Final - winter 2011 - with solution

Thepressuregradientis

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Unformatted text preview: dth and L = length along the y coordinate] 12 Problem 2 (20 points): Water flows between and inclined plane and a plate. The pressure gradient is zero and the flow is driven by gravity and by the motion of the upper plate. See schematic below: g u = U u = 0 L The system is 2‐dimensional and at steady state; the flow is fully developed. a) Simplify the governing equations to describe the fluid motion. [Hint: your analysis will need both the conservation of momentum and the conservation of mass, in differential forms]. Motivate each assumption and simplification. b) Derive an analytical expression of the flow velocity profile in the gap; state what boundary conditions you are using; provide a qualitative sketch of the velocity profile. c) Assuming that the gap between the plates is 1 cm and the angle is 40, how large does the velocity of the upper plate U need to be so that the total flow rate is zero? [viscosity of water = 10‐3 Pasec] Problem 3 (20 points): The cart sketched below is propell...
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This document was uploaded on 03/07/2014 for the course ME 113 at UC Riverside.

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