$($b$)$ A horizontal pipe with a square cross$-$section $($where each side has a length of connects to a divider that separates into $N$ pipes, each with a circular cross$-$section with radius of $r.$ If the speed of the fluid in each of the square pipes corresponds to the speed of the fluid in the circular pipe via $v_{sq}=v_{\text{c}\text{i}\text{r}},$ where $$ is a positive constant, determine $d$ in terms of the variables given in the problem.