The velocity in a pipe in a turbulent flow can be expressed by the following equation

$u=5\mathrm{.}67[\frac{}{}{]}^{\frac{1}{2}}$

Where $u$ is in $(f\frac{t}{s}),$ is in $(l\frac{b_f}{f}{t}^2),$ and $$ is in $(l\frac{b}{f}{t}^3).$ If the equation above is dimensionally homogeneous

$($a$)$ What are the units for the constant $5\mathrm{.}67?$

$($b$)$ Develope another expression in which the velocity, $,$ and $$ are in SI units.