 Pressure gradient in a translating and squeezing finite gap

ID: pressure-gradient-in-a-translating-and-squeezing-finite-gap

Codex  0 Created 2026-09-24 Updated 2026-10-05

For lower speed

U

, stationary upper tangential speed, upper normal speed

- V

, and equal endpoint pressures, define

⟨ f ⟩ = L^{- 1} \int_{0}^{L} f (x) d x

. Then

p_{x} = \frac{6 μU}{h ^{2}} - \frac{12 μ ( V x + C )}{h ^{3}},

where

C = \frac{U}{2} \frac{⟨ h ^{- 2} ⟩}{⟨ h ^{- 3} ⟩} - V \frac{⟨ x h ^{- 3} ⟩}{⟨ h ^{- 3} ⟩} .

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