Air at \(98 \mathrm{kPa}\) and \(20^{\circ} \mathrm{C}\) flows in a horizontal duct of variable cross section. The water column in the manometer that measures the difference between two sections has a vertical displacement of \(5 \mathrm{~cm}\). If the velocity in the first section is low and the friction is negligible, determine the velocity at the second section. Also, if the manometer reading has a possible error of \(\pm 2 \mathrm{~mm}\), conduct an error analysis to estimate the range of validity for the velocity found.