6 Analyze A Lubricated Sliding Contact Between A Tilted Plane And An Infinite Flat Surface As Shown In The Figure Th 1 (195.36 KiB) Viewed 14 times
6 Analyze A Lubricated Sliding Contact Between A Tilted Plane And An Infinite Flat Surface As Shown In The Figure Th 2 (37.42 KiB) Viewed 14 times
(6) 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., u = 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 B by several orders of magnitudes, i.e., h« B. 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. There is a list of assumptions: 1. The flow is steady 2. Gravitational force is extremely small 3. h«B 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 (O/Qy = 0). 7. No-slip boundary condition is applied. (1) 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. (11) Write down the final simplified continuity equation and linear momentum equation for the case. Continuity equation Team neglected Tenn (1) Term [2] based on Assumption (is Continuity equation: ap a(pu) (pv) a(w) + + + at ax dy az S Term 1 Term 2 Term 3 Term 4 , ಅ=6 =
Navier-Stokes equation (x-momentum) lau du ди ou Plat +u+v ax ду SS Term 3 +W 2 ) -- OP +PGx + Ox (2²u a²u a²u + (x² tay2 + az? SS S Term 1 Term 2 Term 4 Term 5 Terms Term 7 Term8 Term 9 IP -X Load 플 u=0 u h Z u=U B
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