Rec1 - sections. However, surface tension pulls the water...

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Recitation 1 (Sept 4, ’07)
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Test Problem 1. A U-tube manometer is built with unequal tube diameters in the two legs. The right side tube diameter D is much larger than the left side tube diameter d=0.1 mm. Bothe sides are open to the atmosphere. Surface tension (capillary action) raises the left side liquid level a distance h above the right side surface. The liquid is water and the surface tension is 0.073 N/m. The water meniscus meets the tube wall at an angle of 45°. By analyzing an appropriate control volume within the water, find h. Ans. H=0.211 m The U tube manometer is a glass tube bent like the letter U. It has two vertical sections, each open at the top. Water partially fills the tube, including part of the vertical sections. If the whole tube were of large diameter, the level of the water would be the same in both vertical
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Unformatted text preview: sections. However, surface tension pulls the water up further in the small diameter section. You analyze it by making a free body out of the water in the small section, bounded at the bottom by a surface at the same elevation as the water in the large section, and at the top by the curved meniscus. The curved surface surface tension is exposed by the control surface cutting the water/air interface at the tube wall. There are two net forces on the water free body: weight and surface tension. Atmospheric pressure acts on the top and bottom of the free body, so it cancels. The surface tension force magnitude is sigma*perimeter, and it is angled upward at 45 degrees. Balancing vertical forces, sigma*pi*d*sin theta = rho*g*pi*d^2/4 * h. Then solve for h....
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Rec1 - sections. However, surface tension pulls the water...

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