A fan is used to supply air through the duct. The relation between the volume flow rate, \(Q\left(\mathrm{~m}^{3} / \mathrm{s}ight.\).) and pressure difference, \(P(\mathrm{~Pa})\) is given below:

Calculate the value of \(Q\) and \(P\) using the Newton-Raphson method. Carry out one iteration and use initial value of \(P=330 \mathrm{~Pa}\) and \(Q=6.5 \mathrm{~m}^{3} / \mathrm{s}\).

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Q=15-75 x 10 6 P2; P = 80+10.5 Q5/3