100511 hw1-f011

100511 hw1-f011 - Q R(t) U P(t P o Lubricant film Lubricant...

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120 A Homework #1 Assigned: Wednesday October 5, 2011 Due: Wednesday Oct.12, 2011 1. A film of lubricant is flowing down a plane under the influence of gravity (see figure below). The film has a thickness . The viscosity of the lubricant is . Perform a dimensional analysis of this problem. 2. An air bubble is grown inside a liquid by blowing air through a cylindrical pipe of radius r at a constant volumetric flow rate Q . The bubble has an instantaneous radius R and an instantaneous pressure P . The liquid is displaced in radial direction due to bubble growth. List important parameters that describe the problem and perform a dimensional analysis.
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Unformatted text preview: Q R(t) U P(t P o Lubricant film Lubricant reservoir L H 3. Liquid is being pumped from a reservoir through a cylindrical pipe of radius R by maintaining a pressure gradient of ( P 1-P 2 ) across the pipe ( P 1 > P 2 ). Derive expressions for conditions that will describe, on an order of magnitude scale, whether the flow is limited by gravity or viscosity. For each case, derive expressions that will describe the magnitude of ( P 1-P 2 ), on an order of magnitude scale, necessary for the liquid to flow in each case. Neglect surface tension. P 1 P 2 H...
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100511 hw1-f011 - Q R(t) U P(t P o Lubricant film Lubricant...

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