   Chapter 9, Problem 51P

Chapter
Section
Textbook Problem

A certain fluid has a density of 1.080 kg/m3 and is observed to rise to a height of 2.1 cm in a 1.0-mm-diaimeter tube the contact angle between the wall and the fluid is zero. Calculate the surface tension of the fluid.

To determine
The surface tension of the fluid.

Explanation
The vertical component of surface tension force equals the weight of the column fluid that is Fcosϕ=mgγ(2πr)cosϕ=[ρ(πr2)h]g and this expression is rearranged for surface tension of the fluid.

Given info: The contact angle between wall and the fluid is 0° , the observed height of the fluid is 2.1cm , the diameter of the tube is 1.0mm , acceleration due to gravity is 9.80m/s2 , and the density of the fluid is 1050kg/m3 .

The formula for the surface tension of the fluid is,

γ=hρgr2cosϕ

• h is observed height of the fluid.
• ρ is density of the fluid.
• g is acceleration due to gravity.
• ϕ is contact angle between wall and the fluid.
• r is radius of the tube.

Substitute 0° for ϕ , 2

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