What is the Dimensional Formula of Coefficient of Viscosity?

In the study of fluid mechanics, the Coefficient of Viscosity is a critical concept. Its dimensional formula is given as follows,

M ¹ L ^-1 T ^-1

In this formula,

• M stands for Mass,
• L represents Length, and
• T denotes Time.

How to Derive the Coefficient of Viscosity?

The Coefficient of Viscosity (η) can be expressed as F × r × [A × v] ^-1 . . . . . (1)

Here, F refers to the tangential force, r is the distance between the layers of the fluid, A is the Area, and v signifies velocity.

Now, Tangential Force (F) equals Mass times Acceleration, which can be expressed as M × [L T ^-2 ]

Therefore, the dimensional formula of force is M ¹ L ¹ T ^-2 . . . . (2)

Also, the dimensional formulas of area and velocity are L ² and L ¹ T ^-1 respectively . . . . (3)

By substituting equation (2) and (3) in equation (1), we get,

Coefficient of viscosity = F × r × [A × v] ^-1

Or, η = [M L T ^-2 ] × [L] × [L ² ] ^-1 × [L ¹ T ^-1 ] ^-1 = [M ¹ L ^-1 T ^-1 ].

Hence, the Coefficient of Viscosity is dimensionally represented as [M ¹ L ^-1 T ^-1 ].

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