Consider the 2D bearing depicted in the figure below. It consists of two faces parallel to...

 

 

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Consider the 2D bearing depicted in the figure below. It consists of two faces parallel to the surface underneath it, each of length L. One face is a height h from the surface, and the other is h from the surface. The surface moves past the bearing, parallel to itself, at a speed Uo in the direction indicated in the figure. The horizontal faces of the bearing are connected by a vertical face as shown. A viscous fluid with viscosity u fills the gap between the bearing and the moving surface, and you may assume that (h1, h) < < L. L h L U (a) Show that the pressure varies linearly underneath each horizontal face, and sketch the pressure distribution under the bearing. Hint: Treat each half of the bearing separately, and think about what boundary condition(s) to apply where they meet. (b) Determine the pressure at x = L. Hint: Start this part by writing out the Reynolds lubrication equation for the entire bearing. (c) Find the total force (per unit depth) that can be supported by the bearing. Can the bearing support a load if h > h? Consider the 2D bearing depicted in the figure below. It consists of two faces parallel to the surface underneath it, each of length L. One face is a height h from the surface, and the other is h from the surface. The surface moves past the bearing, parallel to itself, at a speed Uo in the direction indicated in the figure. The horizontal faces of the bearing are connected by a vertical face as shown. A viscous fluid with viscosity u fills the gap between the bearing and the moving surface, and you may assume that (h1, h) < < L. L h L U (a) Show that the pressure varies linearly underneath each horizontal face, and sketch the pressure distribution under the bearing. Hint: Treat each half of the bearing separately, and think about what boundary condition(s) to apply where they meet. (b) Determine the pressure at x = L. Hint: Start this part by writing out the Reynolds lubrication equation for the entire bearing. (c) Find the total force (per unit depth) that can be supported by the bearing. Can the bearing support a load if h > h?

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To demonstrate linear pressure variation under the bearing we analyze each half separately Left half ... View the full answer