$.)10$ pt $.$ Doran Problem $2\mathrm{.}9$

$2\mathrm{.}9$ Dimensional homogeneity

The terminal eddy size in a fluid in turbulent flow is given by the Kolmogorov seale:

$)$

$(()3$

where $$ is the length scale of the eddies $(m)$ and $$ is the local rate of energy dissipation per unit mass of fluid $(Wk{g}^{-1}).$ Using the principle of dimensional homogeneity, what are the dimensions of the term represented as

$u?$