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Homework_4 - 22.381 HOMEWORK 4 DUE WEDNESDAY FEB 15TH 2012...

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22.381 : HOMEWORK # 4 DUE: WEDNESDAY FEB 15TH, 2012* This is the first homework for chapter # 2. *If you hand in this homework on the due date, it will be graded and available by the 16th of February. (1) (15pts) The following diagram shows two parallel plates that are separated by a small gap. We will examine the flow of water through these plates. A manometer is used to determine the pressure difference between point a and b . Figure 1. The illustration of water flowing through the gap between two parallel plates. Useful information : Equation for the fluid velocity profile in m/s is: u ( y ) = 1 2 μ dp dx ( y 2 - hy ) μ Water = 1 × 10 - 3 Pa · s Height of the channel = 0.0025 m Distance between the two pressure taps = 3 meters (a) If the height difference in the manometer, M = 5 cm , determine the difference in pressure between the upstream pressure tap and the downstream pressure tap. (b) Assume that the pressure gradient ( dp dx ) in the above equation for velocity can be approximated as: dp dx = P b - P a 3 m 1
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2 DUE: WEDNESDAY FEB 15TH, 2012*
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