velocityRatio
plain-language theorem explainer
The velocity ratio across the gap in a Tesla turbine disc stack is defined as the square of the gap width divided by twice the boundary layer thickness. Fluid dynamicists applying Recognition Science to boundary-layer machinery cite this when deriving phi-optimal spacing. The definition is obtained by direct substitution of the parabolic Poiseuille profile between parallel plates.
Claim. The velocity ratio across a gap of width $g$ with boundary-layer thickness $δ > 0$ is given by $v = (g / (2δ))^2$.
background
In the Tesla turbine, fluid spirals inward between smooth discs with momentum transfer via boundary-layer adhesion. The J-cost, defined as the derived cost of a multiplicative recognizer on positive ratios, quantifies strain in the velocity profile. Upstream results from PhiForcingDerived and ObserverForcing establish that recognition events carry non-negative J-cost and that physical quantities occupy discrete phi-tiers.
proof idea
The definition is a direct algebraic expression implementing the parabolic velocity profile formula for Poiseuille flow between plates.
why it matters
This definition supplies the velocity-ratio expression used by phi_disc_spacing_optimal to reach exactly phi at gap $g = 2δ√phi$ and by tesla_turbine_master to certify the turbine as a phi-spiral engine. It realizes the phi fixed point from the forcing chain as a minimum non-trivial J-cost configuration in fluid machinery.
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