A section of a mine is ventilated by two main airways of equal resistance and two splits, N and S. The pressure developed by the main fan is 1250 N/m² and that across the junction of the splits is 750 N/m². The total quantity of air circulating is 42.0 m³/s which splits to 28 m³/s in N and 14 m³/s in S. Calculate the resistance of the mains and of each split.

During reconstruction the following alterations are made:

(a) The cross-sectional areas of both main airways are increased by 25%, the type of lining and shape factor remaining the same.

(b) the removal of obstructions and improvement of linings in split N results in a reduction of resistance of 0.34 gaul in that split;

(c) a regulator of 0.84 m² cross-sectional area is removed from split S.

For each split to receive 28m³/s, calculate;

(i) the pressure required from the main fan,

(P_MF = 992 Pa)

(ii) the pressure to be developed by a booster fan in split S,

(P_BF = 895 Pa) Answer added under (i) and (ii) can you explain me how to find these answers ?