Q.What are meant by turbulent flow and stream-line flow? Find the dimension of coefficient of viscosity. Write down Stokes' law and derive it from dimensional analysis.

Find [η] from its defining relation, then assume F depends on η, r, v as a power law and match dimensions to derive Stokes' law up to the constant.

Streamline (laminar) flow: flow in which every fluid particle passing a given point follows the same smooth path (the path of the particle before it), with layers of fluid sliding over one another without mixing.

Turbulent flow: flow at high velocity in which the motion becomes irregular and chaotic, with eddies and mixing between layers — streamlines are no longer well defined.

Dimension of coefficient of viscosity ($\eta$): from $F=\eta A\dfrac{dv}{dx}$:

$[\eta]=\frac{[MLT^{-2}]}{[L^2][T^{-1}][L^{-1}]}=[ML^{-1}T^{-1}]$

Stokes' law (by dimensional analysis): assume the viscous drag force on a sphere depends on $\eta$, radius $r$, and velocity $v$ as $F=k\,\eta^a r^b v^c$ ($k$ dimensionless). …