12 Chapter 1 Getting Started The SI unit of force,called the newton,is a secondary unit,defined in terms of the base units for mass.length,and time.Newton's second law of motion states that the net force acting on a body is proportional to the product of the mass and the acceleration,written F o ma.The newton is defined so that the proportionality con- stant in the expression is equal to unity.That is,Newton's second law is expressed as the equality F ma (11) The newton,N,is the force required to accelerate a mass of 1 kilogram at the rate of 1 meter per second per second.With Eq.1.1 1N (1 kg)(1 m/s2)=1kg.m/s2 (1.2) FREXAMPL to illustrate the use of the SI units introduced thus far,let us determine the weight in newtons of an object whose mass is 1000 kg,at a place on TAKE NOTE... the earth's surface where the acceleration due to gravity equals a standard value Observe that in the calcu- defined as 9.80665 m/s2.Recalling that the weight of an object refers to the force of lation of force in newtons. gravity,and is calculated using the mass of the object,m,and the local acceleration the unit conversion factor of gravity,g,with Eq.1.1 we get is set off by a pair of verti- F=mg cal lines.This device is used throughout the text to =(1000kg)(9.80665m/s2)=9806.65kg·m/s2 identify unit conversions. This force can be expressed in terms of the newton by using Eq.1.2 as a unit conversion factor.That is. IN F= 9806.65g·m s21kg·mls2 =9806.65N44444 TABLE 1.4 Since weight is calculated in terms of the mass and the local acceleration due to gravity,the weight of an object can vary because of the variation of the acceleration SI Unit Prefixes of gravity with location,but its mass remains constant. Factor Prefix Symbol 102 FOR EXAMPLE if the object considered previously were on the surface of a tera T 109 planet at a point where the acceleration of gravity is one-tenth of the value used in giga G 106 the above calculation,the mass would remain the same but the weight would be one- mega 103 kilo k tenth of the calculated value. 102 hecto h 102 centi C SI units for other physical quantities are also derived in terms of the SI base units.Some 103 milli m of the derived units occur so frequently that they are given special names and symbols. 10~6 micro such as the newton.SI units for quantities pertinent to thermodynamics are given as they 10~9 nano n are introduced in the text.Since it is frequently necessary to work with extremely large 10-12 pico or small values when using the SI unit system,a set of standard prefixes is provided in Table 1.4 to simplify matters.For example,km denotes kilometer,that is,10'm. 1.4.2t English Engineering Units Although SI units are the worldwide standard,at the present time many segments of the engineering community in the United States regularly use other units.A large portion of America's stock of tools and industrial machines and much valuable engi- neering data utilize units other than SI units.For many years to come,engineers in the United States will have to be conversant with a variety of units. In this section we consider a system of units that is commonly used in the United English base units States,called the English Engineering system.The English base units for mass,length, and time are listed in Table 1.3 and discussed in the following paragraphs.English units for other quantities pertinent to thermodynamics are given as they are intro- duced in the text
12 Chapter 1 Getting Started The SI unit of force, called the newton, is a secondary unit, defined in terms of the base units for mass, length, and time. Newton’s second law of motion states that the net force acting on a body is proportional to the product of the mass and the acceleration, written F r ma . The newton is defined so that the proportionality constant in the expression is equal to unity. That is, Newton’s second law is expressed as the equality F 5 ma (1.1) The newton, N, is the force required to accelerate a mass of 1 kilogram at the rate of 1 meter per second per second. With Eq. 1.1 1 N 5 11 kg211 m/s 2 2 5 1 kg ? m/s 2 (1.2) to illustrate the use of the SI units introduced thus far, let us determine the weight in newtons of an object whose mass is 1000 kg, at a place on the earth’s surface where the acceleration due to gravity equals a standard value defined as 9.80665 m/s 2 . Recalling that the weight of an object refers to the force of gravity, and is calculated using the mass of the object, m , and the local acceleration of gravity, g , with Eq. 1.1 we get F 5 mg 5 11000 kg219.80665 m/s 2 2 5 9806.65 kg ? m/s 2 This force can be expressed in terms of the newton by using Eq. 1.2 as a unit conversion factor . That is, F 5 a9806.65 kg ? m s 2 b ` 1 N 1 kg ? m/s 2 ` 5 9806.65 N b b b b b Since weight is calculated in terms of the mass and the local acceleration due to gravity, the weight of an object can vary because of the variation of the acceleration of gravity with location, but its mass remains constant. if the object considered previously were on the surface of a planet at a point where the acceleration of gravity is one-tenth of the value used in the above calculation, the mass would remain the same but the weight would be onetenth of the calculated value. b b b b b SI units for other physical quantities are also derived in terms of the SI base units. Some of the derived units occur so frequently that they are given special names and symbols, such as the newton. SI units for quantities pertinent to thermodynamics are given as they are introduced in the text. Since it is frequently necessary to work with extremely large or small values when using the SI unit system, a set of standard prefixes is provided in Table 1.4 to simplify matters. For example, km denotes kilometer, that is, 10 3 m. SI Unit Prefixes Factor Prefix Symbol 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 1022 centi c 1023 milli m 1026 micro m 1029 nano n 10212 pico p TABLE 1.4 English base units 1.4.2 English Engineering Units Although SI units are the worldwide standard, at the present time many segments of the engineering community in the United States regularly use other units. A large portion of America’s stock of tools and industrial machines and much valuable engineering data utilize units other than SI units. For many years to come, engineers in the United States will have to be conversant with a variety of units. In this section we consider a system of units that is commonly used in the United States, called the English Engineering system. The English base units for mass, length, and time are listed in Table 1.3 and discussed in the following paragraphs. English units for other quantities pertinent to thermodynamics are given as they are introduced in the text. TAKE NOTE... Observe that in the calculation of force in newtons, the unit conversion factor is set off by a pair of vertical lines. This device is used throughout the text to identify unit conversions. c01GettingStarted.indd Page 12 5/13/10 3:28:25 PM user-s146 /Users/user-s146/Desktop/Merry_X-Mas/New
1.5 Specific Volume 13 The base unit for length is the foot,ft,defined in terms of the meter as 1ft=0.3048m (1.3) The inch,in.,is defined in terms of the foot 12 in.1 ft One inch equals 2.54 cm.Although units such as the minute and the hour are often used in engineering,it is convenient to select the second as the English Engineering base unit for time. The English Engineering base unit of mass is the pound mass,Ib,defined in terms of the kilogram as 11b=0.45359237kg (1.4 The symbol lbm also may be used to denote the pound mass. Once base units have been specified for mass,length,and time in the English Engineering system of units,a force unit can be defined,as for the newton,using Newton's second law written as Eq.1.1.From this viewpoint,the English unit of force, the pound force,Ibf,is the force required to accelerate one pound mass at 32.1740 ft/s2. which is the standard acceleration of gravity.Substituting values into Eq.1.1 1Ibf=(1Ib)(32.1740f/s2)=32.1740b·f/s2 (1.5) With this approach force is regarded as secondary. The pound force,Ibf,is not equal to the pound mass,Ib,introduced previously. Force and mass are fundamentally different,as are their units.The double use of the word "pound"can be confusing,however,and care must be taken to avoid error. FREXAMPLE to show the use of these units in a single calculation,let us deter- mine the weight of an object whose mass is 1000 lb at a location where the local acceleration of gravity is 32.0 ft/s2.By inserting values into Eq.1.1 and using Eq.1.5 as a unit conversion factor,we get 1 lbf F=mg=(1000Ib) 32.0 994.591bf 32.17401b·f/s2 This calculation illustrates that the pound force is a unit of force distinct from the pound mass,a unit of mass. 1.5 Specific Volume Three measurable intensive properties that are particularly important in engineering thermodynamics are specific volume,pressure,and temperature.Specific volume is considered in this section.Pressure and temperature are considered in Secs.16 and 1.7 respectively. From the macroscopic perspective,the description of matter is simplified by con- sidering it to be distributed continuously throughout a region.The correctness of this idealization,known as the continuum hypothesis,is inferred from the fact that for an extremely large class of phenomena of engineering interest the resulting description of the behavior of matter is in agreement with measured data. When substances can be treated as continua,it is possible to speak of their inten- sive thermodynamic properties "at a point."Thus,at any instant the density p at a point is defined as m (1.6 Ext Int Properties where V'is the smallest volume for which a definite value of the ratio exists.The volume A.3-Tabs b &c V'contains enough particles for statistical averages to be significant.It is the smallest
The base unit for length is the foot, ft, defined in terms of the meter as 1 ft 5 0.3048 m (1.3) The inch, in., is defined in terms of the foot 12 in. 5 1 ft One inch equals 2.54 cm. Although units such as the minute and the hour are often used in engineering, it is convenient to select the second as the English Engineering base unit for time. The English Engineering base unit of mass is the pound mass, lb, defined in terms of the kilogram as 1 lb 5 0.45359237 kg (1.4) The symbol lbm also may be used to denote the pound mass. Once base units have been specified for mass, length, and time in the English Engineering system of units, a force unit can be defined, as for the newton, using Newton’s second law written as Eq. 1.1 . From this viewpoint, the English unit of force, the pound force, lbf, is the force required to accelerate one pound mass at 32.1740 ft/s 2 , which is the standard acceleration of gravity. Substituting values into Eq. 1.1 1 lbf 5 11 lb2132.1740 ft/s 2 2 5 32.1740 lb ? ft/s 2 (1.5) With this approach force is regarded as secondary. The pound force, lbf, is not equal to the pound mass, lb, introduced previously. Force and mass are fundamentally different, as are their units. The double use of the word “pound” can be confusing, however, and care must be taken to avoid error. to show the use of these units in a single calculation, let us determine the weight of an object whose mass is 1000 lb at a location where the local acceleration of gravity is 32.0 ft/s 2 . By inserting values into Eq. 1.1 and using Eq. 1.5 as a unit conversion factor, we get F 5 mg 5 11000 lb2a32.0 ft s 2 b ` 1 lbf 32.1740 lb ? ft/s 2 ` 5 994.59 lbf This calculation illustrates that the pound force is a unit of force distinct from the pound mass, a unit of mass. b b b b b 1.5 Specific Volume Three measurable intensive properties that are particularly important in engineering thermodynamics are specific volume, pressure, and temperature. Specific volume is considered in this section. Pressure and temperature are considered in Secs. 1.6 and 1.7, respectively. From the macroscopic perspective, the description of matter is simplified by considering it to be distributed continuously throughout a region. The correctness of this idealization, known as the continuum hypothesis, is inferred from the fact that for an extremely large class of phenomena of engineering interest the resulting description of the behavior of matter is in agreement with measured data. When substances can be treated as continua, it is possible to speak of their intensive thermodynamic properties “at a point.” Thus, at any instant the density r at a point is defined as r 5 limVSV¿ a m V b (1.6) where V9 is the smallest volume for which a definite value of the ratio exists. The volume V9 contains enough particles for statistical averages to be significant. It is the smallest 1.5 Specific Volume 13 A Ext_Int_Properties A.3 – Tabs b & c c01GettingStarted.indd Page 13 6/26/10 12:11:23 PM user-s146 /Users/user-s146/Desktop/Merry_X-Mas/New
14 Chapter 1 Getting Started volume for which the matter can be considered a continuum and is normally small enough that it can be considered a"point."With density defined by Eq.1.6,density can be described mathematically as a continuous function of position and time. The density,or local mass per unit volume,is an intensive property that may vary from point to point within a system.Thus,the mass associated with a particular volume V is determined in principle by integration 1m= pdy (1.7 and not simply as the product of density and volume. specific volume The specific volume v is defined as the reciprocal of the density,v 1/p.It is the volume per unit mass.Like density,specific volume is an intensive property and may vary from point to point.SI units for density and specific volume are kg/m'and m/kg,respectively.However,they are also often expressed,respec- tively,as g/cm'and cm'/g.English units used for density and specific volume in this text are Ib/ft'and ft'/lb,respectively. In certain applications it is convenient to express properties such as specific vol- ume on a molar basis rather than on a mass basis.A mole is an amount of a given substance numerically equal to its molecular weight.In this book we express the molar basis amount of substance on a molar basis in terms of the kilomole (kmol)or the pound mole (Ibmol),as appropriate.In each case we use (1.8) M The number of kilomoles of a substance,n,is obtained by dividing the mass,m,in kilograms by the molecular weight,M,in kg/kmol.Similarly,the number of pound moles,n,is obtained by dividing the mass,m,in pound mass by the molecular weight, M,in lb/lbmol.When m is in grams,Eq.1.8 gives n in gram moles,or mol for short. Recall from chemistry that the number of molecules in a gram mole,called Avogadro's number,is 6.022 x 1023.Appendix Tables A-1 and A-1E provide molecular weights for several substances. To signal that a property is on a molar basis,a bar is used over its symbol.Thus, signifies the volume per kmol or Ibmol,as appropriate.In this text,the units used for are m/kmol and ft'/lbmol.With Eq.1.8,the relationship between and v is U=Mv (1.9) where M is the molecular weight in kg/kmol or Ib/lbmol,as appropriate. 1.6 Pressure Next,we introduce the concept of pressure from the continuum viewpoint.Let us begin by considering a small area A passing through a point in a fluid at rest.The fluid on one side of the area exerts a compressive force on it that is normal to the area,Fnormal.An equal but oppositely directed force is exerted on the area by the fluid on the other side.For a fluid at rest,no other forces than these act on the pressure area.The pressure p at the specified point is defined as the limit p=() (1.10) Ext_Int_Properties A.3-Tab d where A'is the area at the "point"in the same limiting sense as used in the defini- tion of density
14 Chapter 1 Getting Started volume for which the matter can be considered a continuum and is normally small enough that it can be considered a “point.” With density defined by Eq. 1.6 , density can be described mathematically as a continuous function of position and time. The density, or local mass per unit volume, is an intensive property that may vary from point to point within a system. Thus, the mass associated with a particular volume V is determined in principle by integration m 5 # V r dV (1.7) and not simply as the product of density and volume. The specific volume y is defined as the reciprocal of the density, y 5 1yr . It is the volume per unit mass. Like density, specific volume is an intensive property and may vary from point to point. SI units for density and specific volume are kg/m 3 and m 3 /kg, respectively. However, they are also often expressed, respectively, as g/cm 3 and cm 3 /g. English units used for density and specific volume in this text are lb/ft 3 and ft 3 /lb, respectively. In certain applications it is convenient to express properties such as specific volume on a molar basis rather than on a mass basis. A mole is an amount of a given substance numerically equal to its molecular weight. In this book we express the amount of substance on a molar basis in terms of the kilomole (kmol) or the pound mole (lbmol), as appropriate. In each case we use n 5 m M (1.8) The number of kilomoles of a substance, n , is obtained by dividing the mass, m , in kilograms by the molecular weight, M , in kg/kmol. Similarly, the number of pound moles, n , is obtained by dividing the mass, m , in pound mass by the molecular weight, M , in lb/lbmol. When m is in grams, Eq. 1.8 gives n in gram moles, or mol for short. Recall from chemistry that the number of molecules in a gram mole, called Avogadro’s number, is 6.022 3 10 23 . Appendix Tables A-1 and A-1E provide molecular weights for several substances. To signal that a property is on a molar basis, a bar is used over its symbol. Thus, y signifies the volume per kmol or lbmol, as appropriate. In this text, the units used for y are m 3 /kmol and ft 3 /lbmol. With Eq. 1.8 , the relationship between y and y is y 5 My (1.9) where M is the molecular weight in kg/kmol or lb/lbmol, as appropriate. specific volume molar basis 1.6 Pressure Next, we introduce the concept of pressure from the continuum viewpoint. Let us begin by considering a small area A passing through a point in a fluid at rest. The fluid on one side of the area exerts a compressive force on it that is normal to the area, Fnormal . An equal but oppositely directed force is exerted on the area by the fluid on the other side. For a fluid at rest, no other forces than these act on the area. The pressure p at the specified point is defined as the limit p 5 limASA¿ a Fnormal A b (1.10) where A9 is the area at the “point” in the same limiting sense as used in the definition of density. pressure A Ext_Int_Properties A.3 – Tab d c01GettingStarted.indd Page 14 6/30/10 11:37:49 AM user-s146 /Users/user-s146/Desktop/Merry_X-Mas/New
1.6 Pressure 15 Horizons Big Hopes For Nanotechnology…………………· Nanoscience is the study of molecules and molec- continuum model may no longer apply owing to the interactions ular structures,called nanostructures,having one or among the atoms under consideration.Also at these scales,the more dimensions less than about 100 nanometers.One nature of physical phenomena such as current flow may depend nanometer is one billionth of a meter:1 nm=10m.To grasp explicitly on the physical size of devices.After many years of fruitful this level of smallness,a stack of 1o hydrogen atoms would have research,nanotechnology is now poised to provide new products a height of 1 nm,while a human hair has a diameter about with a broad range of uses,including implantable chemotherapy 50,o0o nm.Nanotechnology is the engineering of nanostruc- devices,biosensors for glucose detection in diabetics,novel elec- tures into useful products.At the nanotechnology scale,behavior tronic devices,new energy conversion technologies,and 'smart may differ from our macroscopic expectations.For example,the materials',as for example fabrics that allow water vapor to escape averaging used to assign property values at a point in the while keeping liquid water out. If the area a'was given new orientations by rotating it around the given point, and the pressure determined for each new orientation,it would be found that the pressure at the point is the same in all directions as long as the fluid is at rest.This is a consequence of the equilibrium of forces acting on an element of volume sur- rounding the point.However,the pressure can vary from point to point within a fluid at rest:examples are the variation of atmospheric pressure with elevation and the pressure variation with depth in oceans,lakes,and other bodies of water. Consider next a fluid in motion.In this case the force exerted on an area passing through a point in the fluid may be resolved into three mutually perpendicular com- ponents:one normal to the area and two in the plane of the area.When expressed absolute pressure on a unit area basis,the component normal to the area is called the normal stress, and the two components in the plane of the area are termed shear stresses.The mag- Gas at nitudes of the stresses generally vary with the orientation of the area.The state of pressure p stress in a fluid in motion is a topic that is normally treated thoroughly in fluid mechanics.The deviation of a normal stress from the pressure,the normal stress that would exist were the fluid at rest,is typically very small.In this book we assume that the normal stress at a point is equal to the pressure at that point.This assumption yields results of acceptable accuracy for the applications considered.Also,the term pressure,unless stated otherwise,refers to absolute pressure:pressure with respect to the zero pressure of a complete vacuum. Manometer liquid 1.6.1t Pressure Measurement Fig.1.7 Manometer. Manometers and barometers measure pressure in terms of the length of a column of Mercury vapor,Pvapor liquid such as mercury,water,or oil.The manometer shown in Fig.1.7 has one end open to the atmosphere and the other attached to a tank containing a gas at a uniform pressure.Since pressures at equal elevations in a continuous mass of a liquid or gas at rest are equal,the pressures at points a and b of Fig.1.7 are equal.Applying an elementary force balance,the gas pressure is p=Patm pgL (L.11) where patm is the local atmospheric pressure,p is the density of the manometer liquid, g is the acceleration of gravity,and L is the difference in the liquid levels. The barometer shown in Fig.1.8 is formed by a closed tube filled with liquid mer- Mercury.Pm cury and a small amount of mercury vapor inverted in an open container of liquid mercury.Since the pressures at points a and b are equal,a force balance gives the Fig.1.8 Barometer
1.6 Pressure 15 Nanoscience is the study of molecules and molecular structures, called nanostructures, having one or more dimensions less than about 100 nanometers. One nanometer is one billionth of a meter: 1 nm 5 1029 m. To grasp this level of smallness, a stack of 10 hydrogen atoms would have a height of 1 nm, while a human hair has a diameter about 50,000 nm. Nanotechnology is the engineering of nanostructures into useful products. At the nanotechnology scale, behavior may differ from our macroscopic expectations. For example, the averaging used to assign property values at a point in the continuum model may no longer apply owing to the interactions among the atoms under consideration. Also at these scales, the nature of physical phenomena such as current flow may depend explicitly on the physical size of devices. After many years of fruitful research, nanotechnology is now poised to provide new products with a broad range of uses, including implantable chemotherapy devices, biosensors for glucose detection in diabetics, novel electronic devices, new energy conversion technologies, and ‘smart materials’, as for example fabrics that allow water vapor to escape while keeping liquid water out. Big Hopes For Nanotechnology If the area A9 was given new orientations by rotating it around the given point, and the pressure determined for each new orientation, it would be found that the pressure at the point is the same in all directions as long as the fluid is at rest . This is a consequence of the equilibrium of forces acting on an element of volume surrounding the point. However, the pressure can vary from point to point within a fluid at rest; examples are the variation of atmospheric pressure with elevation and the pressure variation with depth in oceans, lakes, and other bodies of water. Consider next a fluid in motion. In this case the force exerted on an area passing through a point in the fluid may be resolved into three mutually perpendicular components: one normal to the area and two in the plane of the area. When expressed on a unit area basis, the component normal to the area is called the normal stress, and the two components in the plane of the area are termed shear stresses . The magnitudes of the stresses generally vary with the orientation of the area. The state of stress in a fluid in motion is a topic that is normally treated thoroughly in fluid mechanics. The deviation of a normal stress from the pressure, the normal stress that would exist were the fluid at rest, is typically very small. In this book we assume that the normal stress at a point is equal to the pressure at that point. This assumption yields results of acceptable accuracy for the applications considered. Also, the term pressure, unless stated otherwise, refers to absolute pressure: pressure with respect to the zero pressure of a complete vacuum. absolute pressure Tank L a b patm Manometer liquid Gas at pressure p Fig. 1.7 Manometer. a patm L Mercury vapor, pvapor b Mercury, ρm Fig. 1.8 Barometer. 1.6.1 Pressure Measurement Manometers and barometers measure pressure in terms of the length of a column of liquid such as mercury, water, or oil. The manometer shown in Fig. 1.7 has one end open to the atmosphere and the other attached to a tank containing a gas at a uniform pressure. Since pressures at equal elevations in a continuous mass of a liquid or gas at rest are equal, the pressures at points a and b of Fig. 1.7 are equal. Applying an elementary force balance, the gas pressure is p 5 patm 1 rgL (1.11) where patm is the local atmospheric pressure, r is the density of the manometer liquid, g is the acceleration of gravity, and L is the difference in the liquid levels. The barometer shown in Fig. 1.8 is formed by a closed tube filled with liquid mercury and a small amount of mercury vapor inverted in an open container of liquid mercury. Since the pressures at points a and b are equal, a force balance gives the c01GettingStarted.indd Page 15 7/1/10 10:35:45 AM user-s146 /Users/user-s146/Desktop/Merry_X-Mas/New
16 Chapter 1 Getting Started Elliptical metal Pointer atmospheric pressure as Bourdon tube Patm Pvapor PmgL (1.12) where pm is the density of liquid mercury.Because the pressure of the mercury Pinion vapor is much less than that of the atmosphere,Eq.1.12 can be approximated gear closely as Patm =PmgL.For short columns of liquid,p and g in Egs.1.11 and 1.12 may be taken as constant. Support Pressures measured with manometers and barometers are frequently Linkage expressed in terms of the length L in millimeters of mercury (mmHg), inches of mercury (inHg),inches of water (inH2O),and so on. FOR EXAMPL3 a barometer reads 750 mmHg.If pm=13.59 g/cm Gas at pressure p and g =9.81 m/s',the atmospheric pressure,in N/m2,is calculated as follows: Fig.1.9 Pressure measurement by a Bourdon tube gage. Patm=PmgL IN 750 mmHg 10'mm kg·m/s2 =105N/m244444 A Bourdon tube gage is shown in Fig.1.9.The figure shows a curved tube having an elliptical cross section with one end attached to the pressure to be measured and the other end connected to a pointer by a mechanism.When fluid under pressure fills the tube.the elliptical section tends to become circular.and the tube straightens This motion is transmitted by the mechanism to the pointer.By calibrating the deflection of the pointer for known pressures,a graduated scale can be determined from which any applied pressure can be read in suitable units.Because of its con- struction,the Bourdon tube measures the pressure relative to the pressure of the surroundings existing at the instrument.Accordingly,the dial reads zero when the inside and outside of the tube are at the same pressure. Pressure can be measured by other means as well.An important class of sensors utilize the piezoelectric effect:A charge is generated within certain solid materials when they are deformed.This mechan- ical input/electrical output provides the basis for pressure measure- ment as well as displacement and force measurements.Another important type of sensor employs a diaphragm that deflects when a force is applied,altering an inductance,resistance,or capacitance. Fig.1.10 Pressure sensor with automatic data Figure 110 shows a piezoelectric pressure sensor together with an acquisition. automatic data acquisition system. 1.6.2 t Buoyancy When a body is completely,or partially,submerged in a liquid,the resultant pressure buoyant force force acting on the body is called the buoyant force.Since pressure increases with depth from the liquid surface,pressure forces acting from below are greater than pressure forces acting from above;thus the buoyant force acts vertically upward.The buoyant force has a magnitude equal to the weight of the displaced liquid (Archimedes principle). FR EXAMPL3 applying Eq.111 to the submerged rectangular block shown in Fig.1.11,the magnitude of the net force of pressure acting upward,the buoyant
16 Chapter 1 Getting Started atmospheric pressure as patm 5 pvapor 1 rmgL (1.12) where rm is the density of liquid mercury. Because the pressure of the mercury vapor is much less than that of the atmosphere, Eq. 1.12 can be approximated closely as patm 5 rm g L. For short columns of liquid, r and g in Eqs. 1.11 and 1.12 may be taken as constant. Pressures measured with manometers and barometers are frequently expressed in terms of the length L in millimeters of mercury (mmHg), inches of mercury (inHg), inches of water (inH2O), and so on. a barometer reads 750 mmHg. If rm 5 13.59 g/cm 3 and g 5 9.81 m/s 2 , the atmospheric pressure, in N/m 2 , is calculated as follows: patm 5 rmgL 5 c a13.59 g cm3 b ` 1 kg 103 g ` ` 102 cm 1 m ` 3 d c9.81 m s 2 d c1750 mmHg2 ` 1 m 103mm `d ` 1 N 1 kg ? m/s 2 ` 5 105 Nym2 b b b b b A Bourdon tube gage is shown in Fig. 1.9. The figure shows a curved tube having an elliptical cross section with one end attached to the pressure to be measured and the other end connected to a pointer by a mechanism. When fluid under pressure fills the tube, the elliptical section tends to become circular, and the tube straightens. This motion is transmitted by the mechanism to the pointer. By calibrating the deflection of the pointer for known pressures, a graduated scale can be determined from which any applied pressure can be read in suitable units. Because of its construction, the Bourdon tube measures the pressure relative to the pressure of the surroundings existing at the instrument. Accordingly, the dial reads zero when the inside and outside of the tube are at the same pressure. Pressure can be measured by other means as well. An important class of sensors utilize the piezoelectric effect: A charge is generated within certain solid materials when they are deformed. This mechanical input/electrical output provides the basis for pressure measurement as well as displacement and force measurements. Another important type of sensor employs a diaphragm that deflects when a force is applied, altering an inductance, resistance, or capacitance. Figure 1.10 shows a piezoelectric pressure sensor together with an automatic data acquisition system. Support Linkage Pinion gear Elliptical metal Pointer Bourdon tube Gas at pressure p Fig. 1.9 Pressure measurement by a Bourdon tube gage. 1.6.2 Buoyancy When a body is completely, or partially, submerged in a liquid, the resultant pressure force acting on the body is called the buoyant force. Since pressure increases with depth from the liquid surface, pressure forces acting from below are greater than pressure forces acting from above; thus the buoyant force acts vertically upward. The buoyant force has a magnitude equal to the weight of the displaced liquid ( Archimedes’ principle ). applying Eq. 1.11 to the submerged rectangular block shown in Fig. 1.11 , the magnitude of the net force of pressure acting upward, the buoyant Fig. 1.10 Pressure sensor with automatic data acquisition. buoyant force c01GettingStarted.indd Page 16 7/1/10 10:35:49 AM user-s146 /Users/user-s146/Desktop/Merry_X-Mas/New