Has anybody ever inflated there bicycle tires with water and done a power study

[alienator]

Making the approximation for steady velocity riding that the water column will began to flow in unison over time yes it would be a straight forward calculations. Otherwise the calculations would be very difficult your are right again. 

I don't see the water flowing with anything but turbulence especially since there is a ∂θ mucking about with the fluid flow. If you were dealing with a straight pipe, then you could probably get away with some steady state approximation of fluid flow. With water wheels, I would be running models through CFD to get a feel for what sort of losses are expected before I made a steady state approximation.

 

[alienator]

Another ****ing double post.

 

[howardjd]

got me again.