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Question (4): (16 marks) (a) State the meaning of the 'No-slip boundary condition', commonly used in Fluid Mechanics. (b) 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. Is 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 his 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 (a/ay=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. (i) Write down the final simplified continuity equation and linear momentum equation for the case. Continuity quetion Team neglected Term (1) Term [2] based on Assumption CI) Continuity equation: öp (pu), a(pv) (pw) де 20 дх ду dz + + Term 1 Term 2 Term Term

Navier-Stokes equation (x-momentum) (ди ди ди P +u + V ax ду ou dz OP (au azu au) āx+p9x +*lax2 + ayz + az? Term 1 Team 2 Term 3 Term 4 Term 5 Term 6 LS Term 7 Term 8 Term 9 X Load u = 0 us h Ex u= U B