### Day 3

```Exam Specifications
Mathematics
Engineering Probability and Statistics
Chemistry
Computers
Engineering Economics
Statics and Dynamics
Strength of Materials
Material Properties
Fluid Mechanics
Electricity and Magnetism
Thermodynamics
15%
7%
9%
7%
7%
8%
10%
7%
7%
7%
9%
7%
BEGINNING OF THERMODYNAMICS
Problem 58
TOPIC:
Thermodynamics (pg 75)
Problem 59
TOPIC:
Thermodynamicss (pg 83)
Problem 60
TOPIC:
Thermodynamicss (pg 75)
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.
Problem 62
TOPIC:
Thermodynamics (pg 75)
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.
Problem 64
TOPIC:
Thermodynamics (pg 75)
Problem 65
TOPIC:
Thermodynamics (pg 75)
A stream has the following composition based on mass fraction.
Please convert the list to mol fraction.
Components
Hydrogen
Methane
Ethane
Propane
N-Butane
mass fraction
0.15
0.25
0.25
0.25
0.10
Problem 66
TOPIC:
Thermodynamics (pg 75)
A stream has the following composition based on mol fraction.
Please convert the list to mass fraction.
Components
Hydrogen
Methane
Ethane
Propane
N-Butane
mol fraction
0.15
0.25
0.25
0.25
0.10
Problem 66
TOPIC:
Thermodynamics (pg 75)
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.
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.
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.
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?
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
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.
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?
For a mixture of 6 hydrocarbon components what is the
condition of the bubble point?
Problem 74
TOPIC:
Thermodynamics (pg 76)
For a mixture of 6 hydrocarbon components what is the
condition of the 50% vapor point?
For a mixture of 6 hydrocarbon components what is the
condition of the 20% vapor point?
Problem 75
TOPIC:
Thermodynamics (pg 76)
Problem 76
TOPIC:
Thermodynamics (pg 76, 77)
Problem 77
TOPIC:
Thermodynamics (pg 76, 77)
Problem 78
TOPIC:
Thermodynamics (pg 78)
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.
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.
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 + 7.53N2. The mass of flue gas per mass of
fuel is:
Problem 82
TOPIC:
Thermodynamics (pg 76)
Combustion Process
Stoichiometric Combustion
C15H32 + 23O2 → 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:
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.
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.
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.
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.
END OF THERMODYNAMICS
BEGINNING OF POWER CYCLES
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.
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?
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.
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.
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.
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.
END OF POWER CYCLES
BEGINNING OF HEAT TRANSFER
(in reference to materials)
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.
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.
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 temperature: 60 C
Outside temperature: 10 C
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 temperature: 60 C
Outside temperature: 10 C
Find the temperature at a radial position of 6.5 cm
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
END OF HEAT TRANSFER
(in reference to materials)
BEGINNING OF FLUIDS
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
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
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
H2
CH4
C2H6
mass flow, kgs/h
1250
4000
525
Problem 99
TOPIC:
Fluids (pg 64)
NEWTONIAN AND NON-NEWTONIAN FLUIDS
(a) Is a pseudoplastic material (like ketchup) shear thinning or shear thickening?
(b) 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
shear thickening?
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
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) :
DP elevation
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
Problem 102
TOPIC:
STATICS
Fluids (pg 62)
Problem 103
TOPIC:
STATICS
Easy to use the conversions of
the previous problem
Fluids (pg 62)
Problem 104
TOPIC:
CAPILLARY RISE
Fluids (pg 62)
Pressure on Submerged Objects
Problem 105
TOPIC:
Fluids (pg 63)
Problem 106
TOPIC:
Pressure on Submerged Objects
Fluids (pg 63)
Problem 107
TOPIC:
Pressure on Submerged Objects
Fluids (pg 63)
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
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?
Problem 110
TOPIC:
Fluids (pg 65)
Reynolds Numbers
(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
Problem 111
TOPIC:
Fluids (pg 71)
Friction Factor for Flow in a Pipe
(a) Oil is flowing in a 4 inch ID CS pipe. The oil rate is 350 gpm.
Calculate the friction factor,
(c) pressure drop per
meter of horizontal pipe
Physical properties; density = 725 kg/m3
viscosity = 0.9 cP
Problem 112
TOPIC:
Fluids (pg 72)
Settling Velocity of a Spherical Particle
(a) 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
Problem 113
TOPIC:
Fluids (pg 244)
Speed of Sound
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 .
Problem 114
TOPIC:
Fluids (pg 68)
Fluid Measurements
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.
END OF FLUIDS
BEGINNING OF STRENGTH of
MATERIALS
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.
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.
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.
Problem 118
TOPIC:
Fluids (pg 33-39)
Modulus of Elasticity
For a stress of 5 Mpsi, calculate the strain in % for:
(a)
(b)
(c)
(d)
Steel
Aluminum
Cast Iron
Wood
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.
Problem 120
TOPIC:
Mechanics (pg 33-39)
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 ?
Problem 122
TOPIC:
Mechanics (pg 33-39)
Problem 123
TOPIC:
Mechanics (pg 33-39)
Problem 124
TOPIC:
Mechanics (pg 33-39)
Problem 125
TOPIC:
Mechanics (pg 33-39)
Problem 126
TOPIC:
Mechanics (pg 33-39)
END OF STRENGTH of
MATERIALS
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