A rapid$-$mix unit is to be designed for treating a raw water of $50,000\frac{m^3}{d}ay.$ Using a detention time of $30$ s conds, determine the size of the tank and the motor horsepower of the mixer, assuming a shaft and a iotor efficiency of $75\%$ and $90\%,$ respectively. Assume a water temperature of $20C,$ a velocity gradient of $\frac{800}{sec}$ and $$ of $10{10}^{-4}k\frac{g}{m}-sec.$