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Unformatted text preview: ME320 Exam 2 Section 1 (Open Book & 1 Sheet of Formula) Prof Kurabayashi Winter 2007 (40 Points) Name:______________________________ Note: In your answers, clearly (1) state your assumptions, (2) draw figures that help you get answers, (3) define parameters if you introduce new ones, and (4) show your all derivation processes. These help you obtain partial credits if you dont come up with complete answers. Problem 1 (18 points) A circular plate of radius r is immersed in a fluid of density and viscosity and it is forced down with a force F onto a flat parallel surface as shown in the figure. The motion is sufficiently slow so that the acceleration and kinetic energy of the fluid can be neglected. The out ward viscous flow between the plates at any radial position can then be assumed to have the same velocity distribution as a fully developed laminar flow between infinite parallel plates of gap h with no body forces (i.e., no gravity effects) present. (a) Derive an expression for the distribution of pressure as a function of radius P ( r ). Express your answer in terms of r , r , , V (the vertical velocity of the plate), and h (= h ( t ) the time-varying gap). (b) Calculate the force F in terms of r , , V 0, and h . (c) Derive an expression for the time t necessary for the plate that was originally very far to move to the position where h = h in terms of r , , V 0, h , and F . Problem 2 (15 points) (a) The capillary rise h of a liquid in a tube varies with tube diameter d , gravity g , fluid density , surface tension Y and the contact angle . (i) find a dimensionless statement of this relation. (ii) if h = 3 cm in a given experiment, what will h be in a similar case if the diameter and surface tension are half as much, the density is twice as much and the contact angle is the same....
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