



unanswered questions or grayed questions are not specifically tested on the exams
but may still be of interest
Answers in bold have been discussed in class
The topics related to answers in italics have been discussed in class, but the
concept question itself has not and probably won’t be unless one of you brings it
up
questions in lavender are less likely to be important for the multiple-choice
portion of the exams
Links below break these questions up by exam (e.g., you need only study up to the exam
1 link for exam 1)
exam 1
exam 2
exam 3
ConcepTest Question
“fluids magnitudes 1”
Later we will learn about buoyancy, a concept
that may already be familiar to you. A
consequence: when you weigh yourself on a
scale, you underestimate your true weight by the
weight of the air you displace.
Typically, what is this error (how many pounds
does a volume of ordinary air the size of an
average person weigh)?
a)
b)
c)
d)
1.5 pounds
0.15 pounds
0.015 pounds
0.0015 pounds
ConcepTest Question
“fluids magnitudes 2”
Water is approximately how many times more
dense than air?
a) 30
b) 100
c) 300
d) 1000
e) 3000
ConcepTest Question
“fluids magnitudes 3”
Comparing any gas to its liquid version (e.g.,
steam to liquid water, nitrogen to liquid
nitrogen, etc.), the gas is 300-3000 times less
dense than the liquid.
a) true
b) false
ConcepTest Question
“fluids magnitudes 4”
A typical barometric pressure is 14.7 psia. What
would the barometric pressure have to rise to for
the windows (simple plates of glass) on a typical
building to shatter?
a) 14.8 psia
b) 15.7 psia
c) 147 psia
d) much higher than 147 psia
ConcepTest Question
“what is psia”
What is the difference between psi, psig, psia?
a) There is no difference
b) Psia is relative to a perfect vacuum,
whereas psig is relative to something else
(typically the barometric pressure) and psi
is ambiguous
c) Psia stands for “pounds per square inch of
area”
ConcepTest Question
“fluids magnitudes 5”
Imagine a building sitting in a world at 14.7
psia. What would the pressure increase in the
building, relative to the outside world, have to
be to cause the windows to shatter?
a)
b)
c)
d)
0.1 psig
1 psig
10 psig
100 psig
ConcepTest Question
“clothes dryer”
If you go outside and feel the exhaust of the
dryer in my house the flow feels “weak”. Which
of the following are likely to increase the mass
flow rate of air leaving the house through the
dryer vent:
a) Cleaning the hose connecting the
dryer to the outside world.
b) Lengthening the hose.
c) Increasing the inside diameter of the
hose.
d) Installing a new hose with a
smoother surface finish
ConcepTest Question
“definition of fluid”
A fluid is:
a) A substance in liquid phase.
b) A substance that deforms
continuously under the action of a
shear stress.
c) A substance that fills the volume of
the container in which it is placed.
ConcepTest Question
“what is a shear stress”
Shear stress:
a) has dimensions of force/unit area.
b)
has units of N.
c) acts in a direction parallel to the pressure.
ConcepTest Question
“no slip”
The no-slip condition:
a. is an effect that really happens in nature.
b. is a statement of experimental observation
that the velocity of the fluid in contact with
a surface is equal to the velocity of that
surface.
c. was determined from fundamental
principles of Newtonian mechanics.
d. depends on the roughness of the surface.
ConcepTest Question
“figure 1.1 question 1”
Given the following diagram for the definition of a
fluid:
Constant F
t0
t1
t2
This figure is a depiction of the behavior of a fluid
under the action of a constant shear force.
Given this, what is the difference in the velocity of
any fluid element between t1 and t2?
a. There is no difference
b. The velocity at t1 is greater than the velocity at t2
c. The velocity at t2 is greater than the velocity at
t1.
ConcepTest Question
“figure 1.1 question 2”
Given the following diagram for the definition of a
fluid:
Constant F
t0
t1
t2
This figure is a depiction of the behavior of a fluid
under the action of a constant shear force.
Given this, what is the difference in the velocity
gradient of the fluid between t1 and t2?
a. There is no difference
b. The velocity gradient at t1 is greater than the
velocity gradient at t2
c. The velocity gradient at t2 is greater than the
velocity gradient at t1.
ConcepTest Question
“figure 1.1 question 3”
Given the following diagram for the definition of a
fluid:
Constant F
t0
t1
t2
This figure is a depiction of the behavior of a fluid
under the action of a constant shear force.
Given this, if the viscosity of the fluid is somehow
made to be infinite and the fluid slip at the top plate
is somehow made to be infinite, which of the
following are true?
a. The magnitude of the horizontal fluid force on
the lower plate is zero
b. All of the fluid has a velocity of zero
c. The upper plate will continue to accelerate
while a force is applied, regardless of how long
the force is applied.
ConcepTest Question
“figure 1.1 question 4”
Given the following diagram for the definition of a
fluid:
Constant F
t0
t1
t2
This figure is a depiction of the behavior of a fluid
element under the action of a constant shear force.
Given this, if the viscosity of the fluid is somehow
made to be zero, which of the following are true?
a. The magnitude of the fluid force on the
lower plate is zero
b. All of the fluid has a velocity of zero
c. The upper plate will continue to accelerate
while a force is applied, regardless of how
long the force is applied.
ConcepTest Question
“what’s a basic equation?”
The basic equations governing fluid mechanics:
a) include conservation of mass and Newton’s
Law of viscosity
b) include conservation of momentum and the
Ideal Gas Equation
c) include conservation of energy and the 2nd law
of thermodynamics
ConcepTest Question
“Hooke’s law”
Hooke’s Law, F=-kx, is a description of the force
exerted by a spring as a function of the deformation
of the spring. Which of the following is true:
a. Hooke’s Law is considered a fundamental
equation, similar to the conservation of mass
equation
b. Hooke’s Law can be used in place of Newton’s
2nd Law if the problem involves a spring
c. Hooke’s Law was developed from observation
of experiments.
ConcepTest Question
“ideal gas equation”
The ideal gas equation is:
a. a fundamental equation similar to the
conservation of mass equation
b. used to describe the behavior of ideal gases
c. a model of real gas behavior.
ConcepTest Question
“Brett Favre 1”
Consider Brett Favre playing football. I am
interested in knowing how many footballs are on the
field of play at any instant in time. Then I am
interested in the:
a. Control Volume Equations applied to the
football field
b. System Equations applied to the football that has
just left Brett’s hand
c. Neither System nor Control Volume Equations
d. LaGrangian or particle view of the football
e. Eulerian view of the field
ConcepTest Question
“Brett Favre 2”
Consider the path that a football thrown by Brett
Favre follows. Suppose that I am interested in the
knowing how far the ball goes. Then I am interested
in the:
a. Control Volume Equations applied to the
football field
b. System Equations applied to the football
c. Neither System not Control Volume Equations
d. LaGrangian or particle view of the football
e. Eulerian view of the field
ConcepTest Question
“differential vs. integral”
Which of the following are true regarding the
difference between the integral and differential
approach. Again consider the football in flight:
a. The integral approach is not useful because it
does not retain sufficient detail of the flow
pattern around the football.
b. The differential approach allows us to determine
flow at any point on the football at any time
during the flight of the football.
c. The combined integral-differential approach is
always the best method.
ConcepTest Question
“skydiver 1”
Consider a skydiver in free fall. Which of the basic
laws apply to this situation?
a. The conservation of energy
b. The second law of thermodynamics
c. The principle of angular momentum
d. The conservation of momentum
e. The conservation of mass
ConcepTest Question
“skydiver 2”
Consider a skydiver in free fall. If we are
interested in estimating terminal velocity, which of
the basic laws would be useful?
a. The conservation of energy
b. The second law of thermodynamics
c. The principle of angular momentum
d. The conservation of momentum
e. The conservation of mass
ConcepTest Question
“skydiver 3”
Consider a skydiver in free fall. If we are
interested in estimating terminal velocity, which of
the following constitutive equations would be
useful?
a. Hooke’s Law, F=-k*x
b. Ideal gas law, p=RT
c. Drag Force, Fdrag = k*V2
ConcepTest Question
“implications of continuum assumption 1”
Because in classical fluid mechanics we treat all
fluids using the concept of the continuum:
a. The effect of individual molecules and atoms in
the fluid can be determined.
b. Each fluid property is assumed to have a definite
value at every point in space.
c. Values of fluid velocity depend on the molecular
concentration in that part of the fluid.
ConcepTest Question
“implications of continuum assumption 2”
For a real fluid (which could be different than the
ideal continuum we will use in this course):
a. Below a certain volume of fluid, the density can
fluctuate irregularly.
b. Above a certain volume of fluid, the density can
increase or decrease due to large-scale effects.
c. The density is defined between the two limits
associated with a. and b.
ConcepTest Q
“body forces and surface forces”
Examples of a body force and a surface force are:
a. Gravity is a body force, shear is a surface force.
b. Gravity is a surface force, pressure force is a
body force.
c. Shear is a body force, pressure is a surface force.
ConcepTest Question
“Newtonian Fluid”
For a Newtonian fluid,
a. The shear stress is proportional to the velocity
gradient in the flow direction
b. The shear stress is proportional to the absolute
viscosity of the fluid
c. The shear stress is proportional to the velocity
gradient perpendicular to the flow direction.
ConcepTest Question
“fluid element at rest”
For a fluid element at rest, the forces acting on the
fluid element include:
a. Gravity forces
b. Shear forces
c. Pressure forces
ConcepTest Question
“gradient operator”
The following is true for the gradient operator:
a. The gradient of a scalar is a vector that points
in the direction of maximum rate of increase
of the scalar
b. Ordinarily, the gradient of pressure is zero for a
fluid at rest.
c. Considering the gradient of pressure at the top
and bottom of a typical swimming pool, the
gradient will be significantly larger near the
bottom.
ConcepTest Question
“Hoover dam”
Consider the hydrostatic forces acting a planar
submerged surface, such as the surface of a dam.
The following is true about the force:
a. The direction of the force is normal to the
surface
b. The magnitude of the force is equal to the sum
total of the pressure force acting on the surface
c. The pressure on the surface of the dam is a
function of elevation
ConcepTest Question
“pressure distributions 1”
Which of the following accurately represents the
distribution of absolute pressure on the surface
indicated? Assume the pressure is atmospheric
outside the container.
(a)
(b)
(c)
(d)
ConcepTest Question
“pressure distributions 2”
Which of the following accurately represents the
distribution of absolute pressure on the surface
indicated? Assume the pressure outside the container
is atmospheric.
(a)
(b)
(c)
ConcepTest Question
“pressure distributions 3”
Considering the below representations of absolute
pressure distributions on the surface indicated, (d)
would be possible if the fluid was ferromagnetic and
we could thereby apply a second body force in a new
direction of our choice.
(a) true
(b) false
ConcepTest Question “manometers”
Two manometers are shown below. One
manometer with a single “U-tube” is connected
between tanks “A” and “B”. The other manometer
has two U-tubes and is connected between tanks
“C” and “D”. The four tanks contain air. The
liquid in both manometers is water. Circle the
letter of the correct statement.
A
B
A
B
C
D
E
C
(PA – PB) = (PC – PD)/2
(PA – PB) = 4(PC – PD)
(PA – PB) = 2(PC – PD)
(PA – PB) = (PC – PD)/4
(PA – PB) = (PC – PD)
D
ConcepTest Question
“integrating pressure”
The pressure force on a submerged surface is
defined by the following
equation:


F    pdA
R
A
When we evaluate the magnitude of the resultant
force:
a. We neglect the minus sign because we know
the direction of the force
b. We include the minus sign to ensure that the
sign of the force is correct
c. We can do either, as long as we know why we
are doing it.
ConcepTest Question
“coordinate transformation 1”
Consider the two coordinate axes shown in the figure
below:
x
x’
a
To transfer from one coordinate system to the other,
the following should be used:
a. x’=x+a
b. x’=-x+a
c. x’=-x-a
ConcepTest Question
“coordinate transformation 2”
h
H
z
d
Consider the diagram above. The absolute
pressure at any point in the fluid is given by:
a. P = gh
b. P  gh  Patm
c. P  gz  g(H  d)  Patm
d. P  gz  g(d)  Patm
ConcepTest Question
“uniform vs constant”
Imagine we are viewing the pipe from an Eulerian
perspective. For the gas inside the pipe, involved
in this steady flow situation, which is/are true?
Gas In
Gas Out
flame
a. The density of the gas is uniform
b. The density is not a function of time
c. The density is a function of position even though
this is a steady flow
ConcepTest Question
“The jellybean jar”
Consider jellybeans being added and removed from a
jellybean jar. Only Sam and Sally act on the jar. If
the jellybeans are being taken from the jar by Sam at
7 jellybeans per minute and added to the jar by Sally
at 5 jellybeans per minute, the rate at which the
number of jellybeans in the jar is changing is:
a. –2 jellybeans
b. 2 jellybeans
c. 2 jellybeans/minute
d. –2 jellybeans/minute
e. Cannot determine from the information given.
ConcepTest Question
“System form of basic equations”
The following is true of the system form of the
basic equations (mass, momentum, angular
momentum, energy, and entropy):
a. The equations apply to a fixed quantity of mass
b. The equations are formulated in extensive
properties
c. There is a general method to convert the system
form to control volume equations
d. All the basic equations are vector equations.
ConcepTest Question
“identifying extensive properties”
Which of the following are extensive properties?
a. temperature
b. internal energy
c. entropy
d. specific internal energy
e. pressure
f. density
g. mass
ConcepTest Question
“what’s an extensive property?”
Extensive properties:
a. Change if the amount of substance we are
considering changes
b. Can be used to determine corresponding
intensive properties, i.e., the extensive properties
per unit mass
c. Include pressure and temperature
d. Can flow in and out of a control volume.
Concept Test Question
“what’s flux”
When a substance is flowing, we often refer to the
flux associated with that flow (e.g., mass flux or
momentum flux). In this context, when we
describe flux, we are referring to:
a. The transfer rate of an intensive property per unit
time
b. The transfer rate of an extensive property
c. The transfer of an extensive property per unit
area
d. “Flux capacitors”, as seen in the movie Back to
the Future
ConcepTest Question
“reading the conservation of mass equation”
Consider the conservation of mass equation:
 

0
 dV   V dA
t CV
CS
In words, this equation reads (select only the
single-best answer below):
a. The mass flow into the control volume is equal
to the mass flow out of the control volume
b. The rate of change of the amount of mass in the
control volume is balanced by the net rate at
which mass flows out through the control
surface
c. The accumulation of mass in the control volume
is balanced by the net rate at which mass flows
into the control volume
d. The fixed amount of mass in the control volume
is balanced by the mass that leaves or enters the
control volume.
ConcepTest Question
“considering the conservation of mass equation”
 

0
 dV   V dA
t CV
CS
The following is/are true for the conservation of
mass equation:
a. It is a scalar equation
b. There are vectors in the equation
c. The first term on the right side is zero for steady
flow problems if the control volume is fixed
d. The first term is zero for a single, continuous,
incompressible fluid if the control volume is
fixed
- exam 1 -
ConcepTest Question
“comparing the mass and momentum basic
equations”
When considering the basic equations, the
following is/are true:
a. For conservation of mass and momentum, the
rate of change of mass and momentum in the
control volume is balanced by the rate at which
mass and momentum are flowing out of the
control surface.
b. For conservation of mass, a. is true, but for
conservation of momentum, the change in the
system momentum can be nonzero.
c. The system and control volume forms of the
conservation of mass equation are the same,
however, for the conservation of momentum
equation, they are different.
ConcepTest Question
“nozzle 1”
Consider the nozzle on a firehose. The nozzle is
connected to the hose via a coupling. When the
firehose is in use, the coupling is:
a. In equilibrium, so there is no force on the
coupling.
b. In tension.
c. In compression.
ConcepTest Question
“nozzle 2”
Consider the flow exiting from a firehose
nozzle when the nozzle is in use. The pressure
of the water at the nozzle exit is:
a. Above atmospheric pressure
b. Below atmospheric pressure
c. Equal to atmospheric pressure
d. It is not possible to determine the pressure
in the water.
ConcepTest Question
“nozzle 3”
Consider the flow from a firehose nozzle when
the nozzle is in use. A1 and A2 represent the
circular areas formed by the nozzle geometry.
p1 and p2 represent the absolute pressures of
the water at the surfaces indicated. One
control volume that could be used to determine
the net pressure force is the following:
In this case, the net pressure force in the xdirection is given by:
a. p1*A1-p2*A2
b. p1*A1-p2*A1
c. p1*A2-p2*A2
d. Need to know the area of the control volume
parallel to A1 and A2.
Concept Test Question
“the unsteady term in the momentum equation 1”
Consider the tank that is filling in the figure below.
The input flow is steady. The tank is not moving.
The rate of change of the x-component of momentum
in the tank is:
y
x

udV
a. t 
CV
 
u

V
 dA
b. 
CS
c. 0
d. Everywhere in the tank the x-component of
momentum is zero, therefore, the rate of change of
the x-component of momentum is zero.
Concept Test Question
“the unsteady term in the momentum equation 2”
Consider the tank that is filling in the figure below.
The tank is not moving. Input flow is steady. The
rate of change of the y-component of momentum in
the tank is:
y
x

a. t  vdV
CV
 
b.  vV  dA
CS
c. 0
d. zero, because the y-momentum of the fluid in the
tank is everywhere zero.
Concept Test Question
“washing the deck 1”
Consider Scott washing the deck. The hose was not
moving at the instant the picture was taken.
y
x
a. the velocity of the water stream could be estimated
from this photo
b. Scott is applying a force on the hose in the xdirection
c. If Scott unscrewed the nozzle and did this again,
the force could be less even if m water was greater.
d. If Scott didn’t apply a force on the hose in the xdirection, the hose would move to the right
e. To determine the force exerted on the hose, we
could use the control volume indicated
Concept Test Question
“washing the deck 2”
Consider the two control volumes indicated for Scott
washing the deck.
y
x
a. the force that Scott is applying to the hose could
depend upon which control volume is used.
b. the force that Scott is applying to the hose could
be different depending on how big the yellow CV is
and how much of the water stream is in it.
c. none of the above
Concept Test Question
“washing the deck 3”
Consider the two control volumes indicated for Scott
washing the deck. Assume the water has just been
turned on to m water = 0.64 lbm/s (steady), so that the
stream of water does not yet fill the yellow CV:
y
x
a. the red CV will not accumulate mass, but the
yellow CV will.
b. the red CV will not accumulate x-momentum, but
the yellow CV will.
c. there is a flux of mass and x-momentum out of the
red CV, but not out of the yellow CV.
ConcepTest Question
“Vxyz”
A bus is moving to the right at U mph. You throw a
water balloon at the bus at V mph after the bus passes
you. A person on the bus sees the balloon hit the bus
at:
V
U
y
z
a. U-V mph
b. V-U mph
c. V+U mph
d. V mph
x
ConcepTest Question
“inertial vs non-inertial”
The difference between an inertial coordinate
system and a non-inertial coordinate system is:
a. An inertial coordinate system is not moving
while a non-inertial coordinate system is.
b. An inertial coordinate system is not accelerating
while a non-inertial coordinate system is.
c. An inertial coordinate system is not rotating
while a non-inertial coordinate system is.
ConcepTest Question
“what do we mean by ‘drag’ ”
Consider a skydiver in free fall. Which of the
following is/are appropriate free body diagrams?
F due to pressure F due to Drag
F due to Drag
and Pressure
a.
c.
b.
Weight
Weight
Weight
ConcepTest Question
“rocket problems”
Consider a rocket in flight:
a. The rocket’s velocity can never be faster than its
exhaust velocity.
b. The rocket’s velocity equals its exhaust velocity
at the maximum speed of the rocket.
c. Relative to a ground reference frame, the
rocket’s exhaust can be moving in the same
direction as the rocket.
d. The rocket’s velocity can exceed its exhaust
velocity
ConcepTest Question
“Angular Momentum I”
Consider conservation of angular momentum. The
angular momentum of a system can be changed by:
a. A system is a quantity of fixed mass and
therefore, fixed angular momentum.
b. The angular momentum of a system can be
changed via a shaft that has a torque acting on it.
c. The angular momentum of a system can be
changed via the action of a force acting at a
distance.
d. A body force like gravity could result in a net
change in angular momentum of a system.
ConcepTest Question
“Angular Momentum II”
OK then, if I now consider a control volume, and not
a closed system, then I can change the angular
momentum in the control volume by:
a. With the flow of mass through the control
surface
b. Also all of that stuff that we agreed upon with
the last question.
ConcepTest Question
“Energy”
Consider conservation of energy for a control
volume:
2
 

V




Q  WShaft  WShear  WOther 
 gz )V  dA
 edV   (u  pv 
t CV
2
CS
a. In this form defines heat transfer to the control
volume as positive in sign
b. Includes pressure in an important work term
c. Is a scalar equation.
ConcepTest Question
“Entropy”
Consider the expression for the second law of
thermodynamics, where the inequality (Eq. 1) has
been replaced by a source term (Eq. 2) representing
the production of entropy due to irreversibilities:

 

1 Q
 sdV   sV  dA    dA (1)
t CV
CS
CS T  A 

 

1 Q
 sdV   sV  dA    dA  S (2)
t CV
CS
CS T  A 
a. The entropy equation (2) is a vector equation
b. The entropy equation indicates that the entropy
of a system can be changed via heat transfer or
entropy production due to irreversibilities
-- exam 2 --
ConcepTest Question
“Continuity I”
The “continuity equation”:
u v w 



0
x
y
z
t
a. is just the differential form of the conservation of
mass equation
b. is called “continuity” because it’s continued
from Chapter 4
c. is called “continuity” because it guarantees that
the fluid is continuous (i.e., doesn’t have gaps
which would be unphysical)
d. can also be written
scalar equation.
 
  V 
 0 but
t
is still a
ConcepTest Question
“Continuity II”
The “continuity equation” is given as Eq. 5.1a in your
text:
u v w 



0
x
y
z
t
The authors obtained this equation…
a. by taking the derivative of the conservation of
mass equation
b. by applying the integral conservation of mass
equation to a differential element
c. using Taylor series expansions to calculate fluid
properties at the faces of a differential element
ConcepTest Question
“Problem 4.10 Extension I”
The
velocity field is given by

V  azˆj  bkˆ, a  10s 1 ,  b  5m / s
What is the combined mass flow rate through the
blue and green faces?
a. Cannot be determined
b. m green  0 and m blue  0 so m combined  0
 
 
c.  V  dA   V  dA
A blue
Agreen
ConcepTest Question
“Problem 4.10 Extension II”
What is the relationship between the mass flow rate
through the green and blue faces?
a. m green  0 and m blue  0 so m combined  0
 
 
c.  V  dA   V  dA =0
A blue
Agreen
d. cannot determine
ConcepTest Question
“Using the 2-D, incompressible continuity equation”
Consider an incompressible fluid with a velocity
field described by the following:

by ˆ
V  axtiˆ 
j
t
For this to be a flow that satisfies conservation of
mass, the following must be true:
a. a = -b
b. a = bt
c. a=-b/t2
d. Because this is not a steady state flow, cannot be
satisfied for all t.
ConcepTest Question
“acceleration in fluids”
Consider the following steady flow where an
incompressible substance is flowing from 1 to 2.
1
2
a. The acceleration of the fluid as it passes through
the nozzle is zero because the flow is steady.
b. The fluid accelerates even though the flow is
steady. The change in velocity can be
determined from conservation of mass:
V1 / V 2  A2 / A1
c. If this is a river and I am riding in a boat in the
dV
river, I will experience dt  0 even though for

dV
this flow, dt  0
ConcepTest Question
“Bernoulli’s equation”
Consider constant altitude, steady flow along a
streamline with a flow that satisfies the
assumptions necessary for Bernoulli’s equation.
Which of the following have a constant value along
the streamline?
a. Static or local pressure
b. Dynamic or velocity pressure
c. Stagnation or total pressure
d. Internal energy
ConcepTest Question
“pitot-static probe”
Imagine you are using a pitot-static probe to measure
the speed of your bicycle at sea level. What is the
value of the static pressure that you would measure?
a. A pressure below atmospheric
b. A pressure above atmospheric
c. A pressure equal to atmospheric
d. A pressure equal to the total pressure.
ConcepTest Question
“reference frames in Bernoulli problems”
.
.
A
A
V
motion
V
vs.
“wind”
“motion”
fill out this table of pressures:
Static
Dynamic
Total
Wind A
p
½ V2
po = p + ½ V2
Wind B
po
0
po
Wind C
p
½ V2
po = p + ½ V2
Motion A
p
0
p
Motion B
po
½ V2
po + ½ V2
Motion C
p
0
p
ConcepTest Question
“Reynolds number 1”
VD
, is considered to be

the most important dimensionless group in fluid
mechanics. This is because:
The Reynolds number,
a. Reynolds number is used to determine the ratio
of flow speed to viscosity
b. Reynolds number is useful in determining the
ratio of the fluid properties of density and
viscosity times the area flow.
c. Reynolds number is useful in indicating flow
regimes, in particular when the flow is laminar
or turbulent.
ConcepTest Question
“Reynolds number 2”
The Reynolds number is considered to be the ratio
of inertial forces to viscous forces. Because of
this:
a. At low Re, i.e. laminar flow, viscous effects
dominate the flow behavior
b. At high Re, i.e. turbulent flow, inertial effects
dominate the flow behavior
c. At specific Re regions, the flow transitions from
laminar to turbulent flow.
ConcepTest Question
“Model Testing 1”
Suppose I want to ensure similarity in model
testing (see section 7-6). Then I need to ensure:
a. Geometric similarity (e.g., model cannot be
scaled down differently in one dimension than in
another)
b. Kinematic similarity (e.g., can’t have shock
waves in real flow but not in model)
c. Dynamic similarity (e.g., can’t have different
Reynolds numbers)
ConcepTest Question
“Model Testing 2”
We know that the total drag force on a submarine
depends on the pressure distribution around the
submarine as well as the effects of viscosity or
friction. What effect might this have on model
testing?
a. Little effect, since drag force will scale with size.
b. Some effect, because the drag force is also
dependent on flow speed.
c. Not certain, however, we will need to calculate a
variety of dimensionless parameters to determine
how we will meet similarity requirements.
ConcepTest Question
“Dimensionless 1”
Given the following set of parameters, L (length) and
d (diameter), one dimensionless group that can be
formed from these parameters is:
a) d2/L
b) d*L2
c) L/d
ConcepTest Question
“Dimensionless 2”
Given the following set of parameters, V
(length/time) and c – the speed of sound
(length/time), the dimensionless group that results
from combining these two parameters is:
a) the Weber number
b) the Mach number
c) the Froude number
d) the Euler number.
ConcepTest Question
“Dimensionless 2”
Given the following set of parameters, Fdrag (Masslength/time2),  (mass/length3), V (length/time) and A
– frontal area (length2), a dimensionless group that
can be formed is called the drag coefficient, Cd. Cd
is equal to:
a
Cd 
b
Cd 
c
Cd 
Fdrag
1
V 2 A
2
Fdrag
V 2 A
Fdrag A
V 2
ConcepTest Question
“The PI theorem”
Use of the Buckingham Pi theorem provides:
a. the number of relevant dimensionless groups
b. dimensionless groups
c. the physical meaning of the dimensionless
groups
d. the function f in 1 = f (2,3, ..)
--exam 3--
ConcepTest Question
“pipe flow 1”
For steady, incompressible flow in the entrance
flow region in a horizontal pipe of constant
diameter, the following is/are true:
a. The average velocity in the pipe is a function of
distance from the entrance
b. The maximum velocity in the pipe increases
with distance from the entrance
c. The pressure drop per unit length along the pipe
decreases with distance from the entrance
ConcepTest Question
“pipe flow 2”
Velocity profiles for fully-developed flow
(Figure 8.10):
When comparing turbulent water
flow in a pipe to laminar flow:
a. The entrance lengths are always shorter for
turbulent flow
b. The wall shear stress tends to be higher for
turbulent flow
c. The pressure drop across 1 m of pipe will tend to
be higher for turbulent flow
d. The maximum shear stress occurs at the wall for
both flows.
ConcepTest Question
“Moody Chart 1”
The Moody chart clearly shows that high-Re pipe
flows generally have lower friction factors “f” than
lower-Re pipe flows. Therefore,
a. The pressure drop per unit length in higher-Re
pipe flows will generally be lower than in lowerRe pipe flows
b. (a) is wrong, and the reason has to do with pipe
roughness effects
c. (a) is wrong, and the reason is because “f” has V2
in the denominator
ConcepTest Question
“drinking straw”
Imagine you are very thirsty and attempt to finish a
12 oz soda in 20 seconds, drinking through a
standard straw (L = 8”, d = ¼”, L/d = 32). For
these conditions the Reynolds number turns out to
be 2299.
a. The flow is laminar, but if you drink much
faster, it could become turbulent.
b. This flow could be fully developed at the straw
exit.
c. If you had a choice between (1) a straw half as
long and (2) a straw twice the diameter, (1)
would allow you to finish the soda faster.
d. Imagine that the carbonation gets to you and the
p across the straw drops. There will be some
smaller but nonzero p for which you will get
no soda.
ConcepTest Question
“understanding piping pressure drops”
The figure below shows pressure drops for water
flow in a ¼” diameter pipe, 10’ long, for water
temperatures of 33 F and 100 F:
1
P
[psia]
10
0.1
a
b
0.01
0.1
1
10
V [ft/s]
a. These pressure drops are way off, it would take
way more than 10 psi to push water through a
10’long section of ¼” pipe at 10 ft/s.
b. Curve a is for 33 F and curve b is for 100 F.
c. The differences between curves a and b are due
almost entirely to viscosity.
d. The more viscous fluid generally results in
greater pressure drop (or greater resistance to
flow), particularly at slow flow speeds.
e. At flow velocities just under 2 ft/s, the more
viscous fluid offers less resistance to flow.
f. (e) is crazy. there must be a small mistake
somewhere in the calculations.
ConcepTest Question
“roughness effect of piping pressure drops”
The figure below shows pressure drops for 33 F
water flow in a ¼” diameter pipe, 10’ long, for
V = 1 ft/s and V = 10 ft/s
35
a
P
[psia]
10
1
b
0.1
1.000x 10-7 0.000001 0.00001
0.0001
0.001
0.01
0.1
RR
a. Curve a is for 1 ft/s and curve b is for 10 ft/s.
b. The “hook” in curve a is too severe, there is no
way you should get 3.5 times the pressure drop
with a roughness of 0.025” in this pipe.
c. Obtaining this pipe with RR < 0.00001 (absolute
roughness of 60 nm) will cost > $10,000
d. For RR = 0.001 (absolute roughness of 0.00025”
or 6 μm), there is not much penalty for
roughness, and this size roughness is affordable
in some types of pipe
e. Curve b lacks a “hook” but if the plot were
extended to the right there would be a hook.
f. The dominant reason curve a is higher than b is
the turbulent velocity profile.
ConcepTest Question
“viscosity effect of piping pressure drops”
The figure below shows pressure drops for 33 F
water flow in a horizontal ¼” diameter pipe, 10’
long, for V = 10 ft/s. A “fudge factor” is included
to mess with the viscosity
10000
100
P
[psia]
1000
10
1
0.0001
0.001
0.01
0.1
1
10
100
1000
10000
actual viscosity is multiplied by this number
a. Lower viscosities generally give lower pressure drops.
b. Lower viscosities always give lower pressure drops.
c. The turbulent range is on the left side of the plot, and the
laminar range is on the right side of the plot.
d. Near transition between laminar and turbulent, lowering
the viscosity can increase the pressure drop.
e. According to the figure, I can get negligible p’s by
reducing the viscosity if I could stay in the laminar
domain.
f. in the turbulent region it looks like VERY small viscosity
(< 10-20×actual) will be required to get a p below 0.001
psi.
g. (f) makes perfect sense, since there should still be some
pressure drop even for inviscid flow in the pipe.
ConcepTest Question
“pipe flow 3”
For fully-developed horizontal turbulent pipe flow:
a. The pressure experienced by a fluid particle
decreases as the particle travels through the
pipe.
b. On average, fluid particles near the pipe
centerline travel fastest.
c. Friction factor, and therefore pressure drop per
unit length, increases as the pipe wall roughness
increases.
ConcepTest Question
“pipe flow 4”
Consider flow in a piping system:
a. The upstream pressure must be higher than the
downstream pressure
b. The average velocity, V , decreases because of
the pressure drop
c. Changes in potential energy of the flow are
balanced by changes in the kinetic energy of the
flow
d. None of the above
ConcepTest Question
“BE vs pipe equation”
The difference(s) between Bernoulli’s equation:
p1


V1
2
2
 gz1 
p2


V2
2
2
 gz 2
and the pipe system equation:
2
2
 p1
  p2

V1
V2
  1




gz




gz
1
2
2   hl T


2
2

  

is/are:
a. If the flow is assumed frictionless and the
velocity is uniform for a given cross section,
there is no difference
b. The pipe system equation is the energy equation
and it is not related to Bernoulli’s equation
c. The pipe system equation considers the entire
pipe flow whereas Bernoulli’s equation
considers only one streamline.
ConcepTest Question
“boundary layer 1”
Consider the external viscous flow over this airfoil:
a) The boundary layer is drawn approximately
to scale
b) This picture is for a stationary airfoil in a
wind tunnel. If this is supposed to represent
your view from the aircraft cabin, the
streamlines would be different.
c) The fluid velocity becomes very slow
(<< U∞) at the stagnation point
d) Bernoulli’s equation can be applied in the
viscous wake region
ConcepTest Question
“drag 1”
Consider a flat plate oriented normal to the flow as
shown.
U
The dominant source of drag on the plate is:
a) Pressure drag, from the pressure distribution
around the plate
b) Friction drag, from the viscous shear of the
fluid
c) Pressure drag and friction drag are of
approximately equal importance in this
situation
ConcepTest Question
“drag 2”
Consider a flat plate oriented parallel to the flow as
shown.
U
The dominant source of drag on the plate is:
a) Pressure drag, from the pressure distribution
around the plate
b) Friction drag, from the viscous shear of the
fluid
c) There is no drag because the plate is parallel
to the flow
d) If the plate were made 1nm thick, there
would be no drag
ConcepTest Question
“streamlining”
The purpose of streamlining is:
a. To reduce the skin friction drag at the cost of
increasing the pressure drag
b. To reduce the pressure drag at the cost of
increasing the skin friction drag
c. To reduce both the skin friction drag and the
pressure drag
d. To increase the lift produced by the object.
“pressure gradients in boundary layers”
As you know, pressure gradients are important
in understanding fluid flow. The following
definitions apply to the direction of the
pressure gradient relative to the flow:
a) A favorable pressure gradient is one where
the pressure is increasing in the direction of
the flow
b) An adverse pressure gradient is one where
the pressure is increasing in the direction of
the flow
c) b) is a trick question. It is not possible for
the pressure to increase in the direction of
the flow
d) A zero-pressure gradient is one where the
pressure is not changing in the direction of
the flow.
e) d) is a trick question. It is not possible for
flow to occur if there is no pressure
gradient.
ConcepTest Question “sphere”
Consider the above figure (Fig. 9.12). The local
pressure p has been measured by inserting a small
pressure transducer in a hole drilled partway into a
sphere, placing the sphere in a wind tunnel, and
measuring the pressure as a function of angular
position of the hole.
The results are then plotted as a dimensionless
parameter Cp. The other terms in Cp are p  (the
static pressure in the freestream, which would
ordinarily be atmospheric pressure) and the
1
freestream dynamic pressure ( V 2 ).
2
From this figure we can deduce:
a) The velocity of the flow is near zero (<< V) at
the front of the sphere (  = 0).
b) The flow reaches a maximum velocity near the
side of the sphere (  in the 70O – 90O range)
c) The velocity of the flow for the theoretical
(inviscid) case decelerates back to near zero on
the back side of the sphere
d) The drag is higher for the laminar case than for
the turbulent case.
e) Differences in drag between the laminar and
turbulent cases can be attributed primarily to the
back of the sphere (  > 120O).
ConcepTest Question “sphere 2”
Consider the turbulent case on Fig. 9.12. At  ~ 90O
the pressure is lower than at higher  values. How
can there be flow against an increasing pressure?
a) Gravity must play a role, like when pressure can
increase in the direction of flow in vertical pipes
b) The flow’s momentum must play a role, like
water can momentarily flow against gravity if I
spill it up a hill.
{perhaps sketch velocities around the sphere to help}
ConcepTest Question “sphere 3”
Comparing the laminar and turbulent cases, which of
the following contribute to the turbulent flow’s
enhanced ability to flow against the adverse pressure
gradient on the back side (  > 90O) of the sphere?
a) The turbulent case has higher momentum
starting at  = 30O
b) The ‘mixing motion’ within the turbulent
boundary layer helps keep the momentum in the
boundary layer high.
ConcepTest Question
“golf ball 1”
Tiger Woods hits 600 golf balls on a driving range.
300 of the golf balls are dimpled while 300 have no
dimples. Analysis of the distance of flight shows that
the golf balls with the dimples traveled an average of
30 yards farther than the undimpled golf balls. This
is because:
a. Tiger hit the dimpled balls harder.
b. The boundary layer on the dimpled balls
transitioned to turbulence nearer the front of the
ball
c. The boundary layer on the undimpled balls
transitioned to turbulence nearer the front of the
ball
d. Neither ball transitioned to turbulence. The
laminar boundary layer resulted in less drag for
the dimpled ball.
ConcepTest Question
“golf ball 2”
Early transition to turbulence from the dimples on
a golf ball result in drag reduction because:
a.
b.
c.
d.
Skin friction drag is reduced
Pressure drag is reduced
The size of the wake zone is reduced
The region on the ball with an attached
turbulent boundary layer is increased.