Problem 2.76 - Problem 2.76 [Difficulty: 5] Geometry of...

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Problem 2.76 [Difficulty: 5] Given: Geometry of rotating bearing Find: Expression for shear stress; Maximum shear stress; Expression for total torque; Total torque Solution: Basic equation τμ du dy = dT r τ dA = Assumptions: Newtonian fluid, narrow clearance gap, laminar motion From the figure r R sin θ () = u ω r = ω R sin θ = du dy u0 h = u h = h a R 1 cos θ + = dA 2 π r dr = 2 π R sin θ R cos θ d θ = Then du dy = μω R sin θ a R 1 cos θ + = To find the maximum τ set θ R sin θ a R 1 cos θ + d d 0 = so R μ ω R cos θ R a cos θ + Ra + R cos θ 2 0 = R cos θ R a cos θ + 0 = θ acos R + = acos 75 75 0.5 + = θ 6.6 deg = τ 12.5 poise 0.1 × kg ms poise 2 × π 70 60 rad s 0.075 × m sin 6.6 deg
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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