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Exam Specifications Mathematics % Engineering Probability and Statistics 7% Chemistry 9% Computers 7% Ethics and Business Practices 7% Engineering Economics 8% Statics and Dynamics 10% Strength of Materials 7% Material Properties 7% Fluid Mechanics 7% Electricity and Magnetism 9% Thermodynamics 7%

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**BEGINNING OF THERMODYNAMICS**

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**Problem 58 TOPIC: Thermodynamics (pg 75)**

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**Problem 59 TOPIC: Thermodynamicss (pg 83)**

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**Problem 60 TOPIC: Thermodynamicss (pg 75)**

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**Problem 61 TOPIC: Thermodynamics (pg 75)**

0.064 kg of octane vapor (MW = 114) is mixed with 0.91 kg of air (MW = 29). The total pressure is 86.1 kPa. What is the partial pressure of air? Assume ideal gas. Let y be the mass fraction, and let x be the mole fraction.

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**Problem 62 TOPIC: Thermodynamics (pg 75)**

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**Problem 63 TOPIC: Thermodynamics (pg 75)**

An isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant. An isochoric process is exemplified by the heating or the cooling of the contents of a sealed, inelastic container: The thermodynamic process is the addition or removal of heat; the isolation of the contents of the container establishes the closed system; and the inability of the container to deform imposes the constant-volume condition.

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Problem 64 TOPIC: Thermodynamics (pg 75)

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Problem 65 TOPIC: Thermodynamics (pg 75) A stream has the following composition based on mass fraction. Please convert the list to mol fraction. Components mass fraction Hydrogen Methane Ethane Propane N-Butane

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Problem 66 TOPIC: Thermodynamics (pg 75) A stream has the following composition based on mol fraction. Please convert the list to mass fraction. Components mol fraction Hydrogen Methane Ethane Propane N-Butane

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Problem 66 TOPIC: Thermodynamics (pg 75)

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**In an isentropic compression of an ideal gas, **

Problem 67 TOPIC: Thermodynamics (pg 75) In an isentropic compression of an ideal gas, p1 = 100 kPa, p2 = 200 kPa, V1 = 10 m3, and k = 1.4. Find V2.

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**In an polytropic compression of an ideal gas, **

Problem 68 TOPIC: Thermodynamics (pg 75) In an polytropic compression of an ideal gas, p1 = 100 kPa, p2 = 200 kPa, V1 = 10 m3, and n = 1.3. Find V2.

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**In an polytropic compression of an ideal gas, **

Problem 69 TOPIC: Thermodynamics (pg 75) In an polytropic compression of an ideal gas, p1 = 100 kPa, p2 = 200 kPa, V1 = 10 m3, and n = 1.3. Find V2.

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**Two copper blocks are initially 50°C and 1 kg, and 100°C and 3 kg.**

Problem 70 TOPIC: Thermodynamics (pg 75) Two copper blocks are initially 50°C and 1 kg, and 100°C and 3 kg. The blocks are brought into contact and reach thermal equilibrium with no outside heat exchanged. What is the final temperature of the blocks?

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**• Dry-bulb temperature = vertical lines **

Problem 71 TOPIC: Thermodynamics (pg 82) Psychrometric Chart • Dry-bulb temperature = vertical lines • Relative humidity = parabolic lines • Wet-bulb temperature = dashed diagonals to the left • Enthalpy = solid diagonals to the left • Humidity ratio = horizontal lines to the right • Dew point = intersection of horizontal lines with sat’n line (left) • Specific volume = steep diagonals

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**Air is 24°C dry bulb with 50% relative humidity. **

Problem 72 TOPIC: Thermodynamics (pg 82) Air is 24°C dry bulb with 50% relative humidity. Find the wet-bulb temperature, humidity ratio, enthalpy, specific volume, and dew-point temperature.

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**For a mixture of 6 hydrocarbon components what is the **

Problem 73 TOPIC: Thermodynamics (pg 76) How many independent properties are required to completely fix the equilibrium state of a pure gaseous compound? For a mixture of 6 hydrocarbon components what is the condition of the dew point? condition of the bubble point?

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**For a mixture of 6 hydrocarbon components what is the **

Problem 74 TOPIC: Thermodynamics (pg 76) For a mixture of 6 hydrocarbon components what is the condition of the 50% vapor point? condition of the 20% vapor point?

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Problem 75 TOPIC: Thermodynamics (pg 76)

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Problem 76 TOPIC: Thermodynamics (pg 76, 77)

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Problem 77 TOPIC: Thermodynamics (pg 76, 77)

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Problem 78 TOPIC: Thermodynamics (pg 78)

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**What is the efficiency of an ideal Otto **

Problem 79 TOPIC: Thermodynamics (pg 78) What is the efficiency of an ideal Otto cycle device with a compression ratio of 6:1? Air is used with k = 1.4.

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**An ideal Otto cycle has the following properties: **

Problem 80 TOPIC: Thermodynamics (pg 78) An ideal Otto cycle has the following properties: TA = 290K, TD = 1350K, TC = 3100K, pA = 100 kPa, a compression ratio of 8, k = 1.4, and QB-C =1740 kJ/kg. The intake is mostly air with some gasoline mixed in. Please find the temperature at state B.

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**Stoichiometric Combustion CH4 + 2O2 → CO2 + 2H2O **

Problem 81 TOPIC: Thermodynamics (pg 76) Combustion Process Stoichiometric Combustion CH4 + 2O2 → CO2 + 2H2O For each mole of CH4, there should be 2 moles of O2. However, in air there are 3.76 moles of N2 for each mole of O2, so CH4 + 2O2 + 2(3.76)N2 → CO2 + 2H2O N2. The mass of flue gas per mass of fuel is:

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**Stoichiometric Combustion C15H32 + 23O2 → 15CO2 + 16H2O **

Problem 82 TOPIC: Thermodynamics (pg 76) Combustion Process Stoichiometric Combustion C15H O2 → 15CO2 + 16H2O For each mole of C15H32 , there should be 23 moles of O2. However, in air there are 3.76 moles of N2 for each mole of O2, so the mass of flue gas per mole of diesel (C15H32) is:

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Problem 83 TOPIC: Thermodynamics (pg 76) Steam Reboiler A steam reboiler is to supply 25e6 kJ/h of heating. The entering steam is saturated at 200o C and leaves as saturated water at nearly the same pressure as the entering steam. Assuming a 2% heat leak to the surroundings please calculate the mass flow rate of steam required.

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Problem 84 TOPIC: Thermodynamics (pg 76) Refrigerant Condenser Refrigerant HFC-134a is to supply 25e6 kJ/h of condensing duty in a distillation column. The entering refrigerant is saturated liquid at 0o C and leaves as saturated liquid at nearly the same pressure as the entering steam. Assuming a 5% heat leak to the surroundings please calculate the mass flow rate of refrigerant required.

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Problem 85 TOPIC: Thermodynamics (pg 81) Pipe Sizing Using the P-H diagram 20000 kgs/h of refrigerant HFC-134a at 100 C and 2000 kPa flow in a pipe from a compressor discharge. If the suggested design velocity is 20 m/s please calculate a rough line size for this material.

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Problem 86 TOPIC: Thermodynamics (pg 81) Valve Pressure Drop Saturated refrigerant HFC-134a at 1000 kPa is reduced to 400 kPa across a well insulated valve. Determine the temperature and the percent vapor at the exit of the valve.

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END OF THERMODYNAMICS

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**BEGINNING OF POWER CYCLES**

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Problem 87 TOPIC: POWER CYCLES (pg 81) Turbo-expander 10,000 kgs/h of refrigerant HFC-134a at 1000 kPa and 200 C is reduced to 100 kPa through a turbine. Assuming a turbine efficiency of 70%, how much power is generated.

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Problem 88 TOPIC: POWER CYCLES (pg 81) Centrifugal Compressor 10,000 kgs/h of refrigerant HFC-134a at 100 kPa and 100 C is compressed to 500 kPa in a centrifugal compressor. Assuming an adiabatic efficiency of 75%, how much power is required?

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Problem 89 TOPIC: POWER CYCLES (pg 81) Refrigeration Condenser 10,000 kgs/h of refrigerant HFC-134a at 100 kPa and 100 C is compressed to 500 kPa in a centrifugal compressor as in problem 89. This compressed refrigerant is then condensed at 500 kPa in a refrigeration condenser. Please calculate the duty in the compressor.

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Problem 90 TOPIC: POWER CYCLES (pg 81) Steam Turbine 100,000 kgs/h of steam at 1000 kPa and 500 C is reduced in pressure through a steam turbine to a pressure of 25 kPa. Please calculate the power generated in the steam turbine. This steam is subsequently condensed, pumped, boiled and superheated to complete the steam power cycle.

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Problem 91 TOPIC: POWER CYCLES (pg 78) Steam Power Cycle Please list the unit operations in a steam power cycle in order starting with the high pressure superheated steam produced in the boiler. This cycle is often called a Rankine Cycle.

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Problem 91 TOPIC: POWER CYCLES (pg 78) Refrigeration Cycle Please list the unit operations in a refrigeration cycle in order starting with the refrigerant in the discharge of the compressor. This is often called a Reversed Rankine Cycle.

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END OF POWER CYCLES

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**BEGINNING OF HEAT TRANSFER**

(in reference to materials)

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Problem 92 TOPIC: HEAT TRANSFER (pg 84) CONDUCTION THROUGH A PLANE WALL The inside of a wall is maintained at 10 C and the outside wall temperature is 50 C. If the wall is 2000 mm thick and has a conductivity of 0.19 W/m K, please calculate the heat transferred through the wall.

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Problem 93 TOPIC: HEAT TRANSFER (pg 84) CONVECTION FROM AN UNINSULATED PIPE An un-insulated pipe with an outside diameter of 6.5 inches has a surface temperature of 100 C. If the surrounding temperature is 30 C and the outside convective film coefficient is 10 W/m2 K, please calculate the heat loss from the pipe per length of line.

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Problem 94 TOPIC: HEAT TRANSFER (pg 84) TEMPERATURE PROFILE IN A CYLINDRICAL WALL Please develop an equation for the temperature profile in the wall of a pipe given the following information: Inside radius: 4 cm Outside radius: 7 cm Inside temperature: 60 C Outside temperature: 10 C

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Problem 95 TOPIC: HEAT TRANSFER (pg 84) TEMPERATURE PROFILE IN A CYLINDRICAL WALL Please calculate the temperature midway through the wall of a pipe given the following information: Inside radius: 4 cm Outside radius: 7 cm Inside temperature: 60 C Outside temperature: 10 C Find the temperature at a radial position of 6.5 cm

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Problem 95 TOPIC: HEAT TRANSFER (pg 84) INSIDE HEAT TRANSFER COEFFICIENT A fluid at room temperature water flows through a 1 inch (inside diameter) tube. The average velocity in the tube is 1.5 m/s. Physical properties are listed below. Please calculate the inside convective film coefficient Viscosity = 1 cP Density = 1000 kg/m3 Heat capacity = 4.18 kJ/kg K Thermal conductivity

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END OF HEAT TRANSFER (in reference to materials)

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BEGINNING OF FLUIDS

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Problem 96 TOPIC: Fluids (pg 62) DENSITY & SPECIFIC GRAVITY Determine the specific gravity of carbon dioxide gas (molecular weight = 44) at 66°C and 138 kPa compared to STP air. Remember the Ideal Gas Law: PV = nRT PV = (m/MW)RT density = P(MW)/(RT) Remember the Corrected Ideal Gas Law: PV = ZnRT PV = (m/MW)ZRT density = P(MW)/(ZRT) where the factor Z is called the compressibility factor

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Problem 97 TOPIC: Fluids (pg 62) DENSITY & SPECIFIC GRAVITY Determine the specific gravity of carbon dioxide gas (molecular weight = 44) at 66°C and 138 kPa compared to STP air. Remember the Ideal Gas Law: PV = nRT PV = (m/MW)RT density = P(MW)/(RT) Remember the Corrected Ideal Gas Law: PV = ZnRT PV = (m/MW)ZRT density = P(MW)/(ZRT) where the factor Z is called the compressibility factor

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Problem 98 TOPIC: Fluids (pg 62) DENSITY & SPECIFIC GRAVITY Determine the density of plant stream with the following composition at 140°C and 200 kPa. Assume that the gas is ideal and hence the compressibility factor is 1. Components mass flow, kgs/h H CH C2H6 525

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Problem 99 TOPIC: Fluids (pg 64) NEWTONIAN AND NON-NEWTONIAN FLUIDS Is a pseudoplastic material (like ketchup) shear thinning or shear thickening? Is a dilatant material (like a reacting polymerketchup) shear thinning or shear thickening? (c) Is a Newtonian Fluid (like water or gasoline) shear thinning or

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Problem 100 TOPIC: Fluids (pg 64) NEWTONIAN AND NON-NEWTONIAN FLUIDS The data below was taken in a rheometer on two different fluids. Please decide the type of fluid represented by the data. Fluid A Fluid B

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Problem 101 TOPIC: Fluids (pg 68) STATICS Easy to use the standard conversions to establish the pressure in a column of liquid (even multiple immiscible liquids) : 0.43 (SG), psi/ft head 9.8 (SG), kPa/m head DP elevation

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Problem 101, continued TOPIC: Fluids (pg 68) STATICS If a pump is to deliver an alcohol (with specific gravity of 0.8) To a tank at an elevation of 25 m, what is the pressure drop due to the elevation. This pressure drop must be overcome by the pump. DP elevation

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Problem 102 TOPIC: Fluids (pg 62) STATICS

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Problem 103 TOPIC: Fluids (pg 62) STATICS Easy to use the conversions of the previous problem

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Problem 104 TOPIC: Fluids (pg 62) CAPILLARY RISE

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**Problem 105 TOPIC: Fluids (pg 63)**

Pressure on Submerged Objects

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Problem 106 TOPIC: Fluids (pg 63) Pressure on Submerged Objects

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Problem 107 TOPIC: Fluids (pg 63) Pressure on Submerged Objects

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Problem 108 TOPIC: Fluids (pg 65) Part (a) Part (b) Assuming that the joint is frictionless, the pressure drop in this Horizontal form is most likely

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Problem 109 TOPIC: Fluids (pg 65) A pipe draws water from a reservoir and discharges it freely 30 m below the surface. The flow is frictionless. What is the velocity at the exit?

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**Reynolds Numbers Problem 110 TOPIC: Fluids (pg 65)**

(a) What is the Reynolds number for water flowing through an open channel 2 m wide when the flow is 1 m deep? The flow rate is 800 L/s. The kinematic viscosity is 1.23 × 10-6 m2/s. (b) What is the Reynolds number for water flowing through a 6 inch ID pipe. The flow rate is 800 L/s. The kinematic viscosity is 1.23 × 10-6 m2/s. (c) What is the local Reynolds number for water flowing across a stationary flat plate with a free stream velocity of 2 m/s at a position of 0.1 m in from the beginning of the plate. The density is 990 kg/m3 and the viscosity is 0.98 cP

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**Friction Factor for Flow in a Pipe**

Problem 111 TOPIC: Fluids (pg 71) Friction Factor for Flow in a Pipe Oil is flowing in a 4 inch ID CS pipe. The oil rate is 350 gpm. Calculate the friction factor, head loss , and pressure drop per meter of horizontal pipe Physical properties; density = 725 kg/m3 viscosity = 0.9 cP

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**Settling Velocity of a Spherical Particle**

Problem 112 TOPIC: Fluids (pg 72) Settling Velocity of a Spherical Particle Calculate the settling (terminal velocity) for a 0.5 mm spherical particle in oil. Assume Stokes Law. (b) Is Stokes Law a valid assumption in this case? Physical properties: density of oil = 725 kg/m3 viscosity of oil = 0.9 cP density of the particle = 900 kg/m3

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**Speed of Sound Problem 113 TOPIC: Fluids (pg 244)**

The exit velocity in the last coil of a pyrolysis furnace is about 0.3 Ma. What is this velocity in m/s? Use air at a temperature of 339K and a heat capacity ratio of k = 1.4 for the calculation of the speed of sound .

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**Fluid Measurements Problem 114 TOPIC: Fluids (pg 68)**

Pressure gauges in a horizontal venturi meter read 200 kPa at a 0.3 m diameter and 150 kPa at a 0.1 m diameter. What is the mass flow rate? There is no change in elevation through the venturi meter. Assume Cv is 1 and the density is 1000 kg/m3.

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END OF FLUIDS

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**BEGINNING OF STRENGTH of**

MATERIALS

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**Problem 115 TOPIC: Mechanics (pg 33) Stress Terms**

Stress is defined as force per unit area. It has the same units as pressure, and in fact pressure is one special variety of stress. However, stress is a much more complex quantity than pressure because it varies both with direction and with the surface it acts on. Compression Stress that acts to shorten an object. Tension Stress that acts to lengthen an object. Normal Stress Stress that acts perpendicular to a surface. Can be either compressional or tensional. Shear Stress that acts parallel to a surface. It can cause one object to slide over another. It also tends to deform originally rectangular objects into parallelograms. The most general definition is that shear acts to change the angles in an object. Hydrostatic Stress (usually compressional) that is uniform in all directions. A scuba diver experiences hydrostatic stress. Stress in the earth is nearly hydrostatic. The term for uniform stress in the earth is lithostatic. Directed Stress Stress that varies with direction. Stress under a stone slab is directed; there is a force in one direction but no counteracting forces perpendicular to it. This is why a person under a thick slab gets squashed but a scuba diver under the same pressure doesn't. The scuba diver feels the same force in all directions.

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**Problem 116 TOPIC: Mechanics (pg 33) Strain Terms**

Strain is defined as the amount of deformation an object experiences compared to its original size and shape. For example, if a block 10 cm on a side is deformed so that it becomes 9 cm long, the strain is (10-9)/10 or 0.1 (sometimes expressed in percent, in this case 10 percent.) Note that strain is dimensionless. Longitudinal or Linear Strain Strain that changes the length of a line without changing its direction. Can be either compressional or tensional. Compression Longitudinal strain that shortens an object. Tension Longitudinal strain that lengthens an object. Shear Strain that changes the angles of an object. Shear causes lines to rotate. Infinitesimal Strain Strain that is tiny, a few percent or less. Allows a number of useful mathematical simplifications and approximations. Finite Strain Strain larger than a few percent. Requires a more complicated mathematical treatment than infinitesimal strain. Homogeneous Strain Uniform strain. Straight lines in the original object remain straight. Parallel lines remain parallel. Circles deform to ellipses. Note that this definition rules out folding, since an originally straight layer has to remain straight. Inhomogeneous Strain How real geology behaves. Deformation varies from place to place. Lines may bend and do not necessarily remain parallel.

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**Problem 117 TOPIC: Mechanics (pg 33) Terms for Behavior of Materials**

Elastic Material deforms under stress but returns to its original size and shape when the stress is released. There is no permanent deformation. Some elastic strain, like in a rubber band, can be large, but in rocks it is usually small enough to be considered infinitesimal. Brittle Material deforms by fracturing. Glass is brittle. Rocks are typically brittle at low temperatures and pressures. Ductile Material deforms without breaking. Metals are ductile. Many materials show both types of behavior. They may deform in a ductile manner if deformed slowly, but fracture if deformed too quickly or too much. Rocks are typically ductile at high temperatures or pressures. Viscous Materials that deform steadily under stress. Purely viscous materials like liquids deform under even the smallest stress. Rocks may behave like viscous materials under high temperature and pressure. Plastic Material does not flow until a threshhold stress has been exceeded. Viscoelastic Combines elastic and viscous behavior. Models of glacio-isostasy frequently assume a viscoelastic earth: the crust flexes elastically and the underlying mantle flows viscously.

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**Modulus of Elasticity Problem 118 TOPIC: Fluids (pg 33-39)**

For a stress of 5 Mpsi, calculate the strain in % for: Steel Aluminum Cast Iron Wood

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**Cylindrical Pressure Vessel**

Problem 119 TOPIC: Mechanics (pg 33-39) Cylindrical Pressure Vessel The internal pressure of a vertical vessel is 15 barg. The external pressure is atmospheric. The inside diameter of the vessel is 1.5 m and has a 15 mm wall thickness. Calculate the stresses at the inside wall and the axial stress.

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**For the next two examples use the following diagram**

Problem 120 TOPIC: Mechanics (pg 33-39) For the next two examples use the following diagram

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**For the next two examples use the following diagram**

Problem 121 TOPIC: Mechanics (pg 33-39) For the next two examples use the following diagram (a) (b) The maximum shear stress is ?

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Problem 122 TOPIC: Mechanics (pg 33-39)

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Problem 123 TOPIC: Mechanics (pg 33-39)

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Problem 124 TOPIC: Mechanics (pg 33-39)

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Problem 125 TOPIC: Mechanics (pg 33-39)

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Problem 126 TOPIC: Mechanics (pg 33-39)

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END OF STRENGTH of MATERIALS

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