CHEN3600 – Computer-Aided Chemical Engineering
Chemical Engineering Department
T.D. Placek
Fall 2012
Bonus E
Auburn University
Bonus E – Fluid Mechanics Explain Questions
During the semester, we have repeatedly discussed the need to prepare for the upcoming
CHEN3AA0 Concept Inventory Exams.
Please consult the description of this exam for additional information.
Please consult this course’s syllabus to find the relevant course outcomes.
As a 10 point (maximum) bonus, provide as a Word document (both in hardcopy and
emailed as an attachment) 5 questions that could be included on the Concept Inventory
Exam that are related to the subject matter covered in CHEN2610 Transport I.
The solution to each question should demonstrate that the student can describe and
explain the underlying fluid mechanics and other principles (math, sciences, physics, etc.).
After listing 5 possible questions, select what you feel are the best two and provide a
complete and acceptable answer. For each of these two questions, also provide two
answers which would not be considered acceptable. Explain why these answers would not
be acceptable.
THERE IS TO BE NO INTERACTIONS WITH FELLOW STUDENTS ABOUT THIS
ASSIGNMENT.
Example Questions (You may not use these)
Air is flowing in a 6” diameter pipe with a length of 100 ft with a half-open gate valve
located in the middle of the pipe section. A senior engineer is talking to a newly hired
engineering over coffee and donuts and he asks, “Did you consider the possibility of
cavitation in your calculations?” How should the newly hired engineer respond?
In applying the Reynold’s Transport Theorem to the case of momentum, what terms appear
on the side of the equation that represents the Lagrangian “point of view” and what
principle is employed to represent this term?
Student Submissions
Student 1
1. You are assigned by your company to a project to design a dam, and you first create
a scale model of the prototype. Before performing similitude to glean information
about the prototype itself, the project manager asks which dimensionless group, the
Reynolds number, Froude number, or Weber number, should be considered as the
most important parameter to model this situation. State any assumptions that
would be made.
2. In relation to pressure gradient effects, explain the origin and concept of boundarylayer separation over a curved surface.
3. When the temperature is increased, explain why viscosity decreases in liquids yet
increases in gases.
4. The Bernoulli equation and the first law of thermodynamics energy equation look
similar but are quite different. Explain the difference between these two equations
and when each is applicable.
5. The Moody diagram is a valuable tool used to relate the resistance coefficient, or
friction factor, Reynolds number, and relative roughness for turbulent flow in
systems. You have used this diagram countless times to solve problems, but one day
you are asked why the friction factor eventually becomes constant as the Reynolds
number increases. How do you respond?
Answers:
Problem 1:
Acceptable Response:
The Froude number should be used for similitude between the model and prototype. By its
definition, the Froude number relates the kinetic forces to the gravitational forces. In a
dam, assuming that the water’s velocity is large enough to discount the negligible viscous
effects of the fluid and that surface tension effects are also negligibly small for the
substantial flow through the dam, gravity is the major force that drives the flow of water
through the process. In this situation, the gravitational force affects the flow pattern of the
system significantly. In contrast, the Reynolds number relates kinetic and viscous forces,
and the Weber number relates kinetic and surface tension forces. Neither viscous nor
surface tension effects are significant in modeling this process so these dimensionless
groups are not important in this situation.
Unacceptable Response:
1. The Reynolds number should be used because water flows in this process with a
kinetic force. Viscous forces are present and contribute to the loss of energy in this
system, which should be taken into account in the analysis.
This response fails to correctly identify the main dimensionless parameter, the Froude
number, and lists the Reynolds number as the main contributor to flow even though
viscous effects have little relevance in the system. The response goes on to needlessly try to
cite that energy loss from viscous dissipation should be taken into account, which is not
relevant to the analysis asked. Overall, the student fails to exhibit an understanding and
distinction among the dimensionless groups.
2. The Froude number should be used because gravity pulls the water down and
makes it go over the dam. The Weber number and Reynolds number are
unimportant.
This response barely answers the question posed and exhibits little understanding of the
dimensionless parameters involved. The student shows he or she remembers that the
Froude number involves gravitational forces but does little to explain why it is more
significant than the other two dimensionless groups posed, which he simply states are
unimportant. Overall, the student inadequately explains the distinctions between the
parameters involved and demonstrates only a simple knowledge of the Froude number.
Problem 5:
Acceptable Response:
The friction factor is defined as the ratio of the shear stress acting at the wall to the kinetic
pressure while the Reynolds number is the ratio of the kinetic to viscous forces of a fluid.
As the Reynolds number increases, a point is reached at which the ratio between the shear
stress at the wall and kinetic pressure becomes stable. As a result, as the Reynolds number
increases, which subsequently increases the velocity due to its definition, the shear stress
at the wall increases at a proportional rate so that the friction factor’s force ratio does not
change. This does not mean, however, that the individual forces are not changing; it simply
means that the force ratio is constant so that the system being analyzed depends only on
the relative roughness elements and Reynolds number.
Unacceptable Answers:
1. The friction factor stabilizes since it reaches a limiting value where it ceases to
change. This occurs over a wide range depending on the various roughness of the
pipes.
This response offers no theoretical backing to justify why the friction factor stabilizes. The
student only states what he or she sees happening on the graph as an answer, which
demonstrates no knowledge of the underlying concepts behind the Moody diagram and the
friction factor.
2. The friction factor stops changing once it enters the turbulent flow region after it
transitions from a laminar profile. This explains why it happens as the Reynolds
number increases since the flow changes from laminar to turbulent over a transition
region at a certain Reynolds number.
This response completely misinterprets and incorrectly answers the posed question. The
Moody diagram provides values for various roughness elements and Reynolds numbers for
fully rough, turbulent flow. Hence, the discussion of the transition from laminar to
turbulent flow is incorrect and does not describe the reason of why the friction factor
stabilizes.
Student 2
Question 1:
Explain what Assumptions must be made to use the Bernoulli equation and explain what
terms are missing for actual flow as to why you must these assumptions.
Question 2:
Explain the significance of the number 2000 in relation to the Reynolds number. Explain
the terms of the Reynolds number.
Question 3:
Compare and contrast skin friction and minor losses in piping systems.
Question 4:
Explain the difference between geometric similitude and dynamic similitude in respect to
modeling. Is a model the same as a prototype? Explain?
Question 5:
Explain the kinetic energy correction factor and when it must be applied and the
implications for laminar and turbulent flow.
Acceptable Answers
Question 1:
Explain what Assumptions must be made to use the Bernoulli equation and explain what
terms are missing for actual flow as to why you must these assumptions.
Question 1: Acceptable answer
The Bernoulli equation is only to be applicable along a streamline. Secondly the Bernoulli
equation is valid if and only if it is a potential flow situation. The terms that are missing
from the Bernoulli equations for actual flow are the losses terms that appear in the energy
equation. The terms that are missing in the case of potential flow have to do with frictional
losses and potential flow ignores all viscous forces that affect the flow close to the wall.
Question 1: Unacceptable answer 1
Assumptions
hL is missing from the equation
-Potential Flow
-Streamline
Why is it a bad answer?
The student just listed his assumptions not why he made them. Explain questions should be
written in sentence format with correct grammar and punctuation. No equations or
symbols should be used.
Question 1: Unacceptable answer 2
Must assume potential flow along a streamline.
𝑃1
𝑉12 𝑃2
𝑉22
+ 𝑧1 +
= + 𝑧2 +
+ ℎ𝐿
𝛾
2𝑔
𝛾
2𝑔
Why is it a bad answer?
The student only answered the first half of the question. Then the student put the energy
equation instead of the Bernoulli equation. The student had the right assumptions
yet wrote the equation wrong. No equations or symbols should be used.
Question 3:
Compare and contrast skin friction and minor losses in piping systems.
Question 3: Acceptable Answer
Similarities include that both skin friction and minor losses both have to do with frictional
losses in a piping system. The differences take shape in the places they occur. Skin
friction occurs as frictional losses at the wall of the pipe, whereas minor losses occur
in the components of a piping system such as elbows and tees.
Question 3: Unacceptable Answer 1
Skin Friction – Frictional losses that occur at pipe wall.
Minor Losses – Losses that occur in components of piping system
Why is it a bad answer?
The student just regurgitated definitions from his/ her fluid mechanics class and doesn’t
give any similarities or differences.
Question 3: Unacceptable Answer 2
Minor losses are the small losses in a piping system and skin friction are the bigger losses
in a piping system.
Why is it a bad answer?
The student showed no knowledge of subject matter and was just trying to pull definitions
out of the air.
Student 3
1. A rubber ducky is floating in a bathtub full of water that is enclosed in an airtight
bathroom. If the air pressure in the bathroom were to increase, what would be the
affect on the ducky?
a. Acceptable: Assume that the water is an incompressible fluid. If the air
pressure in the bathroom was to increase, there would be an increased
downward force applied to the top of the rubber ducky. In order to
counteract the increase in force, the rubber ducky will displace more water
by sinking lower into the water. That is, the buoyant force will increase as a
result of the increase and pressure and the rubber ducky must displace more
water to account for it.
b. Unacceptable: FB=FUp-FDown, FB will increase
i. Unacceptable because it does not demonstrate any knowledge of fluid
mechanics concepts. Nothing is being explained and only an equation
is cited.
c. Unacceptable: The pressure increase will not affect the rubber ducky. Only
the water will be affected and the ducky will remain in the same position.
i. Unacceptable because since water is an incompressible liquid, it will
not be effected by the increase in pressure. This answer does not
show any knowledge or understanding of the employed concepts.
2. A heater is placed in the middle of two points in a slow flowing channel, point 1 and
point 2. The fluid is flowing away from point 1 and toward point 2. How does the
speed of the fluid compare at the two points?
3. Two of the most commonly used dimensionless groups used in fluid mechanics are
the Froude number and the Reynolds number. Explain the differences between the
two groups and describe the situation in which each number would apply (i.e. fluid
moving along a streamline for Froude number).
4. Describe what is meant by boundary layer and how it relates to fully developed flow
regions.
a. Acceptable: The boundary layer is the point sufficiently close to the boundary
in a flow situation in which the velocity changes from the free stream value.
The point at which the boundary layer reaches half the diameter all the way
around a pipe constitutes fully developed flow.
b. Unacceptable: The boundary layer is the part in a flow where the velocity is
zero and fully developed flow is when there is no boundary layer.
i. Unacceptable because it is a nonsensical answer that does not
constitute even an elementary knowledge of the applied concepts
c. Unacceptable: Fully developed flow is when the fluid is flowing at a
maximum velocity yet is still laminar flow. The boundary layer is where the
flow is turbulent.
i. Unacceptable because the answer looks made up and the student is
trying to throw random concepts around in the answer in an attempt
to look like the right answer.
5. Describe what is meant by head loss and how it is applied as it relates to fluid
mechanics.
Student 4
1. Explain the significance of a completely turbulent regime.
2. Explain the significance of the Reynolds number in pipe flow.
Acceptable: In fluid mechanics, the Reynolds number (Re) is a dimensionless
quantity engineers use to estimate if a flow is laminar or turbulent and can be
viewed as the ratio of kinetic to viscous forces, where kinetic forces are associated
with fluid motion. A low Reynolds number implies viscous effects are important,
while a high Reynolds number implies kinetic forces are predominate. In fluid flow,
the Reynolds number indicates where the flow is laminar, transitional, or turbulent.
Unacceptable: The Reynolds number is a number used to measure a flow’s stability
or instability.
Why answer is unacceptable: No citation of major fluid mechanics principles or
concepts, with no demonstration of understanding.
Unacceptable: Re
Why answer is unacceptable: Although the equation is correct, there is no
demonstration of understanding. Citation of the Reynolds number equation is not
sufficient.
3. Describe the relationship between form drag and friction drag.
Acceptable: Form drag is the portion of the total drag force that is associated with
the pressure distribution, i.e. the force resulting from wind contacting a moving
aircraft. Friction drag is the portion of the total drag force that is associated with the
viscous shear-stress distribution. The drag force is the sum of the two forces.
Unacceptable: Form drag acts on the front of an object, and friction drag acts on the
sides.
Why answer is unacceptable: No citation of pressure distribution or viscous
shear-stress distribution. No additional statements or examples to exhibit
understanding of the concept.
Unacceptable: dFD = -p dA cos θ +  dA sin θ
Why answer is unacceptable: Just citing an equation with no demonstration of
knowledge or key concepts.
4. Explain the meaning of boundary-layer thickness and relate it to the process of
boundary- layer separation.
5. Explain the relationship between developing and fully developed laminar and turbulent
flows, identifying the key concept to classification.
Student 5
Sample Problem A:
Explain the concepts of Newtonian and non-Newtonian fluids.
Sample Problem B:
Explain the difference of laminar and turbulent flow.
Sample Problem C:
Explain the concepts of shear, shear stress, and shear rate.
Sample Problem D:
Explain how to solve for laminar flow sphere drag.
Sample Problem E:
Explain the importance of dimensionless numbers, such as the Reynolds number, in
systematically solving problems related to fluid dynamics.
Responses to the questions on the CHEN 3AA0 Exam are marked as either
“acceptable” or “unacceptable.” Several sample answers are provided below.
Acceptable Answer to Sample Problem D:
The drag coefficient of a sphere is particularly useful in applications involving spherical
objects such as particles and droplets. For Reynolds number less than 0.5, the flow around
the sphere is laminar and amenable to analytical solutions. An exact solution for the drag of
a sphere can be found using Stokes’s equation: FD= 3πμV0d. The drag force on the sphere is
essentially the sum of the form drag and friction drag. Form drag is the portion of the total
drag force that is associated with pressure distribution. Friction drag is the portion of the
total drag force that is associated with the viscous shear-stress distribution.
*This is an acceptable answer because major engineering and science concepts are cited
and a properly constructed explanation is then developed using the key concepts.
Unacceptable Answer to Sample Problem D:
Use the Stokes’s equation to find the sphere drag.
*This is an unacceptable answer because it simply cites the name of an equation. It does not
identify the key concepts nor does it demonstrate sufficient knowledge.
Unacceptable Answer to Sample Problem D:
Drag force is the concept that is associated with pressure differences and shear-stress
variabilities.
*This is an unacceptable answer because it is erroneous and insufficient in demonstrating
knowledge of the concepts.
Acceptable Answer to Sample Problem E:
Dimensionless numbers, such as the Reynolds number, are often used in the art of
similitude to predict prototype performance from model observations. To achieve exact
similitude, the model must be a scale model of the prototype, and the values of
dimensionless groups must be the same for the model and the prototype. Only the most
important dimensionless groups are used. Four common independent dimensionless
groups used in Chemical Engineering and fluid dynamics are the Reynolds number (Re),
the Mach number (M), the Weber number (We), and the Froude number (Fr). Because of
the complexity of fluid mechanics problems, the design of fluid systems relies heavily on
these methods of experimenting and similitude, and thus, ultimately, dimensionless
numbers.
* This is an acceptable answer because major engineering and science concepts are cited
and a properly constructed explanation is then developed using the key concepts.
Unacceptable Answer to Sample Problem E:
For fluid dynamics problems, dimensionless numbers are always equal for prototypes and
models. Therefore, the Reynolds number is essential in comparing two flow systems.
*This is an unacceptable answer because it is erroneous and insufficient in demonstrating
knowledge of the concepts.
Unacceptable Answer to Sample Problem E:
Re= ρLV/μ , where Re is the Reynolds number.
*This is an unacceptable answer because it simply cites an equation. It does not identify the
key concepts nor does it demonstrate sufficient knowledge.
Student 6
1) Explain the differences between laminar and turbulent flow, and what may be the
benefits of tripping a fluid into turbulent flow as it enters a pipe rather than allowing it to
develop in a laminar fashion.
2) Explain the differences between the Lagrangian and Eulerian perspectives of flow, and
how the Reynold’s Transport Theorem relates them.
3) Explain the concept of Head loss in a flow system and what each specific term in the
energy equations real world meaning is.
4) Discuss the importance of Similitude, not only in terms of modeling, but also benefits in
industry.
5) Name the different parts of a boundary layer. Explain how and at what point they
develop, and what significance they have to the properties of the flow in that region.
GOOD ANSWERS
1) The differences between laminar and turbulent flow are numerous. Laminar flow is only
common in small pipes with relatively low velocity. There is a uniform parabolic velocity
distribution and no excess energy that must be dissipated through eddies or wakes. Also
the shear stress distribution depends mostly on the viscosity of the fluid. Turbulent flow is
more common in large pipes with high flow rates because that is conducive to a higher
Reynold’s number and the transition from laminar to turbulent flow occurs between a Re of
2000 and 3000. The Velocity distribution turbulent flow is more evenly distributed than
laminar flow but they both have similar drop off to zero at the wall due to the boundary
effects of the fluid. The shear stress distribution in turbulent flow is more a function of the
density instead of the viscosity in laminar flow.
Tripping of a fluid creates the formation of the turbulent boundary layer immediately
rather than letting it develop naturally over the whole entry zone. The cross-stream mixing
that is prevalent in turbulent flow promotes an increase in the effective viscosity of the
fluid, which allows the velocity distribution to spread out and transport more fluid quicker
with fewer losses.
3) Head loss is an account for the losses of mechanical energy that will occur during flow
due to heat produced by the interactions of the fluid particles together, or the interactions
of the fluid particles with different components in the system. These different losses must
be taken into account in order to know how much power must be supplied to pumping
stations, and also how much can be gained from turbines.
The energy equation can be described in words as the head introduced by the flow into the
control volume added to the head added by any pumps is equal to the head taken away
from the control volume by the flow added to the head withdrawn from the system by
turbines added to the head loss due to thermal energy and components in the system.
BAD ANSWERS
1) Laminar flow is smooth and turbulent flow is rough. There are more losses associated
with laminar flow relative to its flow rate. Turbulent flow happens in big pipes with high
flow rates. Tripping the flow would be better because it would allow the flow to develop as
turbulent flow instead of having to develop as laminar and then eventually transition into
turbulent.
-This answer is unacceptable because I have failed to give any description that has
any real meaning to an engineer. And I never explained why tripping the flow into
turbulence is actually better.
3) The head loss is comprised of losses in energy due to thermal energy being created by
the fluid in a system. Some losses are also contributed by components in the system. The
energy equation can be described as “head coming in”+”head being added”=”head going
out”+”head being taken out”+”head being lost”.
-This answer is unacceptable because nothing is specific enough and the wording is
neither concise nor informative in any fashion. The description of power equation lacks any
real depth and each term is rather vague.
Student 7
1. Your Aunt Mabel has been having difficulties with her washing machine. Every time
she uses it there is a loud banging noise in the pipes connected to it. She asks you as
a young Chemical Engineer proficient in fluid mechanics to identify and explain the
undesirable phenomenon and suggest three possible ways of preventing it.
-The cause of the noise is due to water hammer. When a valve is suddenly closed,
pressure moves in a wave upstream of the valve and continues through the pipe at
the speed of sound. The phenomenon is cyclical and often knocking sounds are
audible as the water reverberates up and down the pipe. To prevent water hammer
your Aunt could install a water hammer arrestor, partially close the shut-off valve
for the washing machine thus reducing velocity of the stream by reducing the
flowrate or she could install a larger diameter pipe for the water line to the
appliance. Smaller diameter pipes are more susceptible to water hammer.
Unacceptable answer: Associating the problem with a pressure build up in the pipes.
While partially correct, the answer must include the definition of water hammer and
explain more completely the process of a valve being closed and the positive
pressure wave generated upstream by the forward momentum of the flowing fluid.
A second unacceptable answer would be trying to explain the problem citing
equations for static fluids such as the Bernoulli equation.
2. In words, define and explain the significance of alpha in the Energy Equation. Why
is 𝛼 = 1 for turbulent flow?
3. What is similitude and why is it important of engineers?
-Similitude is a comparison of dimensions, kinematic properties, geometries and any
other aspects of a model to its full scale counterpart. It is important for engineers to test
designs for safety and economic reasons. It is more practical to perform experiments on
a prototype in order to be assured of success in the full sized unit. Similitude makes
sure the ratio of intrinsic properties in the real to the model part is correct.
Unacceptable answer: Merely stating that similitude implies or means ‘similarity’ of one
object to another. Not answering the question is a second unacceptable student
response.
4. Is it valid to use the ideal gas equation of state for gases other than air? Why or why
not? If not, what correction is needed to apply the ideal gas assumptions to non-ideal
gases?
5. What does little b stand for in the Reynolds Transport Theorem?
Student 8
1. A fireman is holding a fire hose with a nozzle attached in order to extinguish a flame.
Assume that the flows into and out of the nozzle are in the positive X-direction and
that the positive Z-direction is pointing upwards. What direction must the fireman
apply force in in order to keep the hose and nozzle assembly stationary when the
water flows through the hose? Cite any relevant equations and/or principles used to
formulate your answer.
Acceptable answer: “The fireman must provide a force on the hose directed in the
positive X-direction and in the positive Z-direction. The net force acting on a control
volume surrounding the nozzle in the X-direction is related to the momentum of
mass entering and exiting the control volume via the linear momentum equation.
∑ 𝐹 = ∫ 𝑣𝜌𝑑∀ + ∫ 𝑣𝑝𝑉 ∙ 𝑑𝐴 = 𝑚̇𝑜 𝑣𝑜 − 𝑚̇𝑖 𝑣𝑖
𝐶.𝑉.
𝐶.𝑆.
Due to the decreased cross-sectional area and pressure of the free jet exiting
the nozzle, the velocity and therefore the momentum of the fluid exiting the nozzle
is greater than that of the fluid entering the CV. Since the net flux of momentum
through the control volume is in the positive X-direction and the momentum
accumulation is zero, the fireman must supply a force in the positive X-direction in
order to keep the conduit from moving with respect to the X-axis.
Since mass is not flowing in or out of the control volume in the Z-direction
and gravitational force is the only force acting on the object in this direction, the
fireman needs to apply force upwards in order to counteract the downward force of
gravity on the hose and keep it from moving in the Z-direction.”
Unacceptable Answer: “The external force must be in the positive Z direction.
Although fluid is entering and exiting the nozzle in the X-direction, the mass flow
rate of the two flows are equal and no force is needed to keep the hose from moving
in the X-direction. The only force the fireman needs to apply is a force on order to
keep the hose from falling.”
Why is it unacceptable? Besides not mentioning what equation he or she used
to arrive at this answer, the student completely ignored the change in
momentum of the fluid in the nozzle. Since the fluid accelerates in the nozzle,
there is a net flux of momentum and therefore a net force is needed in order
to keep the nozzle from moving in the X-direction.
Unacceptable Answer: “The external force must be in the positive X and Z
direction. The momentum equation.”
∑ 𝐹 = ∫ 𝑣𝜌𝑑∀ + ∫ 𝑣𝑝𝑉 ∙ 𝑑𝐴
𝐶.𝑉.
𝐶.𝑆.
Why is it unacceptable? Even though the individual reached the correct
answer and referenced the correct principle, the student does not give any
explanation to how the momentum equation yields her answer. Simply
listing an equation does not prove a given statement, especially if the reader
is not familiar with that equation.
2. A fluid enters a conduit from a large reservoir. When the fluid initially enters the
conduit, the velocity profile of the fluid will change from the initial velocity distribution
(developing flow) towards the final velocity distribution (fully developed flow). What
physical phenomenon causes the velocity profile of the conduit to change? Why does
this phenomenon occur? What happens to the phenomenon when the flow becomes
fully developed?
Acceptable Answer: “The boundary layer is responsible for the changes in velocity
that occur within a developing flow. When the initially moving fluid enters the
conduit, the no-slip condition states that the velocity of the fluid must equal the
velocity at the barrier. Therefore the velocity of the molecules next to the stationary
pipe must have zero velocity. This sudden drop in velocity creates a boundary layer
in which the velocity of the fluid rapidly changes from the free-stream velocity to
zero. As the fluid moves down the conduit, the boundary layers forming near the
wall of the pipe will grow in size with the outermost edge of the boundary moving
closer to the center of the conduit. The flow becomes fully developed when these
boundary layers meet at the center of the pipe at which point every molecule of the
fluid is part of the boundary layer. At this point, the velocity distribution in the fluid
is no longer changing due to the changing boundary layer and the distribution will
be that of the fully developed flow.”
Unacceptable Answer: “The boundary layer. Flow next to a boundary must have a
boundary layer that changes the velocity of the water. The boundary layer
disappears when L/D > 50.”
Why is it unacceptable? Outside of the incomplete sentence that starts the
answer, the student provides little to no explanation for his answer, stating
his (correct) answer but leaving it up to the reader to determine why the
boundary layer forms and how it influences the velocity of the flow. Also, the
student states an equation that not only is not valid for this given question
(that equation tells the user when the flow is fully developed for turbulent
flow only, not what happens to cause the flow to become fully developed) but
is not given any explanation as to why that equation shows what happens
when the flow becomes fully developed.
Unacceptable Answer: “The motion of the fluid is responsible for the changing
nature of the flow. Although the fluid starts out flowing one way, just entering the
pipe causes the distribution of the flow to become fully developed.”
Why is it unacceptable? The student did not even mention the development of
the boundary layer in his or her answer—the ultimate cause of the fluid’s
change in velocity in a conduit. Furthermore, the student did not have an
explicit answer for the final question, leaving it to the reader to determine
what happens to cause the flow to become developed.
3. The atmosphere on Earth consists of a mixture of fluids (gasses) that we call air. Does
the air exert any forces on objects within the Earth’s atmosphere? If it does exert a
force, why do most objects “sink” to the bottom of the atmosphere? If it does not,
explain your reasoning.
4. An engineer wishes to find the discharge of a proposed piping system by building a
scale model of the system. In order for the engineer to obtain accurate results via
similitude, what dimensionless number should the engineer keep constant between the
proposed design and the scale model? Explain your reasoning.
5. Describe the differences between the Lagrangian and Eulerian approaches to fluid
mechanics. How can these two approaches be related to each other?
Student 9
1. You are going to the Doctor for your yearly check-up. The nurse comes in and checks
your heart rate and then she asks to take youR Blood Pressure. She proceeds to
pump up her inflatable device around your arm and waits for about one minute as
the pressure decreases. Explain how the movement of red blood cells produces
a force on the walls of blood vessels.
2. Explain the concept of the Kinetic Energy Correction Factor and how it is
employed.
3. For your high school science project, you are asked to make a model of a Boeing 747
wide-body commercial airliner. Because of your interest in planes and aeronautics
you take it upon yourself to do some research on drag forces. What art of
predicting prototype performance from model observations would you use
and explain how it relates to this project.
4. You notice that over the years your drive way has faded in color. You talk to your
next-door neighbor about the differences in the color of the concrete and he
recommends that you rent a pressure washer from Lowe’s. A pressure washer
consists of a small engine that drives a water pump connected to a high-pressure
hose and a nozzle type mechanism. At the end of the nozzle, a high velocity stream
of water is produced. Are there any losses in this system and explain your
answer.
5. The Titanic is the most memorable ship in commercial liner history. However, the
fate of its first voyage was ill prepared. It was deemed as the unsinkable ship but
ultimately ended up splitting in two parts and sinking to the bottom of the ocean.
For the Titanic to float on water, what must happen? Explain using
engineering principles.
(4) Acceptable: First, there needs to be a control volume established in the system
between the nozzle and pump so the momentum equation can apply. The pressurized
water is then released at the end of the nozzle creating a free jet where there is no
pressure. The possible losses in the system include the kinetic energy loss due to friction of
the hose. Also, some of that high pressure is transferred into energy in the form of heat
because of the sudden decrease to no pressure.
Unacceptable: The loses in the system is mainly the friction in the hose. While water is
moving through, turbulent flow occurs. Based on the momentum equation, there is a loss of
energy. The water is then heated up and comes out as a free jet.
--This explanation will not work because it cites the momentum equation without
specifying a control volume. It shows a lack for demonstrating the idea of loses and friction
is not the only answer. It makes no reference to the initial high pressure and what
happened to it.
(5) Acceptable: For the Titanic to float on water we simply turn to the concept of
buoyancy. Buoyancy is simply a concept that in order for an object to float, it must displace
an equal amount of fluid. In the Titanic’s case, the ship only needed to displace enough
water equal to that of the submerged part of the ship. There is a net upward force equal to
the weight of the displaced fluid.
Unacceptable: The people who made the Titanic were experienced builders. In order
for the Titanic to float the buoyant force must be equal to the specific weight of water times
the volume displaced.
--This is unacceptable because a simple equation was expressed via words and not
variables. The concept of buoyancy is not explained or mentioned.
Student 10
1. Explain the difference between Newtonian and non-Newtonian fluids. Give an
example of each.
2. A hydrometer is a device used to measure the specific gravity of liquids. A typical
hydrometer is a weighted glass tube that floats upright in a liquid and has
graduations to mark specific gravity. Explain the principles that allow the device to
work.
3. What are the general assumptions of the Bernoulli equation and how does it differ
from the general energy equation?
4. What is water hammer, why is it a problem and what is a potential solution to the
problems associated with the phenomena?
5. What is the purpose of dimensional analysis? What is the Reynolds number a
measure of?
3. The Bernoulli equation is applied along a streamline for potential flow, which
means there are no viscous forces, loses, and the fluid is incompressible. The general
energy equation is applied to a real fluid at two different sections and accounts for
average flow velocities and losses.
Unacceptable: The Bernoulli equation assumes there are no viscous forces. The
general energy equation accounts for these losses.
This answer doesn’t account for the fact the Bernoulli equation is applied to a
streamline.
Unacceptable: The Bernoulli equation is applied along a streamline and assumes
there are no viscous forces. The general energy equation is also applied along a
streamline, but losses are included.
This answer is wrong because it states the general energy equation is applied along
a streamline. If this were true, then there would be no accounting of losses in the
general energy equation.
1. A Newtonian fluid has a shear stress directly proportional to the rate of strain of the
fluid. An example of a Newtonian fluid is water. A non-Newtonian fluid does not
have the direct proportionality of shear stress to the rate of strain. A non-Newtonian
fluid would be ketchup.
Unacceptable: Both Newtonian and non-Newtonian fluids follow Newton’s Law of
Viscosity but non-Newtonian fluids don’t follow the relationship proportionally.
Water is Newtonian and ketchup is non-Newtonian
This answer is wrong because non-Newtonian fluids do not follow Newton’s Law of
Viscosity.
Unacceptable: Newton experimented on Newtonian fluids, while Newton did not
run experiments on non-Newtonian fluids. Water is Newtonian and ketchup is nonNewtonian.
This answer is unacceptable because it clearly shows the student doesn’t know what
a Newtonian fluid is and the question was not fully answered.
Student 11
Question 1
What is the difference between the Lagrangian and the Eulerian approach?
Question 2
What is the difference between the Energy equation and the Bernoulli equation?
Question 3
Explain the reason why a rock that is in a lake would sink while a boat that is 1000 times
the weight of the rock would float?
Question 4
Explain why when you put a glass tube in a body of water that the water level inside the
tube rises above the reservoir level?
Question 5
What are the benefits of a dimensionless number rather than a number with dimensions?
Question 2
What is the difference between the Energy equation and the Bernoulli equation?
Correct Answer:
The Bernoulli equation is conservation of kinetic, potential, and flow energies of a
fluid stream and their conversion to each other in regions of flow where net viscous forces
are negligible. The Energy equation is the conversion of mechanical energy to thermal
energy as a result of frictional effects as mechanical energy loss.

Incorrect Answer:
The Bernoulli equation is: (V1)2/2 + p1/y + z1 = (V2)2/2 + p2/y + z2
The Energy equation is: a1(V1)2/2 + p1/y + z1 + hp= a2(V2)2/2 + p2/y +z2 + ht + hL
Reason Why Incorrect:
The reason why this answer is incorrect is because even though these equations are
right it doesn’t explain conceptually why the Bernoulli equation and Energy equation are
different.

Incorrect Answer:
The Bernoulli equation involves only mechanical energy and the Energy equation
involves both mechanical and thermal energy.
Reason Why Incorrect:
The reason why this answer is incorrect is because this doesn’t at all explain how
mechanical energy is applied to the Bernoulli equation nor does it explain how mechanical
and thermal energy is applied to the Energy equation.
Question 3
Explain the reason why a rock that is in a lake would sink while a boat that is 1000 times
the weight of the rock would float?
Correct Answer:
The reason why the boat floats is because according to Buoyant Forces the boat
weighs exactly the same as the volume of water it would displace. The rock sinks because it
weighs more than the volume of water it displaces and exerts the remaining weight on the
bottom surface.
 Incorrect Answer:
The reason why the rock sinks and the boat floats is because the rock is larger than
the boat but weighs less. So the larger the object the more likely it would sink under water.
Reason Why Incorrect:
The reason why this answer is incorrect is because the size of an object doesn’t
affect how an object would float or sink. The buoyancy of an object depends on the weight
of the object and its ability to displace enough water to float.
 Incorrect Answer:
The rock or boat is able to sink/float because the upward force that is produced on a
body that is totally or partially submerged in a fluid when the fluid is in a gravity field
Reason Why Incorrect:
The reason why this answer is incorrect is because this tells the definition of a
buoyant force but doesn’t describe how the rock/boat, sinks/floats.