A developing boundary layer of standard air on a flat plate. The freestream flow outside the boundary layer is undisturbed with \(U=50 \mathrm{~m} / \mathrm{s}\). The plate is \(3 \mathrm{~m}\) wide perpendicular to the diagram. Assume flow in the boundary layer is turbulent, with a \(\frac{1}{7}\)-power velocity profile, and that \(\delta=19 \mathrm{~mm}\) at surface \(b c\). Calculate the mass flow rate across surface \(a d\) and the mass flux across surface \(a b\). Evaluate the \(x\) momentum flux across surface \(a b\). Determine the drag force exerted on the flat plate between \(d\) and \(c\). Estimate the distance from the leading edge at which transition from laminar to turbulent flow may be expected.