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Fundamental units should not be confused with standard units. Standard units of measurement are units that are established and legalized by the government of a country. Whenever standardized units are established, the fundamental units are expressed in terms of the standard units to secure uniformity of procedure and comparison.

2A2. The metric system of measurement. The metric system of measurement is used generally throughout the world, particularly in Europe. It is not in general use in the United States. Because the metric system is a decimal system, it is less subject to arithmetical error than the other common system, the English system of measurement. Since the metric system uses the simple multiplier, 10, it is easy to establish the value of the unit of measure as denoted by the prefix in the name of the unit. The table below explains how the prefix denotes the value of the unit of measure and gives examples of the use of the prefix.

In the metric system the fundamental units of force, length, and time are expressed in the standard units of kilograms, meters, and seconds.

The metric system has been legalized for use in the United States and is frequently used in scientific and laboratory work, because the smaller units facilitate work of extreme accuracy and the use of the simple multiplier, 10, makes computation of work quick and easy.

2A3. The English system of measurement. The English system of measurement is by far the most commonly used in engineering work in the United States. The system is given wide usage primarily because of precedent rather than because of any recommending features such as those encountered in the metric system.

In the English system the fundamental units of force, length, and time are expressed in the standard units of foot, pound, and second. Unlike the metric system, the English system has no common multiplier and the subdivisions of the units of measurement bear no common relation to each other. For example, below are given the units of length and weight and the relationship of the various subdivisions of each.

2A4. Unit of length. Length is usually defined as the distance between two points. In the English system it is expressed in inches, feet, yards, rods, miles, or fractions thereof. The accuracy required in engineering work makes it a general practice for engineers to measure length in thousandths of an inch. Thus, various tolerances, clearances, and minute measurements are expressed by decimal divisions of an inch in thousandths, such as .125 (one hundred twenty five thousandths).

In a problem involving measurement of area, the area of a regular shape may be expressed by the product of two measurements of length. Thus, a square 3 feet by 3 feet has 9 square feet of area. Likewise, a problem of measuring volume, where the shape is adaptable to linear measurement, may be expressed by the product of three measurements of length. Thus, a cube 3 feet by 3 feet by 3 feet has 27 cubic feet of volume.

2A5. Conversion factors of length. Often when using the English system in engineering work it is necessary to convert measurements to the metric system and vice versa. To change units of one system to those of another it is necessary to have a conversion factor that establishes the relation between the two systems for the same quantity. The most commonly used conversion factors between the English and metric systems are:

All English system measurements of length may be reduced to inches and all metric system measurements of length to centimeters. Knowing the basic conversion factor, inches can be converted to centimeters by multiplying inches

2A6. Unit of force. Force is the push, pull, or action upon a body or matter at rest which tends to give it motion. In the English system, the unit of force is the pound. In the metric system, the unit of force is the kilogram.

2A7. Unit of work. The work done upon a body is equal to the average force acting upon the body multiplied by the distance through which the body is moved as a result of the force. In the English system, the unit of work is the foot-pound. For example, if a force of 500 pounds acts upon a body to move it 10 feet, 5000 foot-pounds of work have been done upon this body.

2A8. Units of mass and weight. The mass of a body may be defined as the quantity of matter in a body without regard to its volume or the pull of gravity upon it. The term mass must be distinguished from the term weight which is the measurement of the force of gravity acting upon body at any given point upon the earth's surface. Weight varies with locality, but mass is considered constant. The student must not confuse mass with weight although the units are the same for both. The standard kilogram is defined as the mass of a certain piece of platinum iridium in possession of the International Bureau of Weights and Measures. The fundamental unit of mass, the gram, is one one-thousandth of the standard kilogram.

Kilograms are converted into pounds by multiplying the number of kilograms by 2.205, and conversely pounds are converted into kilograms by multiplying the number of pounds by 0.454. For example, 1 metric ton (1000 kilograms) equals 1000 x 2.205 or 2205 pounds.

2A9. Unit of pressure. Pressure is defined as force per unit area acting against a body. In the English system, the unit of pressure may be expressed as pounds per square inch or pounds per square foot.

Since all forms of matter have weight, the air of the earth's atmosphere has weight. At sea

Gage pressure. Pressure gages are commonly used to determine the pressure existing or to record the peak pressure attained within a container. Most pressure gages make no allowance for atmospheric pressure and normally register zero at existing atmospheric pressure.

Absolute pressure. In practically all pressure problems, atmospheric pressure is present and must be accounted for. When atmospheric pressure is added to the gage or indicated pressure, the total obtained is the absolute pressure. Thus, absolute pressure is the total pressure recorded from a zero point. For example, the scavenging air pressure in a cylinder is 4 psi. If the cylinder is at sea level, the atmospheric pressure of 14.7 psi must be added, making the total 18.7 psi absolute pressure.

2A10. Unit of power. Work has been defined as force acting through a given distance. Power may be defined as the amount of work performed during a unit period of time. The unit of power used by engineers is the horsepower. One horsepower (hp) equals the amount of work necessary to raise 33,000 pounds through a distance of 1 foot in 1 minute. One horsepower also equals the amount of work necessary to raise 550 pounds through a distance of 1 foot in 1 second.

Example: How many horsepower are required to raise a weight of 12,000 pounds through a distance of 22 feet in 2 minutes?
Solution: (12,000 x 22)/(2 x 33,000) = 4 horsepower

2A11. Unit of temperature. Temperature may be defined as the measure of intensity of heat. In simple language, temperature is the measure of hotness (usually referred to as high temperature) or coldness (usually referred to as low temperature) of a body or matter.

Temperature is measured and expressed in degrees according to established standard scales known as the Fahrenheit and centigrade scales. The Fahrenheit scale is established with a range

a. Absolute zero temperature. Absolute zero temperature is theoretically the lowest temperature that can be obtained. It is that temperature at which all molecular motion ceases entirely and at which point the given matter possesses no heat whatsoever. Absolute zero temperature has been determined to be -273 degrees C and -459.6 degrees F. From a practical standpoint, absolute zero is unattainable.

b. Conversion factors of temperature. Since the centigrade scale covers the same temperature range (freezing to boiling points of water) in 100 degrees that the Fahrenheit scale covers in 180 degrees, a centigrade degree equals 9/5 of a Fahrenheit degree. Hence, a centigrade reading may be converted to a Fahrenheit reading by multiplying the centigrade reading by 9/5 and adding 32 degrees. And, conversely, a Fahrenheit reading may be converted to a centigrade reading by subtracting 32 degrees and multiplying by 5/9.

Expressed as a simple equation, the conversion factor is:

F = 9/5 C + 32
C = 5/9 (F - 32)

Example: How many degrees centigrade are 86 degrees Fahrenheit?
Solution: C = 5/9 x (86 - 32) = 30
degrees C.

Example: How many degrees Fahrenheit are 35 degrees centigrade?
Solution: F = 9/5 x 35 + 32 = 95
degrees F.

2A12. Unit of heat. Heat is a form of energy, and the English system unit of heat is the mean British thermal unit (Btu). The British thermal unit is the amount of heat necessary to raise the temperature of 1 pound of water 1 degree F at sea level atmospheric pressure.

Since heat is a form of energy, it cannot be destroyed but may be converted into mechanical energy. One Btu of heat is equivalent to 778 foot-pounds of work. Thus, the conversion factor for power to heat is:

1 hp = 33,000 / 778 = 42.42 Btu per minute

2A13. Unit of time. The standard unit of time in both the English system and the metric system is the second. The second is defined as 1/86,400 part of a mean solar day. The mean solar day is obtained by taking the average length of all the days of the year, a day being measured from the noon of one day to the noon of the next.

2A14. Units of velocity. Velocity may be defined as the rate of movement of a body. If a body moves a specified distance during a specified time at a uniform speed, the velocity may be determined by dividing the distance by the time. There are two types of velocity normally encountered, linear and angular. If the velocity is linear, the movement is in a straight line and the velocity may be expressed in terms such as feet per second, feet per minute, or miles per hour. If the velocity is angular, the movement of the body is rotary or about a central axis, and the velocity may be expressed in revolutions per minute or revolutions per second. In engineering work it is common practice to rate the velocity of shafts, wheels, gears, and other rotating parts in revolutions per minute (rpm).

2B2. Instruments for measuring length. a. General. In engineering and machine work there are several instruments for measuring length, area, and volume. Since the measurement of area and volume often can be obtained by compounding simple measurements of length, instruments used for computing area and volume are also described here.

b. Rulers and tapes. The most common method of obtaining simple measurements of length is by the ruler or tape (Figure 2-1). A ruler may be graduated into feet, inches, or fractions thereof. Rulers and tapes used in engineering work are most frequently made of metal and the fractions of inches may be graduated to subdivisions as small as 1/64 or 1/100 of an inch. Care should be exercised in using metal rulers and tapes, especially if extreme accuracy is required. The margin of error due to

c. Calipers. Engineers and machinists frequently use calipers to secure accurate measurements of inside and outside diameters. Figure 2-2 shows how various caliper settings may be taken and how the registered setting of the calipers may be measured by a ruler or by a micrometer.

d. Micrometer calipers. Engineers frequently rely on the micrometer caliper (Figure 2-3) to obtain measurements accurate to 1/1000 of an inch. This instrument is particularly useful for measuring relatively short lengths and the diameter of journals or cylinders. The common commercial micrometer consists of a frame; an anvil, or fixed measuring point; a spindle; a sleeve, or barrel; and a thimble. The spindle has threads cut 40 to the inch on the portion that fits inside the sleeve. The thimble fits over the end of the sleeve, and rotating the thimble turns the spindle.

Rotating the thimble until the spindle has made one complete turn moves the spindle 1/40 of an inch, which is equal to 0.025 inch. The number of turns the spindle makes is indicated by graduations on the sleeve. Each graduation

The thimble has a beveled edge divided into 25 parts and numbered 0, 5, 10, 15, 20, and back to again. Each of these marks represents 1/25 of a turn or 1/25 of 0.025 which is 1/1000 (0.001) of an inch. A final reading of the micrometer is obtained by multiplying the number of graduations on the sleeve by 25 and adding the number of marks indicated on the beveled edge of the thimble. This gives the reading in thousandths.

For example, in Figure 2-3 the graduations on the sleeve show the spindle has turned 7 revolutions which is equivalent to 7 x 0.025, or 0.175 inch. The thimble has been turned 3 marks, or 0.003 inch. The total reading then is 0.175 plus 0.003, or 0.178 inch.

e. Feeler gages. The feeler gage (Figure 2-4) comes into frequent use in engineering and

Feeler gages are principally used in determining clearances between various parts of machinery. Probably the most common use is determining valve clearance. Various blades are inserted between the tappet and the push rod until a blade of the feeler gage is found that will just slide between the two surfaces without too much friction or sticking. The thickness of the blade then determines the clearance. Or, a particular feeler of proper thickness may be selected and the tappet adjusted until the feeler will just slide between the tappet and push rod with out catching.

f. Bridge gages. Bridge gages are used to measure the amount an engine main bearing has dropped due to wear. Figure 2-5 shows

Bridge gages must be handled with great care. If the tip on the gage or the supporting surfaces becomes burred, worn, or distorted, the gage will give an inaccurate reading.

In taking measurements with thermometers and pyrometers, the operator should bear in mind the possibility of errors in measurement and what effect they may have on his particular problem. An error is the difference between the observed value and the true value and may be expressed as a percentage. Some errors inherent in an instrument may be avoided by periodically checking the calibration of an instrument with one of known accuracy. Sometimes, errors due to the aging or failure of materials in the instrument are unavoidable, such as the deterioration of glass due to aging and repeated stress. A check of the instrument will indicate the

b. Liquid-in-glass thermometers. In the type of thermometer in which a hollow glass stem is filled with a liquid (Figure 2-6) the liquid most commonly used is mercury, although some thermometers are filled with alcohol or pentane. In some cases, where extremely low temperatures are to be recorded, a gas may be used. In the construction of the common mercury thermometer, care is used in sealing the stem to insure that a vacuum exists above the column of mercury in the stem. Otherwise, the mercury would have to compress the air in the stem, and a false reading would result.

To graduate a thermometer (Figure 2-7) the bulb and a portion of the stem holding the mercury are submerged in melting ice and the point at which the mercury stands in the tube is marked 32 degrees if the thermometer is Fahrenheit, or 0 degrees if the thermometer is centigrade. Next, the bulb and stem are placed in a closure in which they are surrounded by steam rising off boiling water at sea level atmospheric pressure. The position of the top of the column of mercury is then marked at 212 degrees if the thermometer is Fahrenheit, or at 100 degrees if the

On Fahrenheit thermometers the distance between the 32 degrees and the 212 degrees marks is graduated and marked into 180 equal parts, each space or subdivision representing 1 degrees F. On centigrade thermometers the distance between the 0 degrees and 100 degrees marks is graduated and marked into 100 equal parts, each space representing 1 degree C. The space above and below these markings is calibrated into the same graduations for the entire temperature range of the thermometer.

Figure 2-7. Method of graduating thermometers.

c. Electrical resistance thermometers. Electrical resistance thermometers (Figure 2-8) make use of the principle that the electrical resistance of various metals varies with their temperature. The resistance is measured by a Wheatstone bridge which is connected to a galvanometer calibrated to read in degrees of temperature. One leg of the balanced bridge circuit is led to the thermometer bulb which is inserted at the point where the temperature is to be measured. A temperature change at the thermometer bulb will change the resistance with regard to the circuit, causing an electrical unbalance in the entire bridge. This unbalance will

Figure 2-8. Electrical resistance thermometer dial and bulb.

d. Thermocouple pyrometers. The thermocouple unit of the pyrometer (Figure 2-9). is made of two wires or strips of dissimilar metals connected at one end and having an electrical connection at the other end. When the two ends or junctions are subjected to different temperatures, an electrical current is generated. This current is measured to give an indication of the differences in temperatures between the two junctions. In submarines the most common application of this instrument is for measuring the exhaust temperature in the exhaust elbows of the engine. One of the two thermocouple wires is made of pure iron and the other is made of constantan, a nickel copper alloy. The wires are twisted together and welded at the tip of the thermocouple and mounted in the closed end of the protecting tube made of pure nickel. The protecting tube is fitted with a terminal head in which the connections are made between the extension leads and the thermocouple wires. These connections between the thermocouple and the

2B4. Instruments for measuring pressure. a. Barometers. The most common instrument in use for measuring atmospheric pressure is the mercury barometer (Figure 2-10). This instrument consists of a long, hollow, glass tube, sealed at one end and with the open end of the tube submerged beneath the surface of an open container of mercury. An increased air pressure acting upon the surface of the mercury in the open container causes the mercury to rise in the tube. The space between the mercury and the sealed end inside the tube is a vacuum so that air will not be compressed in the tube and counteract the pressure exerted outside. The tube containing the column of mercury is calibrated in inches and subdivisions of 1/100 of

Another type of barometer is the aneroid barometer (Figure 2-10). The aneroid barometer consists of an exhausted chamber with corrugated diaphragm walls. Atmospheric pressure causes the diaphragm walls to deflect against the resistance of a spring. The deflections of the diaphragm walls against the spring are recorded by a lever or indicator upon a calibrated face through a delicate system of levers. Some aneroid barometers are so sensitive that they will register a change when raised or lowered only a few feet. Due to the effect of aging and fatigue of the diaphragm construction, aneroid barometers should have their calibrations

b. Pressure gages. Pressure gages (Figure 2-11) of the diaphragm or tube type are generally used for determining the pressure of steam, water, air, and other mediums. The aneroid barometer described above is an example of the diaphragm type pressure gage. However, the tube type gage is considered more accurate. Such a gage is called a Bourdon gage. The simplex pressure gage illustrated in Figure 2-11 is a Bourdon type gage. This gage consists of an elastic metal tube of oval cross section, bent into an arc. The two metals commonly used in making the tube are brass and steel. In low-pressure gages, brass is normally used but if the pressures to be measured exceed 100 psi, the tubes are always constructed of steel. One end of the tube is fixed and the other end is movable. The free end of the tube is connected to a spring-loaded needle through a gear and system of levers. Pressure exerted on the inside walls of the oval tube tends to make the tube straighten

2B5. Instruments for measuring volume. a. Sounding. One of the most common measuring problems in diesel engineering is determining the volume of fluid remaining in fuel oil and lubricating oil tanks. The simplest and most accurate method of determining the volume of fluid in a tank is by sounding. In submarine fuel systems, as fuel is withdrawn from a tank, it is replaced by compensating water. Small sounding tubes of various lengths are installed in the tanks to determine whether there is oil or water at various levels.

b. Fuel oil meters. Fuel oil meters are also used in submarine fuel systems to indicate the amount of fuel withdrawn from the main fuel tanks. Fuel oil meters should be checked frequently for accuracy. Strainers should be

installed in the line to the fuel oil meter to prevent any foreign substance from getting into the meter mechanism and affecting the accuracy of its registration.

c. Liquidometers. In submarines, liquidometers are frequently used to determine: 1) the level of the liquid in a partially filled tank, and 2) the level between two dissimilar liquids in a completely filled tank.

The liquidometer is equipped with a float mechanism, the movement of which actuates a double-acting opposed hydraulic mechanism which registers upon a calibrated dial the volume of the desired liquid.

2B6. Instruments for measuring rotational speed. a. General. Aboard ship it is often imperative to know the rotational speed of an engine or piece of machinery which is generally measured in rpm. Various instruments such as revolution counters, mechanical tachometers, and electrical tachometers, are available for securing this measurement.

The rotating continuous counter may have direct-reading wheels of the cyclometer type or may operate dials or pointers through a gear train. The oscillating or stroke counter is adapted for low speeds only. Rotating counters may be obtained for high-speed work, up to 5000 rpm. It is important that a counter not be used for speeds higher than the speed limits recommended by the manufacturer.

Figure 2-12. Mechanical revolution counter.

c. Mechanical tachometers. Tachometers (Figure 2-13) are measuring instruments that give a direct and continuous indication of rotary speed in rpm. For submarine diesel engines, the mechanical tachometers are usually permanently mounted on a gage board. They are generally driven from the engine camshaft through a gearing and a flexible shaft. In operation, the force produced by the rotation is balanced against a calibrated spring or against the force of gravity. Those used in submarines are usually of the indicator type in which the pointer registers the rpm at the moment, rising and falling with the fluctuations in engine speed.

Figure 2-13. Mechanical tachometer.

d. Electrical tachometers. Electrical tachometers (Figure 2-14) of the indicating type are used with submarine diesel engines. The drive mechanism for the electrical tachometer is actuated by the engine camshaft. The drive in turn powers a tachometer magneto and

the electric current generated actuates an indicator which is calibrated to register engine revolutions per minute. The electrical tachometer possesses the distinct advantage that the indicating instrument may be mounted at a distance from the drive mechanism.

All tachometers should be checked frequently for accuracy. This check can be made by using a mechanical revolution counter which is 100 percent accurate. The tachometer is checked against the counter for several minutes with a stop watch and then the reading on the counter is divided by the number of minutes to check the number of rpm.