Water flows at a velocity $u_{-}1\frac{m}{s}$ over a flat plate of length L $1$ m $.$ Consider two cases of the water temperature are approximately $300$ K and $325$ K $.$ In the laminar and turbulent flow regions, experimental measurements show that the local coefficients are well described by

where $x$ has units of m $.$ Laminar and turbulent coefficients at $300$ K are $400\frac{W}{m^{1\mathrm{.}45}}K$ and $2300\frac{W}{m^{1\mathrm{.}78}}K,$ respectively, and those at $325$ K are $435\frac{W}{m^{145}}K$ and $3000\frac{W}{m^{1\mathrm{.}78}}K,$ respectively. For both temperatures:

a$)$ Find the locations $(x_c)$ where the transition from laminar to turbulent flow begins.

b$)$ Plot the local convection heat transfer coefficients within the ranges

$c0\mathrm{.}01m$ and $x_c.$

$c$