A Flocculation bas$$n designed to treat $50\mathrm{.}000$ m$^3/$day of water is $21$ m long, $15$m wider and $3\mathrm{.}6$m deep. The paddle$-$Wheel units consist of $4$ horizontal shafts that rotate at a rpm$.$ The shafts are located perpendicular to the direction of flow at mid$-$depth of the basin. Each shaft is equipped with four paddle wheels $3$m in diameter and each wheel has four blades $3\mathrm{.}3$m long and $150$ mm wide with two blades located on each side of the wheel. The blades. are $300$ mm apart. Assume the water velocity to be $30\%$ of the velocity of the paddles and that the water temperature is $10\backslash$deg C$.$ Determine:

$1.$ The power input to the water

$2.$ The velocity gradiant

$3.$ The retention time

$4.$ The GT value.