Spring 08 HW 2

# Spring 08 HW 2 - CEE 3304 Spring 2008 HW#2 Viscosity...

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CEE 3304 Spring 2008 CEE 3304, Spring 2008, HW#2 by: Amr A. El-Sayed 1 HW #2 Viscosity, Compressibility, and Static pressure Problem 2.41 Given: A disk is rotated very close to a solid boundary–details are provided in problem statement. Find: a) Ratio of shear stress at r = 2 cm to shear stress at r = 3 cm. b) Speed of oil at contact with disk surface. c) Shear stress at disk surface. Assumptions: Linear velocity distribution: L V dy dV = Solution ω =2 π f f = frequancy in rev/sec θ axis of rotation r r v v s r s = θ r v = ω

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CEE 3304 Spring 2008 CEE 3304, Spring 2008, HW#2 by: Amr A. El-Sayed 2 Tangent velocity (V) = angular velocity ( ω ) × radius of rotation ( r ) Newton’s law of viscosity dy du µ τ = The derivative equation can be approximated to Î L r L V ω = = The shear stress τ will be a function of the linear velocity, V, and thus a function of the disk radius. L r 1 1 = Î 6667 . 0 3 2 2 1 2 1 = = = r r m s rad r V 100 3 0 . 2 × = × = = 0.06 m/s 002 . 0 06 . 0 01 . 0 × = = dy du = 0.3 N/m 2 Problem 2.47 Given: Very small spherical droplet of water. Find: Pressure inside. Refer to Fig. 2-6(a). The surface tension force, σ π × r 2 , will be resisted by the pressure force acting
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## This note was uploaded on 05/19/2008 for the course CEE 3304 taught by Professor Aaelsayed during the Spring '08 term at Virginia Tech.

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Spring 08 HW 2 - CEE 3304 Spring 2008 HW#2 Viscosity...

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