King Fahd University of Petroleum & King Fahd University of Petroleum & MineralsMinerals

Mechanical EngineeringMechanical Engineering

Thermodynamics ME 203Thermodynamics ME 203

BYBY

Dr. Salem Al-DiniDr. Salem Al-Dini

Mission statements of the departmentMission statements of the department

The department is committed to The department is committed to ■ providing highest quality education in mechanical providing highest quality education in mechanical

engineering, engineering, ■ conducting world-class basic and applied research, conducting world-class basic and applied research, ■ addressing the evolving needs of industry and society, and addressing the evolving needs of industry and society, and ■ supporting the development of more competitive new industry supporting the development of more competitive new industry

in the Kingdome of Saudi Arabiain the Kingdome of Saudi Arabia

TextbookTextbookThermodynamics: An Engineering ApproachThermodynamics: An Engineering Approach, by Yunus A. , by Yunus A.

Cengel and Michael A. Boles, Cengel and Michael A. Boles,

ReferencesReferences::

Fundamentals of Engineering ThermodynamicsFundamentals of Engineering Thermodynamics, by Moran, M. J., , by Moran, M. J., and H. N. Shapiro. and H. N. Shapiro.

Fundamentals of ThermodynamicsFundamentals of Thermodynamics, by Sonntag, R. E., , by Sonntag, R. E., Borgnakke, C., and Van Wylen, G. J. Borgnakke, C., and Van Wylen, G. J.

Chapter 1Chapter 1

Introduction and Basic Introduction and Basic ConceptsConcepts

ObjectivesObjectives

■ Identify the unique vocabulary associated with thermodynamics through Identify the unique vocabulary associated with thermodynamics through the precise definition of basic concepts to form a sound foundation for the the precise definition of basic concepts to form a sound foundation for the development of the principles of thermodynamics.development of the principles of thermodynamics.

■ Review the metric SI and the English unit systems that will be used Review the metric SI and the English unit systems that will be used throughout the text. throughout the text.

■ Explain the basic concepts of thermodynamics such as system, state, state Explain the basic concepts of thermodynamics such as system, state, state postulate, equilibrium, process, and cycle.postulate, equilibrium, process, and cycle.

■ Review concepts of temperature, temperature scales, pressure, and Review concepts of temperature, temperature scales, pressure, and absolute and gage pressure.absolute and gage pressure.

■ Introduce an intuitive systematic problem-solving technique.Introduce an intuitive systematic problem-solving technique.

IntroductionIntroduction

■ Thermodynamics can be defined as the since of energy and entropyThermodynamics can be defined as the since of energy and entropy■ An alternate definition: is the since that deals with heat and work and An alternate definition: is the since that deals with heat and work and

those properties of substances that bear a relation to heat and work those properties of substances that bear a relation to heat and work ■ The word thermodynamics stems from the Greek words therme (heat) and The word thermodynamics stems from the Greek words therme (heat) and

dynamics (force). dynamics (force). ■ Thermodynamics is a science that is based in experimental findingsThermodynamics is a science that is based in experimental findings■ These findings have been formalized into certain lawsThese findings have been formalized into certain laws

IntroductionIntroduction

■ Energy cannot be created or destroyed it transforms (conservation of Energy cannot be created or destroyed it transforms (conservation of energy 1energy 1stst law) law)

IntroductionIntroduction

■ Energy has a quality and a quantity (actual process is Energy has a quality and a quantity (actual process is decreasing quality decreasing quality of energy 2of energy 2ndnd law) law)

Application Areas of Thermal-Fluid Application Areas of Thermal-Fluid SciencesSciences

Macroscopic and Microscopic Views of Macroscopic and Microscopic Views of ThermodynamicsThermodynamics

■ As you know, any substance consists of a large number As you know, any substance consists of a large number of molecules. The properties of the substance depend on of molecules. The properties of the substance depend on the behavior of these molecules. the behavior of these molecules.

■ Consider a gas in a container. The pressure of the gas is a Consider a gas in a container. The pressure of the gas is a result of the momentum transfer as the molecules hit the result of the momentum transfer as the molecules hit the walls of the container.walls of the container.

■ However, we do need to know the force exerted by the However, we do need to know the force exerted by the molecule on an infinitesimal area on the wall in order to molecule on an infinitesimal area on the wall in order to find the pressure (microscopic approach) find the pressure (microscopic approach)

■ Instead, it will be sufficient to attach a pressure gauge to Instead, it will be sufficient to attach a pressure gauge to the wall (finite area) and read the average pressure the wall (finite area) and read the average pressure exerted by a large number of molecules on that finite exerted by a large number of molecules on that finite area (macroscopic approach). area (macroscopic approach).

■ That is, the macroscopic approach to That is, the macroscopic approach to thermodynamics is concerned with the thermodynamics is concerned with the average or overall behavior. This average or overall behavior. This approach is called sometimes classicalapproach is called sometimes classical thermodynamics. thermodynamics.

■ On the other hand, the microscopic On the other hand, the microscopic approach to thermodynamics, known as approach to thermodynamics, known as statisticalstatistical thermodynamics, is concerned thermodynamics, is concerned directly with the structure of matter. It is directly with the structure of matter. It is objective is to find (by statistical means) objective is to find (by statistical means) the average behavior of the particles the average behavior of the particles making up a system. This approach is making up a system. This approach is involved and is not used any more in the involved and is not used any more in the remaining of this course. remaining of this course.

■ The macroscopic approach provides a The macroscopic approach provides a direct and easy solution to engineering direct and easy solution to engineering problems. problems.

IntroductionIntroduction

■ Thermodynamics is both a branch of physics and an engineering science. Thermodynamics is both a branch of physics and an engineering science. ■ The scientist is normally interested in gaining a fundamental The scientist is normally interested in gaining a fundamental

understanding of the physical and chemical behavior of fixed quantities of understanding of the physical and chemical behavior of fixed quantities of matter and then, uses the principles of thermodynamics to relate the matter and then, uses the principles of thermodynamics to relate the properties of matter.properties of matter.

■ Engineers are generally interested in studying systemsEngineers are generally interested in studying systems and how they and how they interact with their surroundings. To facilitate this, engineers extend the interact with their surroundings. To facilitate this, engineers extend the subject of thermodynamics to the study of systems through which matter subject of thermodynamics to the study of systems through which matter flows.flows.

Thermodynamic systemsThermodynamic systems■ An important step in any engineering analysis An important step in any engineering analysis

is to describe precisely what is being studied. is to describe precisely what is being studied. ■ In mechanics, if the motion of a body is to be In mechanics, if the motion of a body is to be

determined (Figure 1), normally the first step is determined (Figure 1), normally the first step is to define a free bodyto define a free body and identify all the forces and identify all the forces exerted on it by other bodies (Figure 2). exerted on it by other bodies (Figure 2).

■ Newton’s second law of motion is then Newton’s second law of motion is then applied. applied.

■ In thermodynamics, the term In thermodynamics, the term systemsystem is used to is used to identify the subject of the analysis (e.g. coffee identify the subject of the analysis (e.g. coffee in the cup). in the cup).

■ Once the system is defined and the relevant Once the system is defined and the relevant interactions with other systems are identified, interactions with other systems are identified, one or more physical laws or relations are one or more physical laws or relations are applied.applied.

■ The system is whatever we want to study. It may be as simple as a free The system is whatever we want to study. It may be as simple as a free body or as complex as an entire chemical refinery. We may want to study body or as complex as an entire chemical refinery. We may want to study a quantity of matter contained within a closed, rigid-walled tank or we a quantity of matter contained within a closed, rigid-walled tank or we may want to consider something such as a gas pipeline through which gas may want to consider something such as a gas pipeline through which gas flows.flows.

■ Everything external to the system is considered to be part of the system’s Everything external to the system is considered to be part of the system’s surroundingssurroundings. .

■ The system is distinguished from its The system is distinguished from its

surroundings by a specified boundary surroundings by a specified boundary

which may be at rest or in motionwhich may be at rest or in motion. . ■ It is essential for the boundary It is essential for the boundary

to be determined carefully before to be determined carefully before

proceeding with any thermodynamic analysis.proceeding with any thermodynamic analysis.

■ Two basic kinds of systems are distinguished in thermodynamics study. Two basic kinds of systems are distinguished in thermodynamics study. These are referred to as These are referred to as closed systemsclosed systems and and control volumescontrol volumes..

Closed systems (control mass)Closed systems (control mass)■ A closed systemA closed system refers to a fixed quantity of matter. refers to a fixed quantity of matter.

■ A closed system is used when a particular quantity A closed system is used when a particular quantity of matter is under study. of matter is under study. ■ A closed system always contains the same matter. A closed system always contains the same matter. ■ There can be no transfer of mass across its boundary. There can be no transfer of mass across its boundary. ■ What do we call the system if even energy is not allowed What do we call the system if even energy is not allowed

to cross the boundary?to cross the boundary?■ The figure shows a gas in a piston-cylinder assembly. The figure shows a gas in a piston-cylinder assembly. ■ Let us consider the gas to be a closed system. Let us consider the gas to be a closed system. ■ The boundary lies just inside the piston and cylinder The boundary lies just inside the piston and cylinder

walls, as shown by the dashed lines on the figure. walls, as shown by the dashed lines on the figure. ■ If the cylinder were placed over a flame, the gas would If the cylinder were placed over a flame, the gas would

expand, raising the piston. expand, raising the piston. ■ The portion of the boundary between the gas and the The portion of the boundary between the gas and the

piston moves with the piston. piston moves with the piston. ■ No mass would cross this or any other part of the No mass would cross this or any other part of the

boundary.boundary.

Open system (control volume)Open system (control volume)

■ An open system (control volume)An open system (control volume) is a properly selected region in space. is a properly selected region in space. ■ It encloses a device that involves mass flow such as nozzle, compressor, It encloses a device that involves mass flow such as nozzle, compressor,

turbine. turbine. ■ Flow through such devices is best studied by selecting the region within Flow through such devices is best studied by selecting the region within

the device as the control volume . the device as the control volume . ■ Both mass and energy can cross the boundary of the control volume. Both mass and energy can cross the boundary of the control volume. ■ There are no concrete rules for the selection of the control volume but There are no concrete rules for the selection of the control volume but

proper choice makes the analysis much easier .proper choice makes the analysis much easier .■ The boundary of the control volume is called boundary surfaceThe boundary of the control volume is called boundary surface■ The boundary surface can be real or imaginaryThe boundary surface can be real or imaginary■ A control volume can be fixed in shape and size or it may involve a A control volume can be fixed in shape and size or it may involve a

moving boundary.moving boundary.

Open Systems (continued)Open Systems (continued)

Open Systems (continued)Open Systems (continued)

Properties of a SystemProperties of a System

■ To describe a system and predict its To describe a system and predict its behavior requires knowledge of its behavior requires knowledge of its properties and how those properties are properties and how those properties are related.related.

■ Properties are macroscopic characteristics of Properties are macroscopic characteristics of a system.a system.

■ Any characteristic of a system is called a Any characteristic of a system is called a property. Some familiar properties are property. Some familiar properties are pressure P, temperature T, volume V, and pressure P, temperature T, volume V, and mass m. mass m.

■ Properties describe the state of a system Properties describe the state of a system only when the system is in an equilibrium only when the system is in an equilibrium state.state.

■ Not all properties are independent. Density Not all properties are independent. Density is a dependent property on pressure and is a dependent property on pressure and temperature.temperature.

Density as a propertyDensity as a property■ Density is mass per unit volume;Density is mass per unit volume;■ = mass/volume (kg/m3)= mass/volume (kg/m3)

■ Specific gravity: the ratio of the density of a substance to the density of some Specific gravity: the ratio of the density of a substance to the density of some standard substance at specified temperature (usually water at 4 standard substance at specified temperature (usually water at 4 ooC)C)

■ Specific volume is volume per unit mass.Specific volume is volume per unit mass.■ = Volume/mass, (m3/kg)= Volume/mass, (m3/kg)■ = 1/ = 1/

P

Gases

T

Gases

Volume

P

Liquids

T

Liquids

Water

Extensive and Intensive PropertiesExtensive and Intensive Properties

■ Intensive properties are those that are Intensive properties are those that are independent of the size of system, such as independent of the size of system, such as temperature, pressure, and density. temperature, pressure, and density.

■ Extensive properties are dependent on the size Extensive properties are dependent on the size (or extent) of the system. Mass m, volume V, (or extent) of the system. Mass m, volume V, and total energy E are some examples of and total energy E are some examples of extensive properties.extensive properties.

■ Criteria to differentiate extensive and Criteria to differentiate extensive and intensive properties is illustrated in the intensive properties is illustrated in the Figure.Figure.

■ Extensive properties per unite mass are called Extensive properties per unite mass are called specific properties (i.e. specific volume).specific properties (i.e. specific volume).

StateState

■ A state is defined as a condition of a substance that can A state is defined as a condition of a substance that can be described by certain observable macroscopic be described by certain observable macroscopic properties. (T, P, properties. (T, P, , , etc.) etc.)

■ In above figure, the system does not undergo any In above figure, the system does not undergo any change. All properties can be measured throughout the change. All properties can be measured throughout the system. Hence the condition of the system is completely system. Hence the condition of the system is completely described. This condition is called state 1.described. This condition is called state 1.

■ Now remove some weights. If the value of even one Now remove some weights. If the value of even one property changes, then the state will change to different property changes, then the state will change to different one (state 2).one (state 2).

■ The word State refers to the condition of a system as it The word State refers to the condition of a system as it is described by its properties.is described by its properties.

State 1

m = 2kgT1= 20 °CV1= 1.5 m3

m = 2kgT1= 20 °CV1= 2.5 m3

State 2

EquilibriumEquilibrium

■ Thermodynamics deals with equilibrium Thermodynamics deals with equilibrium states.states.

■ The word equilibrium implies a state of The word equilibrium implies a state of balance.balance.

■ Equilibrium state means that there are no Equilibrium state means that there are no unbalanced potentials (or driving forces) unbalanced potentials (or driving forces) within the system.within the system.

■ A system is said to be in thermodynamic A system is said to be in thermodynamic equilibrium if it maintains thermal, equilibrium if it maintains thermal, mechanical, phase, and chemical equilibrium.mechanical, phase, and chemical equilibrium.

Thermal EquilibriumThermal Equilibrium

■ Thermal equilibrium means that there is no temperature differential Thermal equilibrium means that there is no temperature differential through the system.through the system.

20 °C 30 °C

30 °C

35 °C 40 °C

No thermal equilibrium

32 °C

32 °C 32 °C

32 °C

32 °C

Thermal equilibrium

Mechanical EquilibriumMechanical Equilibrium

■ Mechanical equilibrium means that there is no change in pressure in the Mechanical equilibrium means that there is no change in pressure in the system.system.

(a) Slow compression (quasi-equilibrium)

20 pa 20 pa

20 pa

20 pa 20 pa

(b) fast compression (non quasi-equilibrium)

20 pa

20 pa

90 pa

Phase EquilibriumPhase Equilibrium

■ Phase equilibrium means that the mass of each phase reaches an Phase equilibrium means that the mass of each phase reaches an equilibrium level and stays there.equilibrium level and stays there.

Water

Vapor, P > 0

After some time

Water

Vapor, P = Pv

After long time

Water

Vacuum t= 0, P = 0

At t = 0

Chemical EquilibriumChemical Equilibrium

■ Chemical equilibrium means that the chemical composition of the system Chemical equilibrium means that the chemical composition of the system does not change with timedoes not change with time

The State PostulateThe State Postulate

■ We mentioned earlier that a state is described uniquely by measuring a We mentioned earlier that a state is described uniquely by measuring a few of its properties. The remaining properties will assume certain few of its properties. The remaining properties will assume certain values. The question here is how much is this “few”?. values. The question here is how much is this “few”?.

■ The answer depends on how simple or complex our system is. The answer depends on how simple or complex our system is. ■ If we have a system where the gravitational, electrical, magnetic, If we have a system where the gravitational, electrical, magnetic,

motion and surface tension effects are absent, then this system is called motion and surface tension effects are absent, then this system is called a simple compressible system. a simple compressible system.

■ According to what is called “state postulate”, the number of properties According to what is called “state postulate”, the number of properties required to completely specify the state of such system is two required to completely specify the state of such system is two independent, intensive properties. independent, intensive properties.

The State PostulateThe State Postulate

■ If, however, the gravitational effects are important in the simple If, however, the gravitational effects are important in the simple compressible system, then the elevation z needs to be specified in addition compressible system, then the elevation z needs to be specified in addition to the two properties necessary to fix the state. to the two properties necessary to fix the state.

■ The state postulate requires that the two properties are The state postulate requires that the two properties are independentindependent of of each other. each other.

■ Two properties are considered to be independent if one property is varied Two properties are considered to be independent if one property is varied while the other one is constant. while the other one is constant.

■ Temperature and specific volume are good examples. Temperature and specific volume are good examples. ■ You will see, however, in coming units that temperature and pressure are You will see, however, in coming units that temperature and pressure are

not always independent of each other. They become dependent during not always independent of each other. They become dependent during phase change processes.phase change processes.

Processes and CyclesProcesses and Cycles

■ Any change from one equilibrium state to Any change from one equilibrium state to another is called a process.another is called a process.

■ Process diagrams are very useful in Process diagrams are very useful in visualizing the processes.visualizing the processes.

■ The series of states through which a system The series of states through which a system passes during a process is called a pathpasses during a process is called a path

■ To describe a process completely initial and To describe a process completely initial and final states as well as the path it follows, and final states as well as the path it follows, and the interactions with the surrounding should be the interactions with the surrounding should be specifiedspecified

■ A process with identical end states is called a A process with identical end states is called a cyclecycle

■ Process diagrams plotted by employing Process diagrams plotted by employing thermodynamic properties as coordinates are thermodynamic properties as coordinates are very useful in visualizing the processes.very useful in visualizing the processes.

■ Isothermal process means a Isothermal process means a process at constant T.process at constant T.

■ Isobaric process means a Isobaric process means a process at constant pressureprocess at constant pressure

■ Isochoric process means a Isochoric process means a process at constant volume process at constant volume

Quasi-Equilibrium processQuasi-Equilibrium process■ During a quasi-static or quasi-equilibrium During a quasi-static or quasi-equilibrium

process, the system remains infinitesimally process, the system remains infinitesimally close to an equilibrium state at all times. close to an equilibrium state at all times.

■ A sufficiently slow process that allow the A sufficiently slow process that allow the system to adjust itself internally so that system to adjust itself internally so that properties in one part of the system do not properties in one part of the system do not change any faster than those at other parts.change any faster than those at other parts.

■ Compression is very slow and thus Compression is very slow and thus equilibrium is attained at any intermediate equilibrium is attained at any intermediate state. Therefore, the intermediate states can state. Therefore, the intermediate states can be determined and process path can be be determined and process path can be drawn.drawn.

■ It is an idealized process but many process It is an idealized process but many process closely approximate it with negligible error.closely approximate it with negligible error.

■ Quasi-Equilibrium, Work-Producing Devices Quasi-Equilibrium, Work-Producing Devices Deliver the Most Work (it is the standard to Deliver the Most Work (it is the standard to which other processes can be compared)which other processes can be compared) (a) Slow compression (quasi-equilibrium)

20 pa 20 pa

20 pa

20 pa 20 pa

State 1

State 2 Process path

P

V

Intermediate states

20

Non-Quasi-Equilibrium processNon-Quasi-Equilibrium process

■ Compression process is fast and Compression process is fast and thus equilibrium can not be thus equilibrium can not be attained.attained.

■ Intermediate states can not be Intermediate states can not be determined and the process path determined and the process path can not be defined. Instead we can not be defined. Instead we represent it as dashed line.represent it as dashed line.

(b) Fast compression (non quasi-equilibrium)

20 pa

20 pa

90 pa

State 1

State 2P

V

Non-equilibruim process

20

90

?

Forms of EnergyForms of Energy

■ In absence of magnetic, electric, and surface tension effects, the total energy of a In absence of magnetic, electric, and surface tension effects, the total energy of a system consists of the kinetic, potential, and internal energies and is expressed assystem consists of the kinetic, potential, and internal energies and is expressed as

■ The macroscopic form of energy are those a system possesses as a whole with The macroscopic form of energy are those a system possesses as a whole with respect to some outside reference (i.e. kinetics and potential). respect to some outside reference (i.e. kinetics and potential).

■ The microscopic forms of energy are those related to the molecular structure of the The microscopic forms of energy are those related to the molecular structure of the system , independent of outside reference frames (i.e. internal).system , independent of outside reference frames (i.e. internal).

■ The change in the total energy The change in the total energy EE of a stationary system (closed system) is of a stationary system (closed system) is identical to the change in its internal energy identical to the change in its internal energy UU..

(kJ/kg) 2

basis massunit aon or,

(kJ), 2

(kJ),

2

2

gzv

upekeue

mgzmv

mume

PEKEUE

Forms of Energy (continued)Forms of Energy (continued)

The portion of the internal energy of a system associated The portion of the internal energy of a system associated with thewith the

1.1. kinetic energies of the molecules is called the kinetic energies of the molecules is called the sensible sensible energyenergy..

2.2. phase of a system is called the phase of a system is called the latent energylatent energy..

3.3. atomic bonds in a molecule is called atomic bonds in a molecule is called chemical energy.chemical energy.

4.4. strong bonds within the nucleus of the atom itself is strong bonds within the nucleus of the atom itself is called called nuclear energynuclear energy. .

5.5. Static energy (stored in a system)Static energy (stored in a system)

6.6. Dynamic energy: energy interactions at the system Dynamic energy: energy interactions at the system boundary (i.e. heat and work)boundary (i.e. heat and work)

kgkJeU /1073.6 10235

Temperature and the Zeroth Law of Temperature and the Zeroth Law of ThermodynamicsThermodynamics

■ The zeroth law of thermodynamics states The zeroth law of thermodynamics states that: If two bodies are in thermal that: If two bodies are in thermal equilibrium with the third body, they are equilibrium with the third body, they are also in thermal equilibrium with each also in thermal equilibrium with each other.other.

■ The equality of temperature is the only The equality of temperature is the only requirement for thermal equilibrium.requirement for thermal equilibrium.

Temperature scalesTemperature scales

■ I n thermodynamics it is desirable to have a temperature scale I n thermodynamics it is desirable to have a temperature scale that is independent of the properties of any substance.that is independent of the properties of any substance.

■ Note: it makes no difference to use K or C in formulas involving Note: it makes no difference to use K or C in formulas involving temperature difference. However, you should use Absolute temperature difference. However, you should use Absolute temperature in formulas involving temperature only like the ideal temperature in formulas involving temperature only like the ideal gas low.gas low.

FTRT

CTKT

CTFT

KTRT

FTRT

CTKT

o

o

oo

o

o

328.1

8.1

67.459

15.273

Dimensions and UnitsDimensions and Units

The seven fundamental dimensions and their

units in SI (International System).

Dimensions and UnitsDimensions and Units

SI British System Conversion

Length Meter (m) Foot (ft) 1 ft = 0.3048 m

Time Second (s) Second (s)

Mass

Kg

Slug Pound mass (lbm) 1 slug = 32.2 lbm

1 slug =14.59 kg 1 lbm = 0.4536 kg

Force

Newton (N) 1 N = (1Kg).(1 m/s2)

Pound force (lbf) 1 lbf = (1 slug)(1. ft/s2)

1 lbf = 4.448 N

Definition of

Unit force

Newton (N): is the force required to give a mass of 1 kg an acceleration of 1 m/ s2.

Pound force (lbf) is the force required to give a mass of 1 slug an acceleration of 1 ft/ s2.

°C = (5/9)*(°F –32)

°R = (9/5)*K

Tempe-rature

Degree Celsius.(°C) Absolute Temp.: Kelvin (K).

K = °C + 273.15

Degree Fahrenheit (°F) Absolute Temp.: Rankine (°R)

°R = °F + 459.67

°C = (5/9)*(°F –32)

°R = (9/5)*K

PressurePressure

Pressure is defined as the force exerted by a fluid per unit area. Units in SI are Pa=N/m2. The pressure unit Pascal is too small for pressure encountered in practice.

Therefore, kPa and MPa are commonly used.

Units in British are : psf = lbf/ft2, psi = lbf/in2

You have to convert from psi to psf ( 144 in2 = 1 ft2)

psibarskPaPaatm

kPaMPaPabar

696.1401325.1325.101325,1011

1001.0101 5

Pressure (Continued)Pressure (Continued)

Absolute pressure, is measured relative to absolute vacuum (i.e., absolute zero pressure.)

Gauge pressure, is measured relative to atmospheric pressure

atmabsatmvac

atmatmabsgage

PPPP

PPPP

below pressurefor

above pressurefor

Pressure (continued)

Variation of Pressure with Depth

The pressure variation in a constant density fluid is given as

P + Z = constant Or P1+ Z1 = P2 + Z2

Z is the vertical coordinate ( positive upward). is the specific weight of fluids, (N/m3)

For small to moderate distances, the variation of pressure with height is negligible for gases because of their low density.

g

Pressure (continued)

Pressure at a Point

• The pressure at a point in a fluid has the same magnitude in all direction.

Pressure (continued)

Pressure Variation in horizontal planes

Pressure is constant in horizontal planes provided the fluid does not change. ( this leads to Pascal’s principle.)

. 1

2

1

2

2

2

1

121 A

A

F

F

A

F

A

FPP

Noting that P1 = P2, the area ratio A2/A1 is called the ideal mechanical advantage. Using a hydraulic car jack with A2/A1 = 10, a person can lift a 1000-kg car by applying a force just 100 kg (= 908 N).

The Manometer

A device based on P + Z = constant is called a manometer (Right), and it is commonly used to measure small and moderate pressure differences.

w

f

w

f

w

f

s g

g

S

Specific gravityP2 = Patm + h

FIGURE 1–61FIGURE 1–61Schematic for Example Schematic for Example 1–81–8..

1-17

Barometer and the Atmospheric Pressure

• The atmospheric pressure is measured by a device called a barometer; thus the atmospheric pressure is often referred to as the barometric pressure.

0

( )

B B C C

C vapor

B atm C B

Hg

P Z P Z

P P

P P Z Z

gh

Barometer and the Atmospheric Pressure (continued)

• The standard atmospheric pressure is the pressure produced by a column of mercury 760 mm in height at 0oC. The unit of mmHG is also called the torr in honor of Evangelista Torricelli (1608−1647).

• The atmospheric pressure at a location is simply the weight of the air above that location per surface area. Patm changes with elevation and weather conditions. The length or the

cross-sectional area of the tube has no effect on the height of the fluid column of a barometer.

kPaPkPaP

kPaPkPaP

Patorr

kPatorrmmHgP

mm

Denvermm

atm

5.26;05.54

4.83;88.89

3.1331

325.101760

000,105000

:16101000

Problem Solving TechniqueProblem Solving Technique

Step-by-step approach:1. Problem Statement2. Schematic3. Assumptions4. Physical Laws5. Properties6. Calculations

7. Reasoning, Verification, and Discussion

The assumptions made while solving an engineering problem must be reasonable and justifiable.

Problem Solving Technique (continued)Problem Solving Technique (continued)

A result with more significant digits than that of given data falsely implies more accuracy.

When solving problems, we will assume the given information to be accurate to at least 3 significant digits. Therefore, if the length of a pipe is given to be 40 m, we will assume it to be 40.0 m in order to justify using 3 significant digits in the final results.

ExamplesExamples

■ A pressure gage connected to a tank A pressure gage connected to a tank reads 500 kPa. The absolute pressure in reads 500 kPa. The absolute pressure in the tank is to be determined .the tank is to be determined .

Pabs

Patm = 94 kPa

500 kPa

ExamplesExamples

■ The vacuum gage connected to a tank The vacuum gage connected to a tank reads 15 kPa at a location where the reads 15 kPa at a location where the barometer reading is 750 mmHg. barometer reading is 750 mmHg. Determine the absolute pressure of the Determine the absolute pressure of the tank.tank. The density of mercury is given to The density of mercury is given to be be = 13,590 kg/m3. = 13,590 kg/m3.

Pabs

Patm = 750 mmHg

15 kPa

ExamplesExamples

ExamplesExamples

■ The air pressure in a tank is measured by The air pressure in a tank is measured by an oil manometer. For a given oil-level an oil manometer. For a given oil-level difference between the two columns, the difference between the two columns, the absolute pressure in the tank is to be absolute pressure in the tank is to be determined. The density of oil is given to determined. The density of oil is given to be be = 850 kg/m3. = 850 kg/m3.

■ AIR AIR PPatm = 98 kPa0.60 matm = 98 kPa0.60 m

AIR

Patm = 98 kPa

0.60 m

ExamplesExamples730 mmHg

755 mmHg

h