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Shear Stress and Fluid Mechanics
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[QUOTE="bliz, post: 4499754, member: 487656"] [h2]Homework Statement [/h2] It's a relatively simple problem I'm sure, but I'm a bit confused on how exactly to go about it: There are three parallel plates with water (viscosity of 0.8807 cp @ 30°C) between plates 1 and 2 (plate order of 1 on bottom, 2 in middle, 3 on top), and toluene (viscosity of 0.5179 cp @ 30°C) between plates 2 and 3. The distance between each plate pair is 10 cm and plate 3 (top plate) moves at 3 m/s while plate 1 (bottom plate) is at rest. a) I need to find the velocity of plate 2 at steady-state b) And the F/A (shear stress) on plate 3 that is needed to maintain the 3 m/s velocity [h2]Homework Equations[/h2] Please excuse any formatting issues you may come across. I am new to forums and still learning how to properly format questions and comments. Shear stress = [itex]\tau[/itex][SUB]yx[/SUB] = -[itex]\mu[/itex]*v[SUB]x[/SUB]/y where [itex]\mu[/itex] = viscosity and v[SUB]x[/SUB] = velocity in the positive x direction (the same direction plate 3 is moving in) [itex]\tau[/itex][SUB]yx[/SUB] = F/A [h2]The Attempt at a Solution[/h2] I was a bit unsure initially of how to go about the problem but my attempt was to solve for the shear stress between plates 1 & 2 and plates 2 & 3, and then equate them to get the velocity of the middle plate. So after multiplying dy by both sides and integrating (y from 0 to 10, and v[SUB]x[/SUB] from 0 to v[SUB]2[/SUB] for plates 1 & 2 and from v[SUB]2[/SUB] to 3 for plates 2 & 3), I got the equations: Plates 1 & 2: [itex]\tau[/itex][SUB]yx[/SUB] = -0.08007*v[SUB]2[/SUB] Plates 2 & 3: [itex]\tau[/itex][SUB]yx[/SUB] = -0.15937 + 0.5179*v[SUB]2[/SUB] Equating these gave me the velocity of plate 2 to be 1.178 m/s For the 2[SUP]nd[/SUP] part of the question (solving for F/A), I think you only need to solve for shear stress as that equals F/A. So using v[SUB]2[/SUB], I plugged it into one of the equations to get [itex]\tau[/itex][SUB]yx[/SUB] = F/A = -0.094322 N. The problem I have with my methods is that I'm not too sure about equating the two shear stresses as I see no real reason that they should be equal in the first place. Also, the 2[SUP]nd[/SUP] part of the question specifically asks about the F/A on plate 3, which really makes me think that the shear stress must be different for each plate. While my first answer seems to make sense, I don't think a negative force value for the second one fits, so I would assume that I'm doing something wrong there. Thanks in advance for any help, the hardest part I have with this stuff is that it's really confusing to me what actually needs to be done and which equations to use to get there. [/QUOTE]
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