Question 1 Consider two cyclones with a grade efficiency of G(x) and G(x), respectively. The cyclones are arranged in series such that the overflow of cyclone 1 is the feed to cyclone 2, and the underflow from both cyclones are combined into a single stream. (a) Sketch the system and name each of the streams. (b) Prove that the overall grade efficiency is given by G (x) + G(x) - G(x) G (x)

Consider two cyclones with a grade efficiency of G1(x) and G2(x), respectively. The cyclones are arranged in series such that the overflow of cyclone 1 is the feed to cyclone 2 , and the underflow from both cyclones are combined into a single stream. (a) Sketch the system and name each of the streams. (b) Prove that the overall grade efficiency is given by G1(x)+G2(x)G1(x)G2(x)