Develop an expression for the average mass transfer coefficient for a plate of length \(L\), where part of the flow is turbulent for part of the plate. Assume that there is no transition and that the flow is turbulent right at the point where \(R e_{x}=2 \times 10^{5}\) and onwards. Note that integration in two parts is needed.

Use the expression to find the average mass transfer coefficient for flow of air at velocity \(7.5 \mathrm{~m} / \mathrm{s}\) blowing over a pond of water \(300 \mathrm{~m}\) long. At what point does the flow start to become turbulent?