A model fan with wheel diameter 32 in. is tested at a speed of \(1750 \mathrm{rpm}\). The test fluid is air with density \(0.075 \mathrm{lbm} / \mathrm{ft}^{3}\). At its BEP, the fan produces \(8000 \mathrm{ft}^{3} / \mathrm{min}\) at total pressure rise of 8 in. \(\mathrm{H}_{2} \mathrm{O}\). A geometrically similar fan is to handle \(200,000 \mathrm{ft}^{3} / \mathrm{min}\) of flue gas with density \(0.050 \mathrm{lbm} / \mathrm{ft}^{3}\) and \(30 \mathrm{in} . \mathrm{H}_{2} \mathrm{O}\) total pressure rise. Determine the required size and speed of the flue gas fan. Note any assumptions and/or limitations.