By Spiral plate, do you mean helical type baffles? can you describe a spiral plate heat exchanger, and are you asking about the thermal analysis, or structural (stress) analysis as in TEMA?
you can try integrating with respect to y giving the area under the curve, right? while setting the limits properly. I'm sure you know shear stress = mu*(dV/dy)
also, this is homework
For a simple/rough and incompressible calculation using bernoullis principle:
http://en.wikipedia.org/wiki/Bernoulli%27s_principle
E.g. (v1^2)/2 + g*z1 + P1/p = (v2^2)/2 + g*z2 + P2/p
This obviously ignores the losses but gives an idea. Also, assuming your pouring to atmosphere and using...
Can treat it like a restriction orifice. It will consider the discharge coefficients depending on thickness, viscosity, temperatures, diameters, reynolds #, etc. to give more accurate #'s
The head pressure required might make your container quite high?
could try a belzona coating depending on what your doing
http://www.belzona.com/products.aspx
They are usually painted on smooth, but I can imagine you can't make it rougher when you apply it. Also expensive but good for temps up to 180°C
The actual heat transfer given out by your refrigeration unit will be different than your input power (10KW) if that's the case?. Even with insulation your going to get some loss. I think the actual time to cool it down to steady state temperature won't be long given your power and convection.
Who is the target audience really? I have trouble understanding it, because I don't have the graduate mathematics to know the notations. All these shows that on youtube, news or Nova are interesting, but really, what are they trying to accomplish? I think it is only to gain public interest the...
Thin airfoil theory can give you analytical results:
http://www.desktop.aero/appliedaero/airfoils1/tatderivation.html
of course this only applies to thin airfoils