The laminar flow of a certain aqueous polystyrene sulfonate solution can be represented by the Ostwald-de Waele model with an exponent of 0.500. The solution is contained in a tank that is a vertical cylinder. Solution flows out through a horizontal tube attached to the bottom of the tank. 

(a) If the time for the height of solution in the tank to fall from 10.00 to 9.90 m is 30.0 min, how much time will it take to half-empty the tank (from a height of 10.0 m down to a height of 5.0 m)? 

(b) If the tank has a diameter of 2.0 m and the pipe has a diameter of 0.050 m with a length of 200 m, what is the flow consistency index of the solution? The solution has a density of 1,200 kg/m³.