Prerequisites (top)
Physics I and Math for Engineering Analysis II or equivalent

Text (top)
Franzini et al. (1997) Fluid Mechanics, WCB McGraw-Hill, NY, NY.

Goals (top)
The course deals with general fluid flow and with fluid flow in pipe systems. Topics covered in the area of general fluid flow include hydrostatics, laws of fluid motion, kinematics, dynamics, energy balance, and dimensionless groups. Topics covered in the area of pipe flow include incompressible flow, compressibility, pumps, viscosity, boundary layers, turbulence, and losses. The course includes appropriate laboratory experiments and computer applications.

Learning Activities (top)
Reading the text (before material is covered in class);  listening and responding to lecture (on materials not in the text, or that are difficult to understand);  watching demonstrations;  discussing important concepts;  reviewing examples from the textbook;  solving assigned problems in class and/or at home (singly and in groups);  and conducting experiments.

Evaluation (top)
Multiple choice quizzes cover your knowledge of the textbook.  These occur before material is covered in class.  The solutions to assigned problems are used to evaluate your ability to define and solve fluid mechanics problems.  Laboratory reports are graded to assess your ability to conduct experiments, perform the necessary calculations and write a report.  The exams test your comprehension of the course topics. They are closed notes and books.  You will be given any formulas, conversions, or fundamental facts.

Grading (top)
Grades in the course will be based on the ten point scale  (90-100 = A, 80-89 = B, etc.).  Depending upon class performance, the scale may be adjusted down, e.g., an 89 might be an A.  Points will be awarded according to the following percentages:
    Quizzes, Problems, Participation, Laboratory         30 %
    Semester Exam  (Test 1)                                         35 %
    Comprehensive Final Exam  (Test 2)                      35 %
It is possible to change the distribution, with agreement of all involved.

Turning in work (top)
To get full credit, you must have the correct answer and show appropriate work.  See the Homework Format and Grading document for the format to be used in preparing your homework and for help in interpreting grading.  Assignments are due by the beginning of the designated lecture period, unless otherwise indicated.  Late assignments can be turned in until solutions are posted, but will receive at least a 50 % grade reduction.  Some problems may require the use of spreadsheets or math solvers.  If you have ANY questions about a graded assignment, you must talk to me about it within a week of my return of the assignment to the class.  Please work together on assignments, but do not copy!

Laboratory (top)
Laboratory time is spent watching demonstrations and conducting formal and informal experiments.  Because much of the laboratory equipment is still on-order, this portion of the course will depend on equipment availability.  Additional lecture and class work will be substituted for laboratory, if necessary.

Schedule (top)
A tentative quiz and test schedule available.  Read the chapter before the quiz!

Disabilities (top)
Any student in this course who has a disability that may prevent him or her from fully demonstrating his or her abilities should contact me personally as soon as possible so that we can discuss accommodations necessary to ensure full participation and facilitate your educational opportunity.

Academic Misconduct (top)
You are encouraged to work together on assignments.  However, copying is not acceptable.  Copied assignments will receive a zero grade. Cheating on a test will cause the student to receive a zero grade, at a minimum.  If you are to miss an assignment due date, exam, quiz,  field trip, or laboratory session you must have a valid excuse and notify me prior to the event.

ASCE (top)
You are encouraged to join the American Society of Civil Engineers or other appropriate organization.  If you join (show me your membership card) and attend two on campus ASCE meetings, I will allow you to drop your lowest non-zero quiz grade.

Tentative Quiz and Test Schedule, Fall 1998 (top)

Quiz / Test Quiz on Chapter 1:  Introduction Quiz on Chapter 2:  Fluid Properties Quiz on Chapter 3:  Statics Quiz on Chapter 4:  Basic Fluid Flow Quiz on Chapter 5:  Energy Quiz on Chapter 6:  Momentum and Forces Test on Chapters 1 to 5  Quiz on Chapter 7:  Similitude and Dimensional Analysis Quiz on Chapter 8:  Pressure Conduits, sections 1 - 16 Quiz on Chapter 8:  Pressure Conduits, sections 17 - 28 Test on Chapters 6, 7, 8

Date September 9 September 9 September 14 September 21 September 23 September 28 September 30 October 7 October 12 October 14 October 21

Last updated:  September 24, 1998

Home work assignments for Dr. E's Fluid Mechanics, Fall 98 (top)

• Assignment 1:
• 2.8, 2.13, 2.18.
• Due Monday, September 14.
• Assignment 2:
• 3.6 Change in diameter is at bottom of u-tube.
• 3.12 The centroid of a triangle is?.
• 3.18 Integrate to get vertical force and moment.
• 3.23 Use moments about the buoyancy force to solve for W;  you don't know the specific weight of the fluid!
• Due Monday, September 21.
• Assignment 3:
• 4.1 Graph velocity versus radii, then estimate total flow as nV_iA_i, using your best judgment;  the mean velocity is total flow divided by the total area of the pipe.
• 4.3 Use the ideal gas law to estimate the specific weight;  note that the 50 psi is a gage pressure.
• 4.12 Make a graph that has x from 0 to 3 and y from 0 to 4;  plot the x and y velocities at each node as arrows with length proportional to magnitude;  draw the resultant velocity at each point based on the x and y values; determine the eaquations for the x and y accelerations using equations 4.23 a and b; DON'T calculate the normal and tangential accelerations; DO draw some streamlines.
• Due Wednesday, September 23.
• Assignment 4:
• 5.3 Use the relationship DI = (c/g)DT, where c = specific heat of water = 1.0 Btu/lbmR = 25,000 ft²/s²R, and lbm = pound-mass = mass of one pound under Earth gravity.
• 5.6 Use Bernoulli's, make sure you state why you can assume h_L and Dz are zero.
• 5.10 Use equation 5.27, get density and the speed of sound at 2000 m from Table A.3.
• 5.11 Because it is a closed circuit, all of the power input to the pump ends up as heat energy in the water:  <a> calculate the power imparted to the water by the pump, divide by the pump efficiency, then multiply by one hour to convert from power to energy;  <b> since this energy all ends up as heat, use DI = (c/g)(DT)--in the form Di = c(DT), where i is energy per mass--to calculate the temperature after one hour, c = 25,000 ftlb/slugR, you'll need to convert gallons of water to slugs, watch your units!
• 5.11.2 Use Table A.1 to get the specific weight and vapor pressure of water, solve using the method we used to solve 5.11.1 in class.
• Due Monday, September 28.
• Assignment 5:
• Read the  Homework Format and Grading document and send me an email indicating that you have done so.
• Due Monday, October 5.
• Assignment 6:  NOTE:  for moving blades/pumps/turbines, draw velocity triangles when determining velocities.  It helps!
• 6.4  Hydraulic jumps occur under certain conditions [we'll learn more in water resources, next semester].  Part <a>, solve this just like problems 6.4.2 and 6.4.4.  Use the continuity and impulse-momentum equations.  You can determine F1 as gamma x centroid of the area x area, while F2 is gamma x centroid of area x area plus pressure x area.  Note, in calculating F2 you use both static pressure and the pressure measured by the pressure gauge at the top of the pipe.  The force exerted by "something" on the water, F?/w, is zero because there is nothing there to exert a force on the water!  Now use continuity to write Q, V1 and V2 all in terms of V1 and solve for V1.  Use V1 to get Q.  Part <b>, use Bernoulli's equation, remembering that elevation for open channel flow [e.g., upstream of the hydraulic jump] is the free water surface.  After the hydraulic jump you should use the top of the channel for the elevation [why? because that is where we have a pressure measurement].
• 6.9  First, use the continuity equation to determine the velocity in the 8 inch pipe.  Second, use Bernoulli's to determine pressure in the 8 inch pipe [note that the head loss from the 8 inch pipe to either exit point must be the same, for any type of flow.  Because the flow is frictionless for this problem, it is zero].  Apply Bernoulli's from the 8 inch pipe to either exit--but not BOTH.  Finally, determine the forces using the impulse-momentum equation [as we did for 6.5.1 and 6.5.4, also see sample problem 6.2 to see what to do with split flows].
• 6.33 Do the problem in metric units.  Part (a) - determine the Force exerted in the u direction.  First determine the flows entering and leaving the blades.  Second, determine the velocity of the water relative to the blades (v) at the point where they first "meet" (note:  for this system, V, v, u are all in the same direction where the water enters blade system).  The magnitude (though not the direction) of the water's relative velocity (i.e., its speed) does not change in the blade system, because the flow is assumed to be frictionless.  Thus, v exiting the blade (top and bottom) is equal to v where the water enters the blade.  Calculate the force in the u direction using equation 6.24, where vu is the relative velocity component of the water in the u direction.  Don't forget to calculate the force resulting from each of the deflections caused by the blade.  Part (b) - the power transferred to the blades is simply the force from part (a)  times u, the velocity of the blades.  Part (c)  Calculate the absolute velocity of the water entering and leaving the blade (don't forget there are two velocities leaving the blade).  Absolute velocity is u + v.  Do it in the x and y directions, then calculate the resultant velocity as the "square-root of the squares".  Calculate head (all you've got is velocity head) entering and leaving the blade.  The head entering the blade is the velocity head of the jet.  The energy leaving the blade is 2/3 times the velocity head of the water leaving the "top" of the blade plus 1/3 times the velocity head of the water leaving the "bottom" of the blade.  Why the 2/3 and 1/3?  Because we are calculating energy per weight of water, and the water was split between the two exit points.  The difference in head between exit and entrance is the energy input to the blades.  Calculate the power input to the blades using equation 5.31 and compare to your earlier calculation of power.  Note:  the head you will input to the power equation is the difference between the water head entering and exiting the blades.
• 6.38 Read pages 219 and 220.  Look at sample problem 6.6.  At each radius, determine u (the tangential velocity of the blades), Vr (the radial velocity of the water), and Vu (the velocity of the water in the direction of u).  u is determined from u = wr.  Vr is determined from continuity in the radial direction, assume here that the blades don't take up significant space.  Vu is u + Vr /tanb (see the Figures on page 222 and re-read the second full paragraph on page 220).  Part (a):  T = r Q (r1 Vu1 - r2 Vu2),  this is another version of equation 6.28.  Part (b):  Power = FV = Tw.  Part (c):  Use equation 6.29, realizing the V1 Cosa1 = Vu1, etc.  Check your power calculation, it should equal g Q hm.
• Due Monday, October 12.
• Assignment 7:
• 7.4  Look in Section 7.4
• 7.6  Calculate Reynolds number for the water system.  Determine g for the air, using Tables in Appendix A and equation 2.5.  Determine the kinematic viscosity of the air as m/r, where m is interpolated from a Table in Appendix A and r is g/g.  "Interpolation" means assuming a linear relationship between two variables given in a table (e.g., viscosity and temperature).  A general equation for linear interpolation is (Y2-Y1)/(X2-X1) = (U-Y1)/(Xu-X1), where Y2 and Y1 are the dependent variables in a table (e.g., viscosity at 70 and 60 F), X2 and X1 are the independent variables in a table (e.g., 70 and 60 F), U is the value to be determined (e.g., viscosity at 68 F), and Xu is the given independent value (e.g., 68 F).   Determine the volumetric flow rate (Q) in the air system that will give you the same Reynolds number you got for the water system.  Convert this to weight flow rate (G) using gQ.
• 7.30  The important variables are h (rise in capillary tube), r (radius of capillary tube), s (sufrace tension), and g (specific weight), therefore n = 4. Use the FLT system.  Determine m.  Determine k.  Determine the number of P group, n-k.  This should be 1, thus there is one P group.  For the single P group, determine the exponents that make the group dimensionless.  [Note: set the exponent on h to one.  Also, you will not be able to determine a unique number for the exponent on specific weight;  however, experiments have shown it to be one.]  Realize that if f(P) = 0, then P = Constant.  Call the constant Cr and solve the equation for h. Looking at equation 2.12, what is Cr for a given fluid?
• Due Monday, October 12.
• Assignment 8:
• Do problems 8.13.2, 8.37, and 8.39.  There is one of each of the pipe problems (type 1, 2, and 3).  Solve them like we did in class, but use a spreadsheet to solve the equations for type 2 and 3 problems, which will require iteration. If you missed class or had trouble following what we covered, read section 8.13 (pg. 294).  Turn in your spreadsheet solution for type 2 and 3 problems, making sure that you have documented your work well enough for me to follow it.  Follow all of the homework guidelines and include explanations of the calculations used to create each column in the spreadsheet.  Feel free to turn in the usual hand-written solution for type 1 problems.
• Due Monday, October 19.
• Assignment 9 (Last assignment!):
• Do problems 8.24.6, 8.82, and 8.107.  Please note, we discussed the last two problems in class on Wed.  The first problem is a single pipe with minor losses.  This type of problem was discussed in class on Wed.
• Due Monday, October 19.

Study Guides and Test Review (top)

Two study guides for each chapter are provided.  The Chapter Question Guide contains a list of questions for each chapter.  Reviewing these questions before quiz-time should help you prepare.  The Chapter Review Guide contains a list of the concepts, variables, and relationships you should learn from each chapter.  Reviewing this guide could help for quizzes and tests.

Test 1 Review:  Know the following topics:  Viscosity, Surface Tension, Vapor Pressure, Pressure with Fluid Height, Absolute and Gage Pressures, Barometers, Pressure Measuring Devices, Force on Plane Areas, Center of Pressure, Force on Curved Areas, Buoyancy and Stability, Types of Flow, Flow Rates, Mean Velocity, Equation of Continuity, Velocity and Acceleration Fields, General Energy Equation, Bernoulli's Equation, Relationship between internal energy and temperature, Stagnation pressure, Head, Power, Cavitation, Energy and Hydraulic Grade Lines.  Definitely do not study sections: 2.8, 2.9, 4.10, 5.16-5.19.
 

Grades (top)

Review your grades at any time.  (You need to know your ID name.)