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 cant 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 gonna get some loss. I think the actual time to cool it down to steady state temperature wont 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 [Broken]
of course this only applies to thin airfoils