A flocculation basin designed to treat $50,000$ m$3/$d of water is $21$ m long, $15$ m wide, and $3\mathrm{.}60$

m deep. The paddle$-$wheel units consist of four horizontal shafts that rotate at $4$ 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 $3\mathrm{.}30$ 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 $10$C$.$ Determine: $($a$)$ power input to the water, $($b$)$ velocity gradient and retention

time, and $($c$)$ the Gt value.