derivation for surface tension in a capillary rise
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The capillarity tube is cylindrical in shape. So, the area of cross section is πr² and circumference is 2πr.
volume= area × height
v = πr²h
mass = volume × density
M = πr²hρ
force = mass × acceleration
F = Mg (acceleration is taken as g as the fluid is pulled down only by the gravity)
F = πr²hρg
Surface tension = force ÷ circumference
γ = πr²hρg ÷ 2πr
γ = rhρg ÷ 2
volume= area × height
v = πr²h
mass = volume × density
M = πr²hρ
force = mass × acceleration
F = Mg (acceleration is taken as g as the fluid is pulled down only by the gravity)
F = πr²hρg
Surface tension = force ÷ circumference
γ = πr²hρg ÷ 2πr
γ = rhρg ÷ 2
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