2Exam SpecificationsMathematics %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%
7Problem 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.
9Problem 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.
11Problem 65TOPIC: Thermodynamics (pg 75)A stream has the following composition based on mass fraction.Please convert the list to mol fraction.Components mass fractionHydrogenMethaneEthanePropaneN-Butane
12Problem 66TOPIC: Thermodynamics (pg 75)A stream has the following composition based on mol fraction.Please convert the list to mass fraction.Components mol fractionHydrogenMethaneEthanePropaneN-Butane
14In an isentropic compression of an ideal gas, Problem 67TOPIC: Thermodynamics (pg 75)In an isentropic compression of an ideal gas,p1 = 100 kPa, p2 = 200 kPa, V1 = 10 m3, andk = 1.4. Find V2.
15In an polytropic compression of an ideal gas, Problem 68TOPIC: Thermodynamics (pg 75)In an polytropic compression of an ideal gas,p1 = 100 kPa, p2 = 200 kPa, V1 = 10 m3, andn = 1.3. Find V2.
16In an polytropic compression of an ideal gas, Problem 69TOPIC: Thermodynamics (pg 75)In an polytropic compression of an ideal gas,p1 = 100 kPa, p2 = 200 kPa, V1 = 10 m3, andn = 1.3. Find V2.
17Two copper blocks are initially 50°C and 1 kg, and 100°C and 3 kg. Problem 70TOPIC: 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 nooutside heat exchanged.What is the final temperature of the blocks?
18• Dry-bulb temperature = vertical lines Problem 71TOPIC: 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
19Air is 24°C dry bulb with 50% relative humidity. Problem 72TOPIC: 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.
20For a mixture of 6 hydrocarbon components what is the Problem 73TOPIC: 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 thecondition of the dew point?condition of the bubble point?
21For a mixture of 6 hydrocarbon components what is the Problem 74TOPIC: Thermodynamics (pg 76)For a mixture of 6 hydrocarbon components what is thecondition of the 50% vapor point?condition of the 20% vapor point?
26What is the efficiency of an ideal Otto Problem 79TOPIC: Thermodynamics (pg 78)What is the efficiency of an ideal Ottocycle device with a compression ratioof 6:1? Air is used with k = 1.4.
27An ideal Otto cycle has the following properties: Problem 80TOPIC: 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 gasolinemixed in.Please find the temperature at state B.
28Stoichiometric Combustion CH4 + 2O2 → CO2 + 2H2O Problem 81TOPIC: Thermodynamics (pg 76)Combustion ProcessStoichiometric CombustionCH4 + 2O2 → CO2 + 2H2OFor 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:
29Stoichiometric Combustion C15H32 + 23O2 → 15CO2 + 16H2O Problem 82TOPIC: Thermodynamics (pg 76)Combustion ProcessStoichiometric CombustionC15H O2 → 15CO2 + 16H2OFor 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:
30Problem 83TOPIC: Thermodynamics (pg 76)Steam ReboilerA 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.
31Problem 84TOPIC: Thermodynamics (pg 76)Refrigerant CondenserRefrigerant 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.
32Problem 85TOPIC: Thermodynamics (pg 81)Pipe Sizing Using the P-H diagram20000 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.
33Problem 86TOPIC: Thermodynamics (pg 81)Valve Pressure DropSaturated 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.
36Problem 87TOPIC: POWER CYCLES (pg 81)Turbo-expander10,000 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.
37Problem 88TOPIC: POWER CYCLES (pg 81)Centrifugal Compressor10,000 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?
38Problem 89TOPIC: POWER CYCLES (pg 81)Refrigeration Condenser10,000 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.
39Problem 90TOPIC: POWER CYCLES (pg 81)Steam Turbine100,000 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.
40Problem 91TOPIC: POWER CYCLES (pg 78)Steam Power CyclePlease list the unit operations in a steam power cycle in order starting with thehigh pressure superheated steam produced in the boiler.This cycle is often called a Rankine Cycle.
41Problem 91TOPIC: POWER CYCLES (pg 78)Refrigeration CyclePlease list the unit operations in a refrigeration cycle in order starting with therefrigerant in the discharge of the compressor.This is often called a Reversed Rankine Cycle.
43BEGINNING OF HEAT TRANSFER (in reference to materials)
44Problem 92TOPIC: HEAT TRANSFER (pg 84)CONDUCTION THROUGH A PLANE WALLThe 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.
45Problem 93TOPIC: HEAT TRANSFER (pg 84)CONVECTION FROM AN UNINSULATED PIPEAn 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.
46Problem 94TOPIC: HEAT TRANSFER (pg 84)TEMPERATURE PROFILE IN A CYLINDRICAL WALLPlease develop an equation for the temperature profile in the wall of a pipe given the following information:Inside radius: 4 cmOutside radius: 7 cmInside temperature: 60 COutside temperature: 10 C
47Problem 95TOPIC: HEAT TRANSFER (pg 84)TEMPERATURE PROFILE IN A CYLINDRICAL WALLPlease calculate the temperature midway through the wall of a pipe given the following information:Inside radius: 4 cmOutside radius: 7 cmInside temperature: 60 COutside temperature: 10 CFind the temperature at a radial position of 6.5 cm
48Problem 95TOPIC: HEAT TRANSFER (pg 84)INSIDE HEAT TRANSFER COEFFICIENTA 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 coefficientViscosity = 1 cPDensity = 1000 kg/m3Heat capacity = 4.18 kJ/kg KThermal conductivity
51Problem 96TOPIC: Fluids (pg 62)DENSITY & SPECIFIC GRAVITYDetermine 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 = nRTPV = (m/MW)RTdensity = P(MW)/(RT)Remember the Corrected Ideal Gas Law:PV = ZnRTPV = (m/MW)ZRTdensity = P(MW)/(ZRT)where the factor Z is called the compressibility factor
52Problem 97TOPIC: Fluids (pg 62)DENSITY & SPECIFIC GRAVITYDetermine 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 = nRTPV = (m/MW)RTdensity = P(MW)/(RT)Remember the Corrected Ideal Gas Law:PV = ZnRTPV = (m/MW)ZRTdensity = P(MW)/(ZRT)where the factor Z is called the compressibility factor
53Problem 98TOPIC: Fluids (pg 62)DENSITY & SPECIFIC GRAVITYDetermine 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/hHCHC2H6 525
54Problem 99TOPIC: Fluids (pg 64)NEWTONIAN AND NON-NEWTONIAN FLUIDSIs a pseudoplastic material (like ketchup) shear thinning or shear thickening?Is a dilatant material (like a reacting polymerketchup) shear thinning orshear thickening?(c) Is a Newtonian Fluid (like water or gasoline) shear thinning or
55Problem 100TOPIC: Fluids (pg 64)NEWTONIAN AND NON-NEWTONIAN FLUIDSThe 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
56Problem 101TOPIC: Fluids (pg 68)STATICSEasy to use the standard conversions to establish the pressure ina column of liquid (even multiple immiscible liquids) :0.43 (SG), psi/ft head9.8 (SG), kPa/m headDP elevation
57Problem 101, continuedTOPIC: Fluids (pg 68)STATICSIf 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 tothe elevation. This pressure drop must be overcome by the pump.DP elevation
61Problem 105 TOPIC: Fluids (pg 63) Pressure on Submerged Objects
62Problem 106TOPIC: Fluids (pg 63)Pressure on Submerged Objects
63Problem 107TOPIC: Fluids (pg 63)Pressure on Submerged Objects
64Problem 108TOPIC: Fluids (pg 65)Part (a)Part (b)Assuming that the joint is frictionless, the pressure drop in thisHorizontal form is most likely
65Problem 109TOPIC: Fluids (pg 65)A pipe draws water from a reservoir and discharges it freely 30 mbelow the surface. The flow is frictionless.What is the velocity at the exit?
66Reynolds Numbers Problem 110 TOPIC: Fluids (pg 65) (a) What is the Reynolds number for water flowing through an open channel2 m wide when the flow is 1 m deep? The flow rate is 800 L/s. Thekinematic viscosity is 1.23 × 10-6 m2/s.(b) What is the Reynolds number for water flowing through a 6 inchID 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 astationary flat plate with a free stream velocity of 2 m/s at a positionof 0.1 m in from the beginning of the plate. The density is 990 kg/m3and the viscosity is 0.98 cP
67Friction Factor for Flow in a Pipe Problem 111TOPIC: Fluids (pg 71)Friction Factor for Flow in a PipeOil is flowing in a 4 inch ID CS pipe. The oil rate is 350 gpm.Calculate the friction factor,head loss , andpressure drop permeter of horizontal pipePhysical properties; density = 725 kg/m3viscosity = 0.9 cP
68Settling Velocity of a Spherical Particle Problem 112TOPIC: Fluids (pg 72)Settling Velocity of a Spherical ParticleCalculate the settling (terminal velocity) for a 0.5 mm spherical particlein oil. Assume Stokes Law.(b) Is Stokes Law a valid assumption in this case?Physical properties: density of oil = 725 kg/m3viscosity of oil = 0.9 cPdensity of the particle = 900 kg/m3
69Speed of Sound Problem 113 TOPIC: Fluids (pg 244) The exit velocity in the last coil of a pyrolysis furnace isabout 0.3 Ma. What is this velocity in m/s?Use air at a temperature of 339K and a heat capacity ratio of k = 1.4for the calculation of the speed of sound .
70Fluid 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.
73Problem 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.CompressionStress that acts to shorten an object.TensionStress that acts to lengthen an object.Normal StressStress that acts perpendicular to a surface. Can be either compressional or tensional.ShearStress 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.HydrostaticStress (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 StressStress 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.
74Problem 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 StrainStrain that changes the length of a line without changing its direction. Can be either compressional or tensional.CompressionLongitudinal strain that shortens an object.TensionLongitudinal strain that lengthens an object.ShearStrain that changes the angles of an object. Shear causes lines to rotate.Infinitesimal StrainStrain that is tiny, a few percent or less. Allows a number of useful mathematical simplifications and approximations.Finite StrainStrain larger than a few percent. Requires a more complicated mathematical treatment than infinitesimal strain.Homogeneous StrainUniform 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 StrainHow real geology behaves. Deformation varies from place to place. Lines may bend and do not necessarily remain parallel.
75Problem 117 TOPIC: Mechanics (pg 33) Terms for Behavior of Materials ElasticMaterial 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.BrittleMaterial deforms by fracturing. Glass is brittle. Rocks are typically brittle at low temperatures and pressures.DuctileMaterial 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.ViscousMaterials 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.PlasticMaterial does not flow until a threshhold stress has been exceeded.ViscoelasticCombines elastic and viscous behavior. Models of glacio-isostasy frequently assume a viscoelastic earth: the crust flexes elastically and the underlying mantle flows viscously.
76Modulus of Elasticity Problem 118 TOPIC: Fluids (pg 33-39) For a stress of 5 Mpsi, calculate the strain in % for:SteelAluminumCast IronWood
77Cylindrical Pressure Vessel Problem 119TOPIC: Mechanics (pg 33-39)Cylindrical Pressure VesselThe 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.
78For the next two examples use the following diagram Problem 120TOPIC: Mechanics (pg 33-39)For the next two examples use the following diagram
79For the next two examples use the following diagram Problem 121TOPIC: Mechanics (pg 33-39)For the next two examples use the following diagram(a)(b) The maximum shear stress is ?