Dimension of Surface Tension & its Derivation

Dimension of Surface Tension: Surface tension is the propensity of liquid surfaces that are at rest to condense into the smallest surface area. It is due to Surface Tension that objects ranging from small needles to large ships can float over water while being partially submerged. Due to cohesion, liquid molecules are more drawn to one another, increasing surface tension. The Dimension of Surface Tension is

M¹L⁰T^-2

In this article, we obtain the Dimension of Surface Tension along with its derivations.

Dimension of Surface Tension

Dimension of Surface Tension and Its Derivation

The Dimensional Formula of Surface Tension is

$~=~{M^1L^0T^{~-2}}$

Derivation of Dimensional Formula of Surface Tension

The Dimensional Formula is written as follows.

$~=~{M^{a}L^{b}T^{~c}}$

Where L is Length, M is Mass, T is Time and a, b and c are the powers of M, L and T respectively

To Derive the Dimensional Formula of Surface Tension, we need to know the following

Dimension of Mass = M¹L⁰T⁰

Dimension of Distance = M⁰L¹T⁰

Dimension of Time = M⁰L⁰T¹

Dimension of Velocity = M⁰L¹T^-1

We know that

The Dimensional Formula of Force is M¹L¹T^-2. Click here to view the derivation

$~=~{M^1L^1T^{~-2}}/{M^0L^1T^{~0}}$

$~=~{M^1L^0T^{-2}}$

Hence proved that the Dimension of Surface Tension M¹L⁰T^-2

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