The figure on the right shows two boundary$-$layer

profiles for the flow over a stationary flat plate:

one for laminar flow and another for turbulent

flow. The flow velocity $$ on the x$-$axis is

normalized with the freestream velocity $.$ The y$-$

axis is the vertical distance from the flat plate.

Both profiles are for the same freestream

conditions and the Reynolds number is $100,000.$

Using the above plot, calculate the ratio of the thickness of the turbulent boundary$-$layer to that of

the laminar boundary$-$layer $($calculate $$turb

$$lam

$).$

a$)$ Calculate the shear stress at the wall for a freestream velocity of $5$ m$/$s with air as fluid using

standard $($sea$-$level$)$ atmospheric conditions. Recall that air is a Newtonian fluid. The figures below

are close$-$ups of the laminar boundary$-$layer profile $($left$)$ and turbulent boundary$-$layer profile

$($right$).$ Note that these two plots have different scales on the y$-$axis.

b$)$ Using the figure on the right, calculate the

ratio of the momentum $$ for a unit mass of air

of the turbulent boundary$-$layer profile to that

of the laminar boundary$-$layer profile $($calculate

$$turb

$$lam

$)$ for y values of $1,2,4,6,$ and $10$ mm$.$

Present your results in a plot of $$ vs $.$