A fan that can provide air speeds up to \(30 \mathrm{~m} / \mathrm{s}\) is to be used in a low-speed wind tunnel with atmospheric air at \(23^{\circ} \mathrm{C}\). If one wishes to use the wind tunnel to study flat-plate boundary layer behavior up to Reynolds numbers of \(R e_{x}=10^{7}\), what is the minimum plate length that should be used? At what distance from the leading edge would transition occur if the critical Reynolds number were \(R e_{x, c}=5 \times 10^{5}\) ?