High School

By the method of dimensions, obtain an expression for the surface tension [tex]s[/tex] of a liquid rising in a capillary tube. Assume that [tex]s[/tex] depends on the mass [tex]m[/tex] of the liquid, the pressure [tex]p[/tex] of the liquid, and the radius [tex]r[/tex] of the capillary tube. Assume [tex]K = \frac{1}{2}[/tex].

Answer :

The formula for surface tension in a capillary tube involves surface tension, contact angle, height, tube radius, liquid density, and gravity.

Surface tension (T) of a liquid rising in a capillary tube can be expressed using the formula 2T cos θ h = rpg, where T is the surface tension, θ is the contact angle, h is the height of the liquid, r is the radius of the capillary tube, p is the density of the liquid, and g is the acceleration due to gravity.

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