$1.(30)$ Water is flowing over the bottom of a surfboard as Betty paddles out through calm water. She is paddling at $\backslash (0\mathrm{.}5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ relative to the water, which has a temperature of $17$ C $.$

a$)$ How far from the nose of the board does the flow transition to turbulence naturally

b$)$ Plot the boundary layer thickness vs$.$ x to scale. $("$to scale" means the same size units on the y $-$axis as the x $-$axis$)$ Make the plot up until the location of the flow transition.

c$)$ Use the table in the book and create a dimensional plot of the velocity profile at the location of flow transition $($but still on the laminar side$).$ Velocity will be on the x $-$axis, and distance from the surfboard on the y $-$axis.

d$)$ Plot the local shear stress on surfboard from the leading edge to the point of transition.

e$)$ Integrate that to obtain the average shear stress in the laminar region.

f$)$ If the board is $2$ m long, what is the average shear stress now including the turbulent region? Comment on your answer.