exam1_solns - Name: Sketch of Exam 1 solutions, CE 3502,...

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Name: Sketch of Exam 1 solutions, CE 3502, Fall, 2008 1. The inside of a glass capillary tube (radius r = 1mm) is treated with a polymer coating that increases the contact angle between water and the surface of the tube to θ (=30 o , 60 o ). If this tube is placed in a container of 40° C water open to the atmosphere—How high will the water rise in the tube? (25 points) For equilibrium in the vertical, or z direction, Σ F z = 0. The vertical component of surface tension F s,plate = σ d cos θ c . so F s,plate = σ (2 π r) cos θ c = ρ Vg = ρ π r 2 h g = γ π r 2 h, so h = 2 σ cos θ c / γ r = 2 (7.3 x 10 -2 N/m) cos θ c /(9732 N/m 3 ) r = 7.5mm, 13mm ( θ =30 o , 60 o ) 2. Water at 5° C flows through the venturi section shown, a piezometric tap is adjacent to point 1, and a static tap is inserted at point 2. (The system is not open to the atmosphere at any point. The flow is irrotational, and the water may be considered inviscid and incompressible.) The Manometer fluid has specific gravity S = 0.5.Given s / m 81 . 9 x 2 , s / m 81 . 9 ( v 1 = and d = 3m, what is the deflection in the monometer h? (25 points) h enters directly when calculating pressure differences within the static part of the system. We don’t know pressure anyplace within the static manometer, but we can calculate pressure differences within the fluid part of the system using velocities. The latter gives us a relationship between pressures 1 & 2, so we use the static
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exam1_solns - Name: Sketch of Exam 1 solutions, CE 3502,...

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