Schedule

  Class times: MWF 9:40-10:30.

Tentative outline (keep checking for changes):

• 01/06/03 M: Introduction
• 01/08/03 W: Introduction
• 01/10/03 F: Introduction [1.3, 4, 7 due]
• 01/13/03 M: Lecture [2.2, 5, 8, 9 due]
• 01/15/03 W: Lecture [4.1, 2, 4, 5, 7, 8, 9 due. In 4.2, 9, don't guess but use the appendices in the book. 4.5 and 8 are the same flow; answer using the velocity derivative tensor. In 4.7, explain the discrepancies with 4.2 produced by Stokes' theorem.]
• 01/17/03 F: Lecture
• 01/20/03 M: Martin Luther King, Jr. day
• 01/22/03 W: Lecture
• 01/24/03 F: Lecture [5.1, 5 due. In 5.1, the physical meaning of (d) is the linear x-momentum flowing out through area S_II per unit time; the rest you should be able to figure out. Remember the definition of pressure. In 5.5, use the Leibnitz rule twice. ]
• 01/27/03 M: Lecture [5.2 and spherical finite volume due.]
• 01/29/03 W: Lecture [5.3 due.]
• 01/31/03 F: Lecture [5.11, 12, 14 due. In question 5.11, d is much larger than D, not the other way around. In question 5.14 (13), the pressure is 700 kPa at the nozzle entrance. ]
• 02/03/03 M: Lecture [5.6 due. In question 5.6, take the curl of the differential momentum equation. The book's Z is the height h. Also, assume that it is a Newtonian fluid: there are no viscous stresses if a Newtonian fluid is at rest. ]
• 02/05/03 W: Lecture
• 02/07/03 F: Lecture
• 02/10/03 M: Lecture [5.15, 16 due. In 5.15, it can be assumed that the water jet velocity is constant relative to the cart. In 5.16, it can be assumed that no computer is available and that the flow over the cone is quasi-steady relative to the cone. Also 6.3, 5, 7 due. In 6.3, explain why this flow is not called inviscid but does have an inviscid velocity field. In 6.7, show, using the Cauchy-Schwartz inequality (see math handbook) or your vast knowledge of quadratic forms, that the dissipation is always nonnegative as required by the second law, even in the compressible case, if Stokes' hypothesis is satisfied.]
• 02/12/03 W: Lecture
• 02/14/03 F: Recorded Lecture [7.1, 2 due In 7.1, use a combination of integral continuity and Bernoulli. Stay outside the boundary layers while applying Bernoulli! In 7.2 use the results of 7.1 and integral momentum. The control volume is the rectangle of fluid in the pipe from the entrance to the station where the top and bottom boundary layers just meet each other.]
• 02/17/03 M: Exam 1
• 02/19/03 W: Lecture
• 02/21/03 F: Lecture [7.3, 5, 9, 11, 18 due. In 7.5, use the continuity and NS equations in cylindrical coordinates and make similar approximations as in section 7.2. Assume that only is nonzero. Compare with the plane Couette flow results in section 7.3. Are they the same for small difference in radius? What happens if the gap gets bigger? What happens if the inner rod diameter is small, but the rod spins fast? In 7.9, assume that the water film is thin.]
• 02/24/03 M: Lecture
• 02/26/03 W: Lecture [7.4 due.]
• 02/28/03 F: Lecture
• 03/03/03 M: Lecture [7.16, 17 due.]
• 03/05/03 W: Lecture [13.7]
• 03/07/03 F: Lecture [18.8 due. In 18.8, write the problem for either the streamfunction or the potential and solve using an appropriate method. The boundary conditions are that (a) u=U₀ + U(y) at x=0, 0 < y < h, (b) the flow remains finite at , and (c,d) the duct walls and are streamlines (the vertical velocity component is zero at walls.) Compare the properties of this inviscid ``entrance'' flow with the viscous developed duct flow of chapter 7. (See problems 7.1 and 7.2)]
• 03/10/03 M: Spring Break
• 03/12/03 W: Spring Break
• 03/14/03 F: Spring Break
• 03/17/03 M: Lecture
• 03/19/03 W: Lecture
• 03/21/03 F: Lecture [ 18.3 (a) due. Also answer:

  1.

  Find the real and imaginary parts of: (1+i)², (1+i)(1-i), 1/(1+i), , . Plot the results in the complex plane and find their magnitude and argument.

  2.

  For the following complex potentials, find the velocity potential and the streamfunction , and sketch the streamlines: z, iz, z², , .

  3.

  For the same velocity potentials, find the complex conjugate velocity W in terms of z, the Cartesian velocity components u and v in terms of x and y, and the polar velocity components u_r and in terms of r and .

  ]
• 03/24/03 M: Exam II
• 03/26/03 W: Lecture [Recommended: 18.4.]
• 03/28/03 F: Lecture
• 03/31/03 M: Lecture
• 04/02/03 W: Lecture [18.6 due.]
• 04/04/03 F: Lecture [ Do the exercises on the ``Cylinder'' web page. ]
• 04/07/03 M: Lecture [ Do the exercises on the ``Circulation'' web page. Also determine around the unit circle around the origin by suitably moving around the contour of integration and then approximating the integrand. ]
• 04/09/03 W: Lecture [ 18.19 due. In 18.19, use the mirror method, not Schwartz-Christoffel, and plot the streamlines. ]
• 04/11/03 F: Lecture [ Last two exercises on the ``Residue theorem'' due. Also, for the periodic velocity field , find the mass flow coming out of the singularities and the circulation around them by integrating around them (c.f. the ``Far field'' page.) ]
• 04/14/03 M: Lecture [ Exercises 1, 2, and 6 on the conformal mapping page due. Sketch the Joukowski airfoils for C=1.1 and for C=1.1-0.1i. Or better, use your graphics software to plot it accurately and to scale. ]
• 04/16/03 W: Lecture [ Exercises on the ``Viscous Flow'' page due. ]
• 04/18/03 F: Lecture [ 1. Write down the early-time solution , , , for the potential flow around a circular cylinder of radius r<sub>0</sub> impulsively set into motion with a speed U. 2. The small-time boundary layer solution is , v(x,y,t)=0, . Show that the boundary layer solution at infinite y is the potential flow solution at zero y, and not the potential flow solution at infinite y. 3. Substitute the boundary layer solution above in the boundary layer equations and hence verify that the solution is only valid for small times. In particular that instead of zero, and that the momentum equation is not satisfied at finite times. ]
• 04/21/03 M: [ Exercises on the ``Flat Plate'' and ``Displacement Thickness'' pages due. ]
• 04/23/03 W: Lecture
• 04/25/03 F: Lecture
• 04/29/03: Tuesday Final 12:30-2:30 (FAMU schedule)