Physics

A branch of science that deals with matter and energy and their interactions in the field of mechanics, electricity, nuclear phenomena, and others is called physics. Some of the basic principles of fluids must be studied before subsequent chapters in this book can be understood properly.

Matter

Matter can be defined as anything that occupies space, and all matter has inertia. Inertia is that property of matter by which it will remain at rest or in uniform motion in the same straight line or direction unless acted upon by some external force. Matter is any substance that can be weighed or measured. Matter may exist in one of three states:

• Solid (coal, iron, ice)

• Liquid (oil, alcohol, water)

• Gas (air, hydrogen, helium)

Water is the familiar example of a substance that exists in each of the three states of matter (see Figure 1-1) as ice (solid), water (liquid), and steam (gas).

Figure 1-1 The three states of matter: solid, liquid, and gas. Note that the change of state from a solid to a liquid is called fusion, and the change of state from liquid to a gas is called vaporization.

Body

A body is a mass of matter that has a definite quantity. For example, a mass of iron 3 inches × 3 inches × 3 inches has a definite quantity of 27 cubic inches. It also has a definite weight. This weight can be determined by placing the body on a scale (either a lever or platform scale or a spring scale). If an accurate weight is required, a lever or platform scale should be employed. Since weight depends on gravity, and since gravity decreases with elevation, the reading on a spring scale varies, as shown in Figure 1-2.

Figure 1-2 Variation in readings of a spring scale for different elevations.

Energy

Energy is the capacity for doing work and overcoming resistance. Two types of energy are potential and kinetic (see Figure 1-3).

Potential energy is the energy that a body has because of its relative position. For example, if a ball of steel is suspended by a chain, the position of the ball is such that if the chain is cut, work can be done by the ball.

Kinetic energy is energy that a body has when it is moving with some velocity. An example would be a steel ball rolling down an incline. Energy is expressed in the same units as work (foot-pounds).

As shown in Figure 1-3, water stored in an elevated reservoir or tank represents potential energy, because it may be used to do work as it is liberated to a lower elevation.

Conservation of Energy

It is a principle of physics that energy can be transmitted from one body to another (or transformed) in its manifestations, but energy may be neither created nor destroyed. Energy may be dissipated. That is, it may be converted into a form from which it cannot be recovered (the heat that escapes with the exhaust from a locomotive, for example, or the condensed water from a steamship). However, the total amount of energy in the universe remains constant, but variable in form.

Figure 1-3 Potential energy and kinetic energy.

Joule’s Experiment

This experiment is a classic illustration (see Figure 1-4) of the conservation of energy principle. In 1843, Dr. Joule of Manchester, England, performed his classic experiment that demonstrated to the world the mechanical equivalent of heat. It was discovered that the work performed by the descending weight (W in Figure 1-4) was not lost, but appeared as heat in the water—the agitation of the paddles having increased the water temperature by an amount that can be measured by a thermometer. According to Joule’s experiment, when 772 foot-pounds of work energy had been expended on the 1 pound of water, the temperature of the water had increased 1°F. This is known as Joule’s equivalent: That is, 1 unit of heat equals 772 foot-pounds (ft-lb) of work. (It is generally accepted today that ft-lb. be changed to lb.ft. in the meantime or transistion period you will find it as ft-lb. or lb.ft.)

Figure 1-4 Joule’s experiment revealed the mechanical equivalent of heat.

Experiments by Prof. Rowland (1880) and others provide higher values. A value of 778 ft-lb is generally accepted, but 777.5 ft-lb is probably more nearly correct, the value 777.52 ft-lb being used by Marks and Davis in their steam tables. The value 778 ft-lb is sufficiently accurate for most calculations.

Heat

Heat is a form of energy that is known by its effects. The effect of heat is produced by the accelerated vibration of molecules. Theoretically, all molecular vibration stops at -273°C (known as absolute zero), and there is no heat formed. The two types of heat are sensible heat and latent heat.

Sensible Heat

The effect of this form of heat is indicated by the sense of touch or feeling (see Figure 1-5).

Sensible heat is measured by a thermometer. A thermometer is an instrument used to measure the temperature of gases, solids, and liquids. The three most common types of thermometers are liquid-in-glass , electrical, and deformation.

The liquid-in-glass generally employs mercury as the liquid unless the temperature should drop below the freezing point of mercury, in which case alcohol is used. The liquid-in-glass is relatively inexpensive, easy to read, reliable, and requires no maintenance. The thermometer consists of a glass tube with a small uniform bore that has a bulb at the bottom and a sealed end at the top. The bulb and part of the tube are filled with liquid. As the temperature rises, the liquid in the bulb and tube expand and the liquid rises in the tube. When the liquid in the thermometer reaches the same temperature as the temperature outside of the thermometer, the liquid ceases to rise.

Figure 1-5 The radiator is an example of sensible heat.

In 1714, Gabriel Daniel Fahrenheit built a mercury thermometer of the type now commonly in use.

Electrical thermometers are of the more sophisticated type. A thermocouple is a good example. This thermometer measures temperatures by measuring the small voltage that exists at the junction of two dissimilar metals. Electrical thermometers are made that can measure temperatures up to 1500°C.

Deformation thermometers use the principle that liquids increase in volume and solids increase in length as temperatures rise. The Bourdon tube thermometer is a deformation thermometer.

Extremely high temperatures are measured by a pyrometer. One type of pyrometer matches the color (such as that of the inside of a furnace) against known temperatures of red-hot wires.

Figure 1-6 shows the Fahrenheit, Celsius, and Reaumur thermometer scales. Figure 1-7 illustrates the basic principle of a thermocouple pyrometer.

Figure 1-6 Three types of thermometer scales.

Latent Heat

This form of heat is the quantity of heat that becomes concealed or hidden inside a body while producing some change in the body other than an increase in temperature.

When water at atmospheric pressure is heated to 212°F, a further increase in temperature does not occur, even though the supply of heat is continued. Instead of an increase in temperature, vaporization occurs, and a considerable quantity of heat must be added to the liquid to transform it into steam. The total heat consists of internal and external latent heats. Thus, in water at 212°F and at atmospheric pressure, considerable heat is required to cause the water to begin boiling (internal latent heat). The additional heat that is required to boil the water is called external latent heat. Figure 1-8 shows a familiar example of both internal and external latent heat.

Figure 1-7 Basic principle of a thermocouple pyrometer. A thermocouple is used to measure high temperatures. In principle, when heat is applied to the junction of two dissimilar metals, a current of electricity begins to flow in proportion to the amount of heat applied. This current is brought to a meter and translated in terms of heat.

Figure 1-8 Domestic setting for illustrating internal (left) and external (right) latent heat.

Unit of Heat

The heat unit is the amount of heat required to raise the temperature of 1 pound of water 1°F at the maximum density of the water. The British thermal unit (abbreviated Btu) is the standard for heat measure. A unit of heat (Btu) is equal to 252 calories, which is the quantity of heat required to raise the temperature of 1 pound of water from 62°F to 63°F.

Assuming no loss of heat, 180 Btu are required to raise the temperature of 1 pound of water from 32°F to 212°F. If the transfer of heat occurs at a uniform rate and if six minutes are required to increase the temperature of the water from 32°F to 212°F, 1 Btu is transferred to the water in (6 × 60) ÷ 180, or 2 seconds.

Specific Heat

This is the ratio of the number of Btu required to raise the temperature of a substance 1°F to the number of Btu required to raise the temperature of an equal amount of water 1°F. Some substances can be heated more quickly than other substances. Metal, for example, can be heated more quickly than glass, wood, or air. If a given substance requires one-tenth the amount of heat to bring it to a given temperature than is required for an equal weight of water, the number of Btu required is 010

(0.1), and its specific heat is 011

(0.1).

Example

The quantity of heat required to raise the temperature of 1 pound of water 1°F is equal to the quantity of heat required to raise the temperature of 8.4 pounds of cast iron 1°F. Since the specific heat of water is 1.0, the specific heat of cast iron is 0.1189 (1.0 ÷ 8.4).

Thus, the specific heat is the ratio between the two quantities of heat. Table 1-1 shows the specific heat of some common substances.

Transfer of Heat

Heat may be transferred from one body to another that is at a lower temperature (see Figure 1-9) by the following:

• Radiation

• Conduction

• Convection

When heat is transmitted by radiation, the hot material (such as burning fuel) sets up waves in the air. In a boiler-type furnace, the heat is given off by radiation (the heat rays radiating in straight lines in all directions). The heat is transferred to the crown sheet and the sides of the furnace by means of radiation.

Contrary to popular belief that heat is transferred through solids by radiation; heat is transferred through solids (such as a boilerplate) by conduction (see Figure 1-10). The temperature of the furnace boilerplate is only slightly higher than the temperature of the water that is in contact with the boilerplate. This is because of the extremely high conductivity of the plate.

Conduction of heat is the process of transferring heat from molecule to molecule. If one end of a metal rod is held in a flame and the other end in the hand, the end in the hand will become warm or hot. The reason for this is that the molecules in the rod near the flame become hot and move rapidly, striking the molecules next to them. This action is repeated all along the rod until the opposite end is reached. Heat is transferred from one end of the rod to the other by conduction. Conduction depends upon unequal temperatures in the various portions of a given body.

Table 1-1 Specific Heat of Common Substances

Convection of heat is the process of transmitting heat by means of the movement of heated matter from one location to another. Convection is accomplished in gases and liquids.

In a place heated by a radiator, the air next to the radiator becomes warm and expands. The heated air becomes less dense than the surrounding cold air. It is forced up from the radiator by the denser, colder air. Most home heating systems operate on the principle of transmission of heat by convection.

Nearly all substances expand with an increase in temperature, and they contract or shrink with a decrease in temperature. There is one exception to this statement for all temperature changes, the exception being water. It is a remarkable characteristic of water that at its maximum density (39.1°F) water expands as heat is added and that it also expands slightly as the temperature decreases from that point.

Figure 1-9 Transfer of heat by radiation, conduction, and convection. It should be noted that the air, not the water, is the cooling agent. The water is only the medium for transferring the heat to the point where it is extracted and dissipated by the air.

Figure 1-10 Differences in heat conductivity of various metals.

Increase in heat causes a substance to expand, because of an increase in the velocity of molecular action. Since the molecules become more separated in distance by their more frequent violent collisions, the body expands.

Linear expansion is the expansion in a longitudinal direction of solid bodies, while volumetric expansion is the expansion in volume of a substance.

The coefficient of linear expansion of a solid substance is the ratio of increase in length of body to its original length, produced by an increase in temperature of 1°F.

Expansion and contraction caused by a change in temperature have some advantages, but also pose some disadvantages. For example, on the plus side, rivets are heated red-hot for applying to bridge girders, structural steel, and large boilerplates. As the rivets cool, they contract, and provide a solid method of fastening. Iron rims are first heated and then placed on the wheel. As the iron cools, the rim contracts and binds the wheel so that it will not come off. Common practice is to leave a small space between the ends of the steel sections that are laid end on end. This is to allow for longitudinal expansion and contraction. Table 1-2 shows values that can be used in calculation of linear expansion.

Some of the disadvantages of expansion and contraction caused by change in temperatures are setting up of high stresses, distortion, misalignment, and bearing problems.

Pressure

Pressure (symbol P) is a force exerted against an opposing body, or a thrust distributed over a surface. Pressure is a force that tends to compress a body when it is applied.

If a force is applied in the direction of its axis, a spring is compressed (see Figure 1-11). The resistance of the spring constitutes an opposing force, equal and opposite in direction to the applied force. Pressure is distributed over an entire surface. This pressure is usually stated in pounds per square inch (psi).

If a given force is applied to a spring, the spring will compress to a point where its resistance is equal to the given force.

In Figure 1-11b, the condition of the pressure system is in a state of equilibrium.

Table 1-2 Linear Expansion of Common Metals (between 32°F and 212°F)

Metal	Linear Expansion per Unit Length per Degree F
Aluminum	0.00001234
Antimony	0.00000627
Bismuth	0.00000975
Brass	0.00000957
Bronze	0.00000986
Copper	0.00000887
Gold	0.00000786
Iron, cast	0.00000556
Iron, wrought	0.00000648
Lead	0.00001571
Nickel	0.00000695
Steel	0.00000636
Tin	0.00001163
Zinc, cast	0.00001407
Zinc, rolled	0.00001407
Volumetric expansion = 3 times linear expansion.

Figure 1-11 The nature of pressure: (a) spring in its normal state; and (b) pressure system in state of equilibrium.

Problem

The total working area of the plunger of a pump is 10 square inches. What is the amount of pressure on the plunger when pumping against 125 psi (see Figure 1-12)?

Figure 1-12 The distribution of pressure over a surface. A pressure of 125 psi is exerted on each sector (1 square inch).

Solution

Since 125 pounds of pressure are exerted on each square inch of the working face of the plunger, and since the area of the working face of the plunger is 10 square inches, the total pressure exerted on the plunger face is 1250 pounds, as shown here:

10 sq in × 125psi = 1250 lb

The ball-peen hammer is used for peening and riveting operations. The peening operation indents or compresses the surface of the metal, expanding or stretching that portion of the metal adjacent to the indentation. As shown in Figure 1-13, the contact area is nearly zero if the flat and special surfaces are perfectly smooth. However, perfectly smooth surfaces do not exist. The most polished surfaces (as seen under a microscope) are similar to emery paper. Therefore, the contact area is very small. As shown in Figure 1-14, the pressure, in psi, is multiplied when applied through a spherical contact surface.

Figure 1-13 Theoretical contact area (a) and actual contact area (b) of flat and spherical surfaces.

Figure 1-14 The pressure (psi) is multiplied when it is applied to the flat surface through a spherical contact area.

Problem

If the ball-peen of a machinist’s hammer is placed in contact with a flat surface (see Figure 1-14) and a weight of 100 lb is placed on the hammer (not including the weight of the hammer), how many pounds of pressure are exerted at the point of contact if the contact area is 0.01 square inch?

Solution

If the contact area were 1 square inch in area, the pressure would equal 100 pounds on the 1 square inch of flat surface. Now, if the entire 100-pound weight or pressure is borne on only 0.01 square inch (see Figure 1-14), the pressure in psi is equal to 10,000 psi (100 ÷ 0.01).

Perhaps another example (see Figure 1-15) may illustrate this point more clearly.

Figure 1-15 Pressure per square inch of flat surface.

Problem

Lay out entire surface ABDC equal to 1 square inch, and divide the surface into 16 small squares ( 020

square inch), placing a 5-pound weight on each small square. The area of each small square is 021

, or 0.0625 square inches. If all the 5-pound weights are placed on one small square (as in the diagram), the total weight or pressure on that small square is 80 pounds (5 × 16), or, on 0.0625 square inches of surface.

In the left-hand diagram (see Figure 1-15), the 5-pound weights are distributed over the entire 1 square inch of area, the pressure totaling 80 psi of surface (5 × 16). In the right-hand diagram, the sixteen 5-pound weights (80 lb) are borne on only 0.0625 square inches of surface. This means the total weight or pressure (if each of the sixteen small squares were to bear 80 pounds) would be 1280 psi of surface (16 × 80).

Atmospheric Pressure

Unless stated otherwise, the term pressure indicates pressure psi. The various qualifications of pressure are initial pressure, mean effective pressure, terminal pressure, backpressure, and total pressure.

The atmospheric pressure is due to the weight of the Earth’s atmosphere. At sea level it is equal to approximately 14.69 psi. The pressure of the atmosphere does not remain constant at a given location, because weather conditions are changing continually.

Figure 1-16 illustrates atmospheric pressure. If a piston having a surface area of 1 square inch is connected to a weight by a string passing over a pulley, then, a weight of 14.69 pounds is required to raise the weight from the bottom of the cylinder (assuming air tightness and no friction) against the atmosphere that distributes a pressure of 14.69 pounds over the entire face area of the piston (area = 1 square inch). Then the system is in a state of equilibrium, the weight balancing the resistance or weight of the atmosphere. A slight excess pressure is then required to move the piston.

Figure 1-16 Atmospheric pressure.

Atmospheric pressure decreases approximately 0.5 pounds for each 1000-foot increase in elevation. When an automobile climbs a high mountain, the engine gradually loses power because air expands at higher altitudes. The volume of air taken in by the engine does not weigh as much at the higher altitudes as it weighs at sea level. The mixture becomes too rich at higher altitudes, causing a poor combustion of fuel.

A perfect vacuum is a space that has no matter in it. This is unattainable even with the present pumps and chemical processes. Space in which the air pressure is about one-thousandth of that of the atmosphere is generally called a vacuum. Partial vacuum has been obtained in which there are only a few billion molecules in each cubic inch. In normal air, there are about four hundred billion times a billion molecules of gas to each cubic inch.

Gage Pressure

Pressure measured above that of atmospheric pressure is called gage pressure. Pressure measured above that of a perfect vacuum is called absolute pressure. Figure 1-17 illustrates the difference between gage pressure and absolute pressure.

Figure 1-17 Absolute pressure (left) and gage pressure (right).

In the cylinder containing the piston (the left of Figure 1-17), a perfect vacuum exists below the piston, as registered by the value 29.921 inches of mercury (explained later) on the vacuum gage A. The equivalent reading on the absolute pressure gage B is zero psi. If the piston is removed from the cylinder (the right of Figure 1-17), air rushes into the cylinder. That is, the vacuum is replaced by air at atmospheric pressure, the vacuum gage A drops to zero, the absolute pressure gage B reads 14.696, and the pressure gage C indicates a gage pressure of zero.

Barometer

A barometer is an instrument that is used to measure atmospheric pressure. The instrument can be used to determine height or altitude above sea level, and it can be used in forecasting weather.

The barometer reading is expressed in terms of inches of mercury (in. Hg). This can be shown (see Figure 1-18) by filling a 34-inch length of glass tubing with mercury and then inverting the tubing in an open cup of mercury. The mercury inside the glass tubing falls until its height above the level of the mercury in the cup is approximately 30 inches (standard atmosphere). The weight of the 30-inch column of mercury is equivalent to the weight of a similar column of air approximately 50 miles in height.

The barometer reading in inches of mercury can be converted to psi by multiplying the barometer reading by 0.49116. This value corresponds to the weight of a 1-inch column of mercury that has a cross-sectional area of 1 square inch.

The barometer readings (in. Hg) are converted to atmospheric pressure (psi) in Table 1-3. The table calculations are based on the standard atmosphere (29.92 inches of mercury) and pressure (14.696 psi). Thus, 1 inch of mercury is equivalent to 0.49116 psi (14.696 ÷ 29.921).

Problem

What absolute pressure reading corresponds to a barometer reading of 20 inches of mercury?

Solution

The absolute pressure reading can be calculated by means of the formula:

barometer reading (in. Hg) × 0.49116 = psi

Therefore, the absolute pressure reading is (20 × 0.49116), or 9.82 psi.

In an engine room, for example, the expression “28-inch vacuum” signifies an absolute pressure in the condenser of 0.946 psi (14.696 − 13.75). This indicates that the mercury in a column connected to a condenser having a 28-inch vacuum rises to a height of 28 inches, which represents the difference between the atmospheric pressure and the pressure inside the condenser 13.804 pounds (14.73 − 0.946).

Figure 1-18 The basic principle of the barometer and the relation of the Fahrenheit scale, barometric pressure reading, and absolute pressure.

Gravity

The force that tends to attract all bodies in the Earth’s sphere toward the center point of the earth is known as gravity. The symbol for gravity is g. The rate of acceleration of gravity is 32.16 feet per second. Starting from a state of rest, a free-falling body falls 32.16 feet during the first second; at the end of the next second, the body is falling at a velocity of 64.32 feet per second (32.16 + 32.16).

Table 1-3 Conversion of Barometer Reading to Absolute Pressure

Barometer (in. Hg)	Pressure (psi)
28.00	13.75
28.25	13.88
28.50	14.00
28.75	14.12
29.00	14.24
29.25	14.37
29.50	14.49
29.75	14.61
29.921	14.696
30.00	14.74
30.25	14.86
30.50	14.98
30.75	15.10
31.00	15.23

Center of Gravity

That point in a body about which all its weight or parts are evenly distributed or balanced is known as its center of gravity (abbreviated c.g.). If the body is supported at its center of gravity, the entire body remains at rest, even though it is attracted by gravity. A higher center of gravity and a lower center of gravity are compared in Figure 1-19, as related to the center of gravity in automobiles.

Centrifugal Force

The force that tends to move rotating bodies away from the center of rotation is called centrifugal force. It is caused by inertia. A body moving in a circular path tends to be forced farther from the axis (or center point) of the circle described by its path.

If the centrifugal force balances the attraction of the mass around which it revolves, the body continues to move in a uniform path. The operating principle of the centrifugal pump (see Figure 1-20) is based on centrifugal force.

Figure 1-19 Comparison of the height of the center of gravity in an earlier model automobile (left) and later model (right).

Figure 1-20 The use of centrifugal force in the basic operation of a centrifugal pump.

Centripetal Force

The force that tends to move rotating bodies toward the center of rotation is called centripetal force. Centripetal force resists centrifugal force, and the moving body revolves in a circular path when these opposing forces are equal—that is, the system is in a state of equilibrium (see Figure 1-21).

Figure 1-21 The state of equilibrium between centrifugal and centripetal force.

If a body O (see Figure 1-22) is acted upon by two directly opposed forces OA and OC, those forces are equal. If it is also acted upon by another pair of directly opposed forces OB and OD, the various forces balance and the resultant reaction on the body O is zero (that is, the body remains in a state of rest).

Figure 1-22 State of equilibrium existing as a resultant of directly opposed forces.

Force

A force is completely defined only when its direction, magnitude, and point of application are defined. All three of these requirements can be represented by a line or vector, so that its direction, length, and location correspond to given conditions.

As shown in Figure 1-23, a force of 4000 pounds can be represented by drawing a line to a convenient scale (1 inch = 1000 pounds), which requires a line AB 4 inches in length, drawn in the direction of and to the point where the force is applied. Note that the arrowhead is placed at the point where the force is applied.

Figure 1-23 A line or vector is used to represent a force and its intervals, its direction, and its point of application. The arrowhead indicates the point of application of the force.

Resultant of Directly Opposed Forces

If the lines OA and OB (see Figure 1-24) are used to represent two directly opposed forces acting on the point O, and the forces OA and OB are equal to 4000 pounds and 2000 pounds, respectively, these opposed forces can be represented by a single line OC or force, which is equal to 2000 pounds (4000 - 2000). Thus, the resultant of forces OA and OB is a single force OC. The broken line in the illustration indicates the subtraction of the smaller force OB.

Figure 1-24 Diagram used to determine the resultant of two directly opposed forces.

Resultant of Forces at an Angle

If two forces OA and OB are acting on a common point O, an angle is formed (see Figure 1-25) in which the two forces can be represented by the lines OA and OB whose lengths represent 4000 pounds and 2000 pounds, respectively.

Figure 1-25 Diagram of two forces acting on a common point at an angle to each other.

To determine the direction and intensity of the resultant force, a parallelogram of force can be constructed (see Figure 1-26). The parallelogram can be constructed from the diagram in Figure 1-25. The broken line BC is constructed parallel to line OA, and the broken line AC is drawn parallel to line OB. The diagonal OC represents the direction and intensity (by measuring its length) of the resultant force that is equivalent to the forces OA and OB.

Figure 1-26 Determining the resultant of two angular forces by the parallelogram-of-forces method.

Components of a Force

The components of a force can be determined by reversing the process of determining the resultant of two forces. A component of force is a single force that was used to compound the resultant force derived by the parallelogram-of-forces principle.

For example, the reaction caused by the thrust of a connecting rod on the crank pin (see Figure 1-27) may be considered. The thrust can be divided into two component forces.

Figure 1-27 Determining the components of a force by means of the parallelogram-of-forces method.

One component force acts in a direction tangent to the circle described by the crank pin, which causes the crank to turn. The other component force acts in the direction of the axis of the crank arm, which causes the shaft to press against its bearing. A diagram (see Figure 1-27) can be constructed to determine the components of a force.

From point O, project a line OC equal in length to the thrust of the connecting rod (see Figure 1-27). Complete the parallelogram of forces to obtain points B and A, their lengths OB and OA representing the components of force in direction and intensity.

Motion

Motion is usually described as a change in position in relation to an assumed fixed point. Motion is strictly a relative matter because there can be no motion unless some point or object is regarded as stationary (see Figure 1-28).

As shown in Figure 1-28, the man is rowing the boat at a speed of 4 miles per hour against a current flowing at 2 miles per hour in the opposite direction. The boat is moving at 4 miles per hour with respect to the water, and the water is moving at 2 miles per hour with respect to the Earth.

Figure 1-28 Motion.

The familiar example of the ferryboat crossing the river, pointing upstream to counteract the motion of the water, is used to illustrate apparent and actual motion (see Figure 1-29). The line OA represents the apparent motion (both distance and direction) of the boat. However, regarding the Earth as stationary, the line OB represents the actual motion of the boat. If the water is regarded as stationary, the boat is moving in the direction represented by the line OA.

Newton’s Laws of Motion

The noted physicist, Sir Isaac Newton, announced the three laws of motion as follows:

• First Law of Motion—If a body is at rest, it tends to remain at rest. If a body is in motion, it tends to remain in motion in a straight line until acted upon by a force.

• Second Law of Motion—If a body is acted on by several forces, it tends to obey each force as though the other forces do not exist, whether the body is at rest or in motion.

• Third Law of Motion—If a force acts to change the state of a body with respect to rest or motion, the body offers a resistance that is equal and directly opposed to the force. In other words, to every action there is an equal and opposite reaction.

Figure 1-29 Apparent and actual motion.

Types of Motion

The rate of change of position in relation to time is termed velocity. Velocity is also the rate of motion in a given direction (as the rotation of a sphere) in relation to time. The rate of increase in velocity or the average increase of velocity in a given unit of time is called acceleration.

A train traveling at a rate of 30 miles per hour is an example of linear velocity. A line shaft rotating at a rate of 125 revolutions per minute is an example of rotary velocity. Figure 1-30 shows linear motion and rotary motion.

Tangential motion is the equivalent of rotary motion, but is regarded as moving in a straight line or tangential direction. Tangential motion or velocity is used in belting calculations. As shown in Figure 1-31, the circumference of a 1-foot diameter pulley is 3.1416 feet. Thus, for each revolution of the pulley, the belt travels the tangential equivalent distance AB, or 3.1416 feet.

Example

If a 4-foot diameter pulley is rotating at 100 rpm, what is the tangential speed of the belt? The calculation is as follows:

tangential speed = circumference × rpm

tangential speed = 4 × 3.1416 × 100

tangential speed = 12.566 × 100

tangential speed = 1256.6 feet per minute

Figure 1-30 Linear motion and rotary motion.

Figure 1-31 The tangential equivalent distance of rotary motion.

Vibrating motion that describes a path similar to the arc of a circle is called oscillating motion. A familiar example of oscillating motion is the pendulum of a clock. A vibrating motion that makes a path similar to a straight line is called reciprocating motion. The movement of the crosshead of an engine is an illustration of reciprocating motion. Figure 1-32 shows oscillating and reciprocating motion.

Figure 1-32 Oscillating type of engine (left) and reciprocating type of engine (right).

The oscillating-type engine (see Figure 1-32) is sometimes used on board ship as a capstan engine. It can be noted that the to-and-fro path of point A is similar to the arc of a circle whose center point is the center point of the pivot about which the cylinder oscillates. In the right-hand diagram, note that the point B on the crosshead moves up and down or reciprocates in a straight line path.

The movement of a point through equal space in equal intervals of time is called constant motion. The movement of a point through unequal spaces in equal intervals of time is called variable motion. Figure 1-33 illustrates both constant motion and variable motion.

In the movements of the crank pin and piston of an engine (see Figure 1-33), the rate of motion from the position of the crank pin at the beginning of the stroke (position A) is constant as it rotates to position B. This means that it passes through equal arcs in equal intervals of time. Perpendiculars from points 1, 2, 3, and so on, locate the corresponding positions a, b, c, and so on, of the piston. As shown in the diagram, the traversed spaces (Aa, ab, and so on) are unequal. Therefore, the motion is variable. The diagram represents the true relation where there is no distortion, as with a Scotchyoke mechanism. However, when a connecting rod is used, there is distortion caused by the angularity of the connecting rod.

Figure 1-33 Constant motion and variable motion.

Momentum

The power of a body to overcome resistance by means of its motion is termed momentum. Momentum is the quantity of motion in a moving body.

Momentum is measured by multiplying the quantity of matter in a body by its velocity. A numerical value of momentum can be expressed as the force (in pounds) steadily applied that can stop a moving body in 1 second. Therefore, momentum is equal to the mass of a body multiplied by its velocity in feet per second or:

Following is the formula for determining momentum:

in which the following is true:

W is the weight (in pounds)
V is velocity (in feet per second)
g is attraction caused by gravity (32.16)

Inertia

The property of matter that causes a body to tend to remain at rest (if it is already at rest); or to keep moving in the same direction unless affected by an outside force (if it is moving), is called inertia (symbol I). This gives rise to two states of inertia known as static inertia and dynamic inertia (see Figure 1-34).

Figure 1-34 Static inertia with respect to a body at rest (top) and dynamic inertia with respect to a body in motion (bottom).

Friction

The resistance to motion of two moving objects that touch is called friction. Friction is caused partially by the natural adhesion of one body to another. However, its chief cause is the roughness of surfaces that are in contact. Even a glossy, polished surface is not smooth when viewed with a powerful magnifying glass or microscope.

Coefficient of Friction

The ratio of the force required to slide a body along a horizontal plane surface to the weight of the body is the coefficient of friction. The coefficient of friction is equivalent to the tangent of the angle of repose.

The angle of repose is the largest angle with the horizontal at which a mass of material (such as an embankment or pile of coal) can remain at rest without sliding. This angle varies with different materials.

Laws of Friction

The first laws of friction were given by Morin in about 1830, but they have been modified by later experiments. As summarized by Kent, the laws of friction are as follows:

• Friction varies approximately as the normal pressure with which the rubbing surfaces are pressed together.

• Friction is approximately independent of the area of the surfaces, but it is slightly greater for smaller surfaces than for larger surfaces.

• Friction decreases with an increase in velocity, except at an extremely low velocity and with soft surfaces.

As applied to lubricated surfaces, the laws of friction for perfect lubrication (surfaces completely separated by a film of lubricant) are as follows:

• The coefficient of friction is independent of the materials making up the surfaces.

• The coefficient of friction varies directly with the viscosity of the lubricant, which varies inversely with the temperature of the lubricant.

• The coefficient of friction varies inversely as the unit pressure and varies directly as the velocity.

• The coefficient of friction varies inversely as the mean film thickness of the lubricating medium.

• Mean film thickness varies directly with velocity and inversely as the temperature and unit pressure.

As applied to imperfect lubrication, that is, surfaces partially separated (which may range from nearly complete separation to nearly complete contact) by a film of lubricant, the laws of friction are as follows:

• The coefficient of friction increases with an increase in pressure between the surfaces.

• The coefficient of friction increases with an increase in relative velocity between the surfaces.

Machinery cannot be operated without lubrication (notwithstanding the alleged antifriction metals) because of the tiny irregularities in a smooth metal surface. A lubricant is used to keep the rubbing parts separated by a thin film of oil, thus preventing actual contact so far as possible.

Work and Power

The expenditure of energy to overcome resistance through a certain distance is work. It is difficult to understand horsepower without an understanding of the difference between work and power (see Figure 1-35). Power is the rate at which work is done (that is, work divided by the time in which it is done).

The standard unit for measuring work is the foot-pound (ft-lb). The foot-pound is the amount of work that is done in raising a weight of 1 pound through a distance of 1 foot, or in overcoming a pressure of 1 pound through a distance of 1 foot (see Figure 1-36).

Figure 1-35 The difference between work (left) and power (right).

Figure 1-36 One foot-pound.

James Watt is believed to have adopted the term horsepower. He used it for his steam engine, to represent the power or capacity of a strong London draft-type horse for doing work during a short time interval. The term was used as a power rating for his steam engines. The present standard unit for measuring power is horsepower (hp). It is defined as 33,000 foot-pounds per minute. In other words, one horsepower is required to raise a weight of the following:

• 33,000 lb a height of 1 foot in one minute

• 3300 lb a height of 10 feet in one minute

• 33 lb a height of 1000 feet in one minute

• 3.3 lb a height of 10,000 feet in one minute

• 1 lb a height of 33,000 feet in one minute

A formula that is generally used to calculate engine horsepower is as follows:

in which the following is true:

P is the mean effective pressure in psi
L is the length of stroke, in feet
A is the area of piston, in square inches (0.7854 × d²)
N is the number of revolutions per minute (rpm)

Since the stroke of an engine is usually given in inches rather than in feet, and the revolutions per minute are given rather than the piston speed, the previous formula involves extra calculations for these items, as well as the extra multiplication and division introduced because of the constants. Therefore, the formula can be reduced to its lowest terms, as follows:

Thus, the constant 0.000004 can be used for most calculations. By changing the order of the factors, the formula is simplified to:

hp = 0.000004 d² LNP

According to its definitions and the manner in which it is derived, the various types of horsepower are nominal, indicated, brake, effective , hydraulic, boiler, and electrical. Figure 1-37 shows the various types of horsepower.

Basic Machines

For many years the basic mechanical contrivances that enter into the composition or formation of machines were referred to as mechanical powers. Since these mechanical contrivances are regarded in a more static than dynamic sense (that is, the consideration of opposing forces in equilibrium rather than tending to produce motion), it is more correct to refer to them as basic machines. Strictly speaking, the term power is a dynamic term relating to the time rate of doing work. When the elements of a machine are in equilibrium, no work is done. Therefore, it is incorrect to refer to the basic machines as mechanical powers.

It should be understood that the action of all the basic machines depends on the principle of work, which is: The applied force, multiplied by the distance through which it moves, equals the resistance overcome, multiplied by the distance through which it is overcome.

Figure 1-37 Various types of horsepower.

Following are the basic machine:

• Lever

• Wheel and axle

• Pulley

• Inclined plane

• Screw

• Wedge

These machines can be reduced further to three classes of machines, as follows:

• A solid body turning on an axis

• A flexible cord

• A hard and smooth inclined surface

The Principle of Moments is important in studying the basic machines. This important principle can be stated as follows: “When two or more forces act on a rigid body and tend to turn it on an axis, equilibrium exists if the sum of the moments of the forces which tend to turn the body in one direction equals the sum of the moments of those forces which tend to turn the body in the opposite direction about the same axis.

Lever

fulcrum