CHAPTER II FUNDAMENTAL LAWS INVOLVED IN STEAM ENGINEERING IN the awful throes of the French Revolution and the immediate years following, the old saying that "every cloud has its silver lining" proved true in certain lines of scientific advancement, for the metric system of units was conceived and put into practice at that period. Our modern system of Arabic numerals, now practically universally adopted throughout the civilized world, required over five hundred years of human fumbling FIG. 10.-Mechanical energy in and competition with the old reciprocating units at Redondo. Roman method of numerical representation, before a complete replacement was accomplished, so intensely are we all creatures of habit and slaves to tradition. And so it is that although a period of a century is now passed since the institution of the metric system, modern central station engineering practice is still entangled with Fahrenheit scales, boiler horsepowers, mechanical horsepowers, myriawatts, Baume scale readings for gravity, inches of mercury vacuum, pounds pressure per sq. in., feet and inches-all units related so unscientifically and empirically as to cause bewilderment in itself. In the following discussion, however, the authors will endeavor to set forth the various units of expression in such simple language that it is hoped that even the beginner may have little difficulty in understanding their meaning. Let us first get some conception of the need for units of measurement and how such units are fundamentally conceived. Newton's Laws of Motion.-Fable has it that Sir Isaac Newton, when a boy in England lying one day under an apple tree and gazing upward, saw an apple fall to the ground. The contemplation of this phenomenon led Newton to give to the world three fundamental laws upon which modern engineering science is built. Briefly these laws are as follows: Law 1. Every body continues in a state of rest or a state of uniform motion in a straight line except in so far as it may be compelled by force to change that state. Law 2. Change of motion is proportional to impressed force and takes place in the direction of the straight line in which the force acts. Law 3. To every action there is always an equal and contrary reaction; or the mutual actions of any two bodies are always equal and oppositely directed. Hence a force is said to be acting according to Law 1 whenever the physical conditions are such that velocity is changed in magnitude or direction. Thus, when a train of cars is started or stopped, a force is necessary to cause this phenomenon, and this is evidently a change in the magnitude of the velocity. On the other hand, in the rotation of a fly wheel, the velocity may change solely in direction without a change in magnitude, and yet a force be necessary to maintain its parts in equilibrium. Hence a force may be considered as a push or a pull acting upon a definite portion of a body, but this tendency may be counteracted in whole or in part by the action of other forces. In the latter instance. the force is usually denoted as pressure, and it is the consideration of this latter case, or the consideration of pressures, that will largely concern our attention in the generation of steam in a boiler. Three Fundamental Units of Length, Mass and Time.-In considering Law 2, it is seen that there is some inherent property in matter that makes it difficult to set it in motion. Physicists have defined this quality of matter as being the inertia of a body. Inertia is expressed quantitatively in engineering practice in terms of its mass, which is measured in pounds. In order that these quantities, force and mass, now introduced may be quantitatively measured, it is necessary to have some fundamental units upon which to base our computations. Three units only are fundamentally required; namely, a unit of length, a unit of mass, and a unit of time. Scientific practice has deduced for these units the centimeter, the gram, and the second, which are well known and need no further illustration. In engineering practice, however, especially among English-speaking people, the foot, the pound, and the second seem to be in almost universal usage. We shall consequently largely express our deductions in terms of these latter units. Velocity, Acceleration, and Force Defined.-Having now decided upon the three fundamental units of measurement, let us look into other fundamental definitions and secondary units to be employed. Since engineering science must deal with motion and the change of motions per unit of time, it is necessary that we have units wherein to measure them. Change of distance per unit of time is known as velocity and is expressed in feet per second. A change in distance may, however, be undergoing a change, and this phenomenon is known as acceleration, which is measured by the change of velocity in feet per second. Since a force P is fundamentally defined as being proportional to the change in motion of a body, it follows that a force is equal to a constant, M, multiplied by the change in motion, or, in other words, multiplied by the acceleration, a. When M is in pounds mass and a is acceleration in ft. per sec. per sec., the force P is measured in poundals. The pound force is the unit, however, that has been universally adopted in engineering practice. The pound is such a force as will give to a pound mass the same change of motion per second as is acquired by a body falling freely to the earth's surface. A body falls to the earth's surface with an acceleration of g ft. per sec. per sec., wherein g has an average value of about 32.16. We have then the fundamental mathematical expression for force in pounds as follows: P = Ma Whenever, however, it is necessary to ascertain the mass M in pounds from the known weight W of the body in lb., it is necessary of course to divide W by g in order to ascertain the W mass. Thus we have in this case P = a (la) Thus, if an automobile weighing 3000 lb. accelerates from a stand-still to forty miles per hour in fifteen seconds, we compute the force required to accomplish this as follows: Since this total force must be supplied from the engine cylinder this now gives us a preliminary clew as to how the total engine cylinder area is to be proportioned. Engineers oftentimes find a more direct method of deriving the laws of motion by considering that the resistance which a body offers to its rate of change in velocity is called its inertia. The word "mass" has been invented as a quantitative unit by which inertia may be measured; hence we may forget any particular physical meaning of the word "mass" and consider it merely as a constant, the same as the Greek letter enters into the area of a circle or its circumference, when speaking of them in reference to the diameter. Mr. William Kent, the late author of Kent's "Mechanical Engineers Pocketbook," was the first to discuss this in scientific. magazines, and it has later been used with much effectiveness and clearness by consulting engineers in establishing the fundamentals of mechanics. Bodies acquire different changes of motion per second, or, in other words, different accelerations at different points on the earth's surface. A formula has been established by means of which proper corrections may be made. A concrete illustration of this will appear in the next chapter wherein a mercury column is used to measure atmospheric and vacuum pressures at different latitudes and altitudes. It is unfortunate that mass and force have the same unit of expression, for they are definite distinct physical concepts and should be carefully distinguished in order to avoid confusion. Conception of Work and Power.-In Law 2 we are informed that the change of motion takes place in the direction of the straight line in which the force acts. It is often convenient to note quantitatively the product of the force and the distance |