Analyze a lubricated sliding contact between a tilted plane and an infinite flat surface, as shown in the figure. The to

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Analyze a lubricated sliding contact between a tilted plane and
an infinite flat surface, as shown
in the figure. The top surface is tilted and stationary, i.e.,
𝑢𝑢=0. Its width is infinite (very long
in the y-direction, normal to the paper). The bottom surface moves
with a constant velocity U
that drags the lubricating fluid into the gap. The gap size ℎ is
smaller than the bearing length 𝐵𝐵
by several orders of magnitudes, i.e., ℎ≪𝐵𝐵. The weight of the thin
fluid film in the gap can be
neglected. Hydrodynamic pressure P is generated by the fluid flow
through the gap, that
balances the bearing load. The flow is laminar.
here is a list of assumptions:
1. The flow is steady.
2. Gravitational force is extremely small.
3. ℎ≪𝐵𝐵
4. The bottom surface is infinite in the x-y plane (y is normal to
the page).
5. The fluid is incompressible and Newtonian.
6. The velocity field is purely two-dimensional, which implies that
v = 0 and all y
derivatives (𝜕𝜕 𝜕𝜕𝜕𝜕⁄ =0).
7. No-slip boundary condition is applied.

(i) Simplify the continuity equation and the Navier-Stokes equation
(x-momentum). List out
the term(s) to be neglected and specify the assumption that is
based on, in the format as
shown below.
(ii) Write down the final simplified continuity equation and linear
momentum equation for
the case.