The dimension of coefficient of viscosity η is:

The dimension of the coefficient of viscosity, often denoted as η (eta), can be expressed in terms of fundamental physical dimensions. In the International System of Units (SI), viscosity is measured in units of pascal-seconds (Pa·s) or N·s/m^2, which are equivalent. The dimension of the coefficient of viscosity η can be represented as:

[η] = [Pa·s] = [N·s/m^2] = [kg/(m·s)]

Where:

[η] represents the dimension of the coefficient of viscosity (η).
[Pa] represents pascals, the unit of pressure (1 pascal = 1 N/m^2).
[s] represents seconds, the unit of time.
[N] represents newtons, the unit of force.
[m] represents meters, the unit of length.
[kg] represents kilograms, the unit of mass.
So, the dimension of the coefficient of viscosity η is [kg/(m·s)].