Question $3$

Experiments show the boundary layer begins to transitions from laminar to turbulent at a Reynolds number of $500,000.$ Assume the boundary layer thickness can still be predicted using the assumption of laminar flow at this location.

$($a$)$ Determine the boundary layer thickness $($in cm $)$ at $\backslash (\backslash$mathrm$\{$x$\}\_\{\backslash$mathrm$\{$cr$\}\}\backslash )$ for air $($density is $\backslash (1\mathrm{.}25\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ viscosity $\backslash (0\mathrm{.}000018\backslash$mathrm$\{$~Pa$\}-\backslash$mathrm$\{$s$\}\backslash ))$ at $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$($a$)$ The same air flows over a flat roof with the dimension of $3$ m by $3$ m $.$ Determine the drag force exerted on the roof, and the shear stress on the roof surface.