One of the most challenging problems in environmental remediation is isolated blobs of contaminated fluid that become trapped in soils by capillary forces (i.e., surface tension). The pore space can be analyzed by analogy to a thin-diameter glass tube. Under the conditions given, what is the maximum length of water, I, that can be retained in the vertical glass tube shown? [mm] • contact angle 0 = 0° • surface tension - 72 dyn/cm = 0.072 N/m • tube diameter D = 2.0 mm • neglect the small volume of water above the meniscus • the weight of water completely removes the curvature in the lower air-water interface

Structural Analysis
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Author:KASSIMALI, Aslam.
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One of the most challenging problems in environmental remediation is isolated blobs of
contaminated fluid that become trapped in soils by capillary forces (i.e., surface
tension). The pore space can be analyzed by analogy to a thin-diameter glass tube.
Under the conditions given, what is the maximum length of water, I, that can be
retained in the vertical glass tube shown? [mm]
• contact angle 0 = 0⁰
• surface tension o= 72 dyn/cm = 0.072 N/m
• tube diameter D = 2.0 mm
•
●
neglect the small volume of water above the meniscus
the weight of water completely removes the curvature in the lower air-water interface
Transcribed Image Text:One of the most challenging problems in environmental remediation is isolated blobs of contaminated fluid that become trapped in soils by capillary forces (i.e., surface tension). The pore space can be analyzed by analogy to a thin-diameter glass tube. Under the conditions given, what is the maximum length of water, I, that can be retained in the vertical glass tube shown? [mm] • contact angle 0 = 0⁰ • surface tension o= 72 dyn/cm = 0.072 N/m • tube diameter D = 2.0 mm • ● neglect the small volume of water above the meniscus the weight of water completely removes the curvature in the lower air-water interface
Expert Solution
Step 1: Capillary Rise

Capillary rise is the movement of a fluid in a thin tube above the general level of the fluid, when the tube is held vertically in the fluid.


The expression for capillary rise (h) can be written as:

h equals fraction numerator 4 cross times sigma cross times cos open parentheses theta close parentheses over denominator gamma cross times d end fraction

sigma: surface tension of the fluid

theta: contact angle between tube and the fluid surface

gamma: specific weight of the fluid

d: diameter of the tube

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