Answers in Bold Have Been Discussed in Class

 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) 1.5 pounds b) 0.15 pounds c) 0.015 pounds d) 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) 0.1 psig b) 1 psig c) 10 psig d) 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”

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”

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. 2 Drag Force, Fdrag = k*V 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 C D

A (PA – PB) = (PC – PD)/2 B (PA – PB) = 4(PC – PD) C (PA – PB) = 2(PC – PD) D (PA – PB) = (PC – PD)/4 E (PA – PB) = (PC – PD) ConcepTest Question “integrating pressure”

The pressure force on a submerged surface is defined by the following equation:

FR    pdA 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:

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”

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

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 x- direction 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:

 a. udV t  CV  b. uV dA 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:

 vdV a. t  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.

a. the velocity of the water stream could be estimated from this photo b. Scott is applying a force on the hose in the x- direction 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 x- direction, 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.

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:

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:

y x z a. U-V mph b. V-U mph c. V+U mph d. V mph 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. b. c. 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  edV   (u  pv   gz)V  dA t CV CS 2 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   V   0 but is still a t scalar equation. 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”

x 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  0so m˙ combined  0     c. V dA  V dA Ablue Agreen ConcepTest Question “Problem 4.10 Extension II”

What is the relationship between the mass flow rate through the green and blue faces? z

a. m˙ green  0 and m˙ blue  0so m˙ combined  0     c. V dA  V dA=0 Ablue 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 V  axtiˆ  ˆj 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.

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  0 even though for dt  dV this flow,  0 dt 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 2 2 Wind A p ½ V po = p + ½ V

Wind B po 0 po 2 2 Wind C p ½ V po = p + ½ V Motion A p 0 p 2 2 Motion B po ½ V po + ½ V Motion C p 0 p ConcepTest Question “Reynolds number 1”

VD The Reynolds number, , is considered to be  the most important dimensionless group in fluid mechanics. This is because: 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 (Mass- length/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:

F C  drag a d 1 V 2A 2 F b C  drag d V 2A F A c C  drag d 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 lower- Re 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: 10

1 ] a i s p [

P  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 10 ] a i s p [

P 1 

0.1 1.000x10-7 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

1000 ] a i s 100 p [

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: p V 2 p V 2 1  1  gz  2  2  gz  2 1  2 2 and the pipe system equation:  p V 2   p V 2   1   1  gz    2   2  gz   h  1 1   2 2  lT   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.

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. Skin friction drag is reduced b. Pressure drag is reduced c. The size of the wake zone is reduced d. The region on the ball with an attached turbulent boundary layer is increased.