Schedule

  Class times: MWF 9:40-10:30 in A 226 CEB or as announced.

Tentative outline (keep checking for changes):

• 01/07/03 W: Lecture.
• 01/09/03 F: Lecture.

• 01/12/03 M: Lecture.
• 01/14/03 W: Lecture. [1.2, 1.3, 1.7 due.]
• 01/16/03 F: Lecture. [2.1, 2.2, 2.5 due.]

• 01/19/03 M: Martin Luther King, Jr. day
• 01/21/03 W: Lecture.
• 01/23/03 F: Lecture.

• 01/26/03 M: Lecture. [Due: 4.1, 1.1, 4.4 (functions T(x₁,x₂),b₁(t),b₂(t) are given), 4.2 (do not guess, use the appendices!), 4.7 (integrate around a circle around the origin in (c), but around an arbitrarily shaped contour in (b)) (comment on the error in the Stokes' result in (b)), 4.9. ]
• 01/28/03 W: Lecture.
• 01/30/03 F: Lecture.

• 02/02/03 M: 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. ]
• 02/04/03 W: Lecture. [5.16, 17 due 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. In question 5.17, the book means that a part with diameter D/4 of the incoming stream enters the cone, while the remainder between D/4 and D continues to pass around the outside of the cone. ]
• 02/06/03 F: Lecture.

• 02/09/03 M: Lecture. [5.1, 5.3 due.]
• 02/11/03 W: Lecture.
• 02/13/03 F: Lecture.

• 02/16/03 M: Exam 1.
• 02/18/03 W: Lecture. [Spherical finite volume due.]
• 02/20/03 F: Lecture. [5.2 due.]

• 02/23/03 M: Lecture. [5.6 and 5.8 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. ]
• 02/25/03 W: Lecture.
• 02/27/03 F: Lecture.

• 03/01/03 M: Lecture. [6.3 and 6.5 due. In 6.3, explain why this flow is not called inviscid but does have an inviscid velocity field. In 6.5, look up the incompressible continuity equation and momentum equations in cylindrical coordinates (Appendix C, constant viscosity and density,) substitute in the given velocities, (), verify that the continuity equation is already satisfied, and find the single scalar pressure field that ensures that the three momentum equations are also all satisfied. The pressure must of course be the same pressure in all three equations. ]
• 03/03/03 W: Lecture.
• 03/05/03 F: Lecture.

• 03/08/03 M: Spring Break.
• 03/10/03 W: Spring Break.
• 03/12/03 F: Spring Break.

• 03/15/03 M: Lecture.

  [Due: (A) Find the continuity equation and momentum equations in cylindrical coordinates for an incompressible fluid when v_r=v_z=0 and neither velocity nor pressure depends on z. Work these equations out as far as possible, finding the most precise expression for the pressure and partial differential equation for . (B) Now assume that the flow is steady. Also, assume that that the streamlines are complete circles; this will allow you to say something more about the integration constants of the pressure field, since the pressure must return to the same value when increases by 2. Solve the resulting ordinary differential equation for . (C) Put in the boundary condition that at r=R_i, the fluid ends at a cylinder rotating with an angular speed , giving the boundary condition at r=R_i. Also put in the boundary condition that at a larger r=R_o, the fluid meets an outer rotating cylinder: at r=R_o. Use these boundary conditions to find the integration constants in the expression for . (D) Identify the special flow fields that arise when (a) and , and (b) R_i=0. You can find these derivations in graduate fluid books like Curry's, but try to do it from scratch.]

• 03/17/03 W: Lecture.
• 03/19/03 F: Lecture.

• 03/22/03 M: Exam II.
• 03/24/03 W: 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.]
• 03/26/03 F: Lecture.

• 03/29/03 M: Lecture. [18.1, 18.2, and the first part of 18.3 due. In 18.3, use the trig addition formulae on page 44 of the math handbook and the relationships with hyperbolic functions on page 58 to write the sine in terms of real functions and i only.]
• 03/31/03 W: Lecture. [Due:

  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 .

  ]
• 04/02/03 F: Lecture.

• 04/05/03 M: Lecture. [18.6 due.]
• 04/07/03 W: Lecture.
• 04/09/03 F: Lecture. [18.4, 18.5, 18.9 due.]

• 04/12/03 M: Lecture. [18.7, 18.19 due. Also integrate the pressure distribution on the surface of a cylinder with circulation in a cross flow to find the force on the cylinder.]
• 04/14/03 W: Lecture. [Due: (1) Compute the Reynolds number of your car (based on driving velocity and height, and of a plane of characteristic size 20 m flying at Mach 0.8 in standard conditions.

  (2) What is the flow velocity of water in a pipe of diameter 0.1 m if the Reynolds number based on diameter and average velocity is 1.

  (3) List other nondimensional numbers than the Reynolds number that need to be the same for flows that look similar to be really similar. Think of high-speed planes, ships, etcetera. ]

• 04/16/03 F: Lecture. [Due: (1) Identify the boundary layer coordinates and velocity components for the boundary layer around a circular cylinder in terms of more usual coordinates.

  (2) For the same case, identify the boundary velocity u_e just above the boundary layer and the pressure p_e just above the boundary layer from the potential flow solution. ]

• 04/19/03 M: Lecture. [Due: (1) Using the results of the previous homework, formulate the boundary layer problem for the impulsively started cylinder.

  (2) Rewrite the Navier Stokes equations for the exact problem in terms of the boundary layer variables and compare them to the boundary layer approximation. What terms are lost in the boundary layer approximation? ]

• 04/21/03 W: Lecture.
• 04/23/03 F: Lecture. [Due: (1) Find the shear force on a plate of length 0.5 m moving flush through air at a speed of 0.5 m/sec

  (2) Derive the steady boundary layer problem along a semi-infinite plate if instead of a uniform flow, there is a sink sitting at the nose of the plate. In other words, the potential flow just above the boundary layer is .

  (3) Solve the previous boundary layer problem. The boundary layer solution is again similar, but the boundary layer thickness is now linear in x. In other words, u(x,y)=u_e(x) f'(y/x), where ]

• 04/27/03: Tuesday final 3:00-5:00 pm (ignore FSU schedule).