Q$89.$ Water enters a two$-$dimensional, square channel of constant width, $h=75\mathrm{.}5mm,$ with uniform velocity, $U.$ The channel makes a $90$ bend that distorts the flow to produce the linear velocity profile shown at the exit, with $v_{\text{m}\text{a}\text{x}}=2v_{\text{m}\text{i}\text{n}}.$ Evaluate $v_{\text{m}\text{i}\text{n}}.$ If $U=7\mathrm{.}5\frac{m}{s}.$

$($a$)5\frac{m}{s}$

$($b$)10\frac{m}{s}$

$($c$)2\mathrm{.}5\frac{m}{s}$

$($d$)15\frac{m}{s}$