In writing this book it has been the intent of the Author to produce a work for the guidance of engineers in the practical design of hydro-electric plants, which would have the characteristics of accuracy, clearness and completeness. Scientific discussions of various hypotheses and theories have been omitted except in cases where their incorporation in the text has been essential to the understanding of the subjects treated.

Where a divergence of views exists among engineers, the only wise procedure is to follow safe, current practice, and this fact has guided the preparation of certain portions of this work. However, the Author has been compelled to take issue with a few conclusions which are, generally, accepted by the engineering profession, as in the theory of uplift pressure under solid dams.

Certain of the methods of treatment are new. In every case, a consistent adherence to the physics of the problem has been maintained, and in practically every instance, the physical phenomena are apparent in the equations and mathematical discussions. Seldom have abstract mathematics been employed and only under stress of absolute necessity.

A number of new and original formulae appear for the first time, here. Among these may be mentioned the exact formulae for solid dams, and for the magnitude and location of the resultants of forces acting on dams.

Occasional repetitions, both of statements and conclusions, will be found. The object of these duplications is for the purpose of making complete any single chapter or section of the book. Treatises of this character are seldom read through consecutively, but are used for reference, and it is both an annoyance and a waste of time to search through every part of a book for data on some single subject. The avoidance of this necessity has been one of the objects that has been attempted in this book. Likewise, and for the same reason, frequent repetitions of the meaning of the symbols used in the formula will be found. Engineers who, in impatience and annoyance, have been accustomed to hunt back through many pages to determine what the symbols mean in a much needed formula, will appreciate this feature.

This work was written as a single volume, but its magnitude has compelled its separation into two volumes, and the division has been made as well as the conditions and the judgment of the Author would allow. Some of the material in Volume I belongs, in a measure, to the subjects which comprise Volume II, and vice versa.

An effort has been made to eliminate all errors, particularly in the formula. The Author, and publishers, will be truly grateful to any reader who will advise them of any incorrect formulae and, also, of statements or discussions which appear obscure and wanting in clearness. Obscurity is as great a fault as a wrong formula. Criticisms from engineers who are new in the art are of particular value.

When any substance having weight passes from one elevation to a lower elevation, energy is released and under certain conditions this energy may be converted into mechanical power and made useful for industrial purposes. Obviously, the energy is proportional to the weight of the body or substance, and it is also proportional to the vertical distance through which it travels in passing from the higher to the lower elevation.

Algebraically, the energy released by any downward moving body is

Energy = Weight X Height.

If the weight be given in pounds, and the height in feet, the energy is in units of foot-pounds.

If a body pass from one elevation to a lower one, the energy is given out only during the time of movement of the body, and it ceases as soon as the body reaches the lower level toward which it travels. Hence, for a continuous delivery of energy there must be a continuous supply of bodies or substance having weight.

A stream of falling water fulfils all the conditions necessary to produce a continuous supply of power, having weight, fall and continuity.

The power - which is the rate at which energy is delivered - depends on the quantity of water flowing continuously and the height through which it falls.

It must be noted that the height of fall is the difference in elevation between the surface of the water at its upper position and the surface at its lower position, measured vertically. No matter what path the water follows in passing from the upper to the lower level, and no matter how long this path may be, the vertical height of the upper surface above the lower level is the useful fall and is called the “head.”

The most important factor in the development of a water power is to determine; in advance, the actual amount of power that may be obtained continuously, over a long period of years. Failure to give this subject the attention and careful investigation which its importance deserves has resulted in financial disaster in many instances.

In the United States, the Government has long maintained gauges at different points on most of the large rivers, and their records are available and may be used in computing the available power without making any additional observations on the stream itself. In many countries, however, the engineer is dependent on his own observations, and as these cannot be carried over a long number of years, he must resort to the methods of computation from the rainfall, the drainage of the stream, the local conditions as to the character of the country, its vegetable growths, and whether its geological formation is such that underground storage reservoirs exist which supply springs that continue to feed the streams during dry weather. With these data, reinforced by experience, an approximate determination of the minimum stream flow may be arrived at.

The character and extent of the underbrush, shrubbery and trees; the proportion of wooded area to that denuded of trees; the proportion under cultivation; all have an influence on the variation in the flow. Trees and shrubs tend to hold the rain water and make it move slowly toward the stream - so slowly that much of it is absorbed into the earth and then reaches the river or its tributary creeks only by percolation which greatly retards its movement. These effects combine to equalize the amount of water which is given to the stream by each rainfall. Rains come intermittently and are of varying volume. The flow of streams would be equally intermittent and variable as to volume if it were not for these retarding influences. Where springs are numerous, they tend to keep the stream flow up in dry weather and these are valuable when they discharge enough water to be of real assistance.

The minimum flow sometimes may be increased by means of storage. When a dam is built across a stream and a lake of considerable area is formed, the water thus accumulated may be partially drawn off during the dry season, the total water passed through the water wheels being that furnished by the stream plus that taken from the lake. Generally, the power is not used throughout the full 24 hr. per day, and if the storage area is sufficiently great, the water which flows during the night is accumulated in the lake, and on the following day the water available for power is that supplied by the stream flow plus that impounded during the previous night. In this way, the power furnished by a given stream may be greatly increased during a part of the day, as is more definitely pointed out in the paragraph on "Load Factor" in Chapter IV.

For the purpose of forming extensive storage lakes, dams of great height and length are often constructed, instead of small dams, further up the stream, with canals or flumes leading to the foot of the falls, which would cost much less and would serve just as well, if the question of storage were not involved.


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