1. A vertical concentric annulus, with outer radius r, and inner radius r, is lowered into fluid of surface tension o and contact angle 0< 90°. Derive an expression for the capillary rise h in the annular gap, if the gap is very narrow.

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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1. A vertical concentric annulus, with outer radius r, and inner radius r, is
lowered into fluid of surface tension o and contact angle 0 < 90°. Derive an
expression for the capillary rise h in the annular gap, if the gap is very
narrow.
2. A solid cylindrical needle of diameter d, length L, and density o n may "float"
on a liquid surface. Neglect buoyancy and assume a contact angle of 0°.
Calculate the maximum diameter needle able to float on the surface.
3. Derive an expression for the capillary height change h, as shown, for a fluid
of surface tension Y and contact angle 0 between two parallel plates W apart.
Evaluate h for water at 20°C if W = 0.5 mm.
Transcribed Image Text:1. A vertical concentric annulus, with outer radius r, and inner radius r, is lowered into fluid of surface tension o and contact angle 0 < 90°. Derive an expression for the capillary rise h in the annular gap, if the gap is very narrow. 2. A solid cylindrical needle of diameter d, length L, and density o n may "float" on a liquid surface. Neglect buoyancy and assume a contact angle of 0°. Calculate the maximum diameter needle able to float on the surface. 3. Derive an expression for the capillary height change h, as shown, for a fluid of surface tension Y and contact angle 0 between two parallel plates W apart. Evaluate h for water at 20°C if W = 0.5 mm.
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