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Unformatted text preview: BME C101/C201. INTRODUCTION TO BIOMEDICAL ENGINEERING
FALL 2010 ‘ PROBLEM SET 5 Due November 3, 2010 (Wednesday) Please either (1) put your homework in my mailbox in 5121 Engineering V by noon or (ii) give
them to the teaching assistants in their discussion sections or oﬁice hours. 1. Let’s consider the van der Waals interactions between two cylinders separated by a
closest distance of approach equal to d. If d is kept the same, but the cylinders are
increased dramatically in size, would the overall van der Waals interaction energy
between the two cylinders increase or decrease? Why? Plot shear stress vs. strain rate for both a pseudoplastic ﬂuid and a dilatant ﬂuid. Also
explain why the slope changes as strain rate is increased. Consider laminar ﬂow of a Newtonian ﬂuid down and through a thin rectangular plate
(see figure below). The distance between the two parallel walls is 21. The height and width of the plate are h and w, respectively. Note that the ﬂow is due to both gravity and
a pump. Accordingly, the pressure at any 2 position is notjust 1 atm + pgh. However, you are told that dP/dz = or, where 0t is a constant. Assuming fully developed flow,
derive an expression for the velocity proﬁle, keeping in mind that x=0 is located at the
center of the plate. % <——>
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\7 = 4xy>‘<  2y29 in units of m/s. Let the density and viscosity be p kg/m3 and u kg/(m*s), respectively.
Derive an expression for the pressure gradient in the xdirection _a_P_
6x and evaluate this gradient at (x,y,z)=(2,2,1), where each coordinate is in meters. 5. An incompressible Newtonian fluid has the following velocity proﬁle
\7 = 2x2)? — 229  4xz:3'~ in units of m/s. Let the density and viscosity be p kg/m3 and u kg/(m*s), respectively.
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