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The surface of C where the glass sat is smooth, then the glass may have a slightly concave bottom and the water, with capillary action, managed to form a seal between the two surfaces. Even if the glass bottom and surface C are both flat, capillary action can still form a seal around the edge leaving a void in the centre, causing the same effect of lower v. ...
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The key is what's called "scale separation". For continuum hydrodynamics to work, there has to exist a length scale that is much smaller than the smallest length scale on which any interesting fluid-mechanical phenomena happen, so that it's safe to treat that length scale as differentially small; yet that same length scale must also be much larger ...
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Seems to me that the source in this case is θ2 since the sign convention normally is -Q for inward flow. This site https://www.ecourses.ou.edu/cgi-bin/eBook.cgi?doc=&topic=fl&chap_sec=07.3&page=theory provides an example where θ2 is the source angular displacement.
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Wavelength is with reference to Kolmogorov's theory of turbulence. Kolmogorov postulated a theory for how turbulence is conveyed from large to small scale eddies, as you described. The wavelength and frequency origins are buried deep in the mathematics of the theory. Basically, the theory postulates an energy spectrum for turbulence, which divides the energy ...
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It might help to consider the special case of Hatton's excellent answer, where the velocity is very small. A small piston at one end of a tube, then an expansion to a large piston at the other end, is an idealised hydraulic jack. When not moving it is considered to have the same pressure at each end, so can support a car at the large end with a small force ...
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The static pressure is the compressive longitudinal stress exerted by the pipe walls on the fluid and vice versa, but perhaps more importantly in this context, it is also the compressive longitudinal stress exerted on every little parcel of fluid by the parcels of fluid next to it, in every direction. If the pressure didn't decrease along the length of the ...
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If inlet flow = outlet flow, then your system will quickly reach a state of equilibrium. The pump spins to transfer fluid from node 5 to node 1. There would be some minor pressure difference due to pipe flow resistance. Probably not enough to break the static friction on cylinder seals (approx 100 psi for a typical 3000 psi cylinder). Even if you did have ...
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I'm going to post this as an answer even though it isn't one.
I was hoping the OP would post the actual substitutions into the Bernoulli equation to support their observation that you measure a different height of water if you watch the car roll past compared with sitting on the car. (which is ridiculous, of course).
Notice that so far, three of the four ...
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