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1. Undergrads: Compute the scale factors spherical coordinates.
(Look up the definition on www.mathworld.com if you need to.)
Then use the formulas given in the handout of Thursday 2/23/06
to generate specific formulas for div, grad, and curl in spherical coordinates.
You can check your answers against what's given on mathworld.com.
GRADS: Using the definition of "div" given here
perform a similar derivation, but in general orthogonal
curvilinear coordinates, to obtain the formula for div given in the handout
of Thursday 2/23/06.
2. Verify, or find the error in, my computation of the equatorial deepening of the Earth's ocean due to the planet's spinning.
3. Make a Maple plot of the pressure field for the potential flow around a cylinder that we derived on Thursday 2/23/06.
4. I want to do a kitchen-sink-type experiment to test some predictions we'll be developing next week for viscous flow through a pipe. We'll find a formula for the total flow rate in terms of the pressure drop, the viscosity, the length of the pipe, and most particularly the radius of the pipe - I want to test the radius-dependence. What I was thinking of is to blow air through straws of various radii and collect it in inverted measuring cylinders under water. One of the difficulties will be ensuring the pressure drops are known, or at least the same for all the straws. See if you can come up with a practical way of doing this. Please answer this on a separate sheet from the rest, because I, rather than the Grader, will be reading this one.