters. To find the true boundaries of the catchment basins, it is necessary to ascertain exactly the position of the ridge lines or watersheds of the country. In compact formations, where the quantity of water flowing underground is inappreciable, the ridge lines pass through the highest points on the surface. In the more porous rocks-chalk and sandstone, for example—the boundary of the catchment basin depends upon the configuration of the retentive substratum. The great catchment basins are divisible into a number of smaller basins drained by the tributaries; these again into the still smaller basins which supply the feeders; and so on. level. In this country surfaces below the sea-level are kept dry only Surfaces by artificial means; those above low-water mark and below below seahigh-water mark by the opening and shutting of flood-gates, and those below low-water mark by pumping. § 2. ON THE FLOW OF WATER. In a mass of water at rest the pressure is of the same in- Pressure in tensity at all points (1) at the same level. The difference of the water. intensities of the pressures at two points at different levels— the density of water being supposed constant-is the weight of a vertical column of water whose height is the difference of elevation of the two points, and whose base is a unit of area. The intensities of the pressures at points at different depths below a given level or horizontal surface, less the intensity at that surface, are proportional to the depths. The difference of the pressures per square foot at a given Head of prespoint in a mass of water, and on a surface open to the atmo- sure. sphere at the same level, divided by the weight of a cubic foot of water, is called feet of head of pressure at the given point when the pressure of the atmosphere is the less, and feet of vacuum Vacuum. when the pressure of the atmosphere is the greater. 66 The total head at a given point in a mass of water is the sum Total head. of the head of pressure and the height of the point above a fixed or datum" level. To express this in symbols, let p denote the head of pressure, x the height above the datum (or the head of elevation), and H the total head at the given point: then In a mass of water at rest, the total head is the same at all points. (1) When "pressure at a point" is spoken of, a "point" must be held to mean a very small surface. A pressure at a point in the true sense is an impossibility. Loss of head. Volume of flow. Mean velocity. Relation be head and velocity in a perfect fluid. In order to acquire velocity from a state of rest, or an increase of velocity, a fluid particle must pass from a point of greater to a point of less total head; in other words, the particle must lose head. The volume of flow of a stream is the quantity of water it discharges in a given time. The volume of flow is usually expressed in cubic feet per second. The mean velocity of a stream at a given cross section is found by dividing the volume of flow by the area of the cross section. Let Q denote the volume of flow in cubic feet per second, A the area of the cross section in square feet, and v the mean velocity in feet per second: then In a stream of water the velocity is different at different points in the same cross section, the greatest velocity being in the middle, and the least at the borders. If a fluid particle could pass from a point of greater to a tween loss of point of less total head without resistance, the loss of head required to produce in it any given velocity from a state of rest would be equal to the height of fall required to produce the same velocity from a state of rest in a body falling freely. Let v denote the given velocity, and g the acceleration of gravity in feet per second: then in a body falling freely Work. Energy. Let x+ denote the total head at a point at which the particles of a fluid are at rest, x+p the total head at a point at which the particles acquire the given velocity, and h the loss of head: then in a perfect fluid Motion against resistance is called work. Work is measured by the product of the resisting force into the distance through which that force is overcome. The ordinary unit of work is the foot-pound-the amount of work required to raise one pound avoirdupois one foot high. Energy means capacity for doing work. When a force acts upon and moves a body, energy is said to be exerted. By the actual energy of a moving body is meant the amount of work which the body must do before it returns to rest. The energy that has been exerted on a falling body at any point in its descent is measured by the product of the weight of the body into the height fallen through. In a stream, the energy that has been exerted per unit of volume of flow at any cross section is measured by the product of the weight of that unit into the loss of head. When a body does no work while falling, its actual energy at Energy and any point in the descent is equal to the energy that has been work. exerted; that is, after falling through a given height, and before returning to rest, the body must do an amount of work equivalent to raising itself (i.e., overcoming the force which urges it downwards) through the height through which it has fallen. Take a pendulum, for example. When a body does work while falling, its actual energy is less than the energy that has been exerted, and the height through which it must raise itself before returning to rest is less than the height through which it has fallen by the height which, multiplied into its weight, represents the work done. Take the weights of a clock, for example. In this case the actual energy is nothing (nearly), and the whole (nearly) of the energy exerted is expended while falling. In a falling body the height fallen through, and in a stream the loss of head, is called the height due to the energy exerted; the height through which a moving body must raise itself before returning to rest is called the height due to the actual energy, or the height due to the velocity; and the difference of the heights due to the energy exerted and the actual energy, the height due to the work done. of head and velocity, and A stream of water has to overcome a force which acts between Relation the surface of its conduit and the particles in contact, and, in between loss consequence of the retardation of these particles, a force which acts between the particles of water themselves and opposes work done in their flow at different velocities. Hence every particle in a a stream of stream of water does work. The height due to the work done water. is most conveniently expressed in terms of the height due to the velocity, and the relation between the loss of head and the velocity produced from a state of rest by the following equation: h in which represents the height due to the energy that has been شرح exerted, the height due to the actual energy, and F the 28 2g The height due to the work done; or, briefly, the friction. When the velocities at the two cross sections are equal, that is, when v=v and the whole of the energy due to the loss of head between the two cross sections is expended while passing. Effect of loss pipe. In an open channel the head of pressure is nothing on the of head in an upper surface of the stream, and the same at all points at open channel the same depth below the upper surface. The loss of head, and in a close h=(x+)-(x+p), in an open channel, therefore, takes place wholly in diminution of the head of elevation. In a close pipe the loss of head may take place wholly in diminution of the head of pressure, in which case the head of pressure at the source, or the vacuum at the outlet, must be produced by pumping; or it may take place partly in diminution of the head of pressure, and partly in diminution of the head of elevation, in which case the stream may flow by its own weight. The head of pressure p at any point in a stream flowing in a close pipe is called the depth of that point below the line of virtual declivity. Feet of vacuum and velocity in a When, as in the suction-pipe of a pump, water acquires velocity, and flows from a place of no head of pressure to a place where the pressure is less than that of the atmosphere, suction-pipe. let a denote the feet of vacuum, x, the height above the datum of the service of the water in the source, and x the height above the datum of the bucket at top stroke: then Syphon. Work done in a stream. Factor of friction in a straight uniform channel. At the sea-level the maximum value of q varies from 32 to 35. Water may flow in a pipe from a place of no head of pressure, through a space in which the pressure is less than that of the atmosphere, to another place of no head of pressure, provided that, when x, is the height of the higher of the two places of no head, and x the highest point between them— (xx) is not greater than (9 - F 22). 2g (9) Water flowing above the line of no head of pressure is said to flow in a syphon. No permanent flow can be maintained in a syphon, because the air in the water (and all water contains air) disengages, collects in the summit, and in time destroys the vacuum upon which the flow depends. The work done by a stream of water may be divided into the following parts: (1.) The work done in traversing the conduit, supposing the course to be a right line. (2.) The work done in changing the direction of the motion at knees and bends. (3.) The work done in changing the velocity at sudden enlarge ments. (1.) Let s denote the length of the part of the girth of the conduit in contact with the stream, and the length of the conduit then is is the area of the frictional surface. Let A, as before, denote the sectional area of the stream: then, for a straight uniform conduit |