$[4]$ Air at $300$ K flows over a flat plate at a speed of $U_{}=2\frac{m}{s}.$ Calculate the boundary layer thicknesses at distances of $0\mathrm{.}1$ m and $0\mathrm{.}3$ m from the leading edge of the plate. Also calculate the difference in the mass flow rates per unit width of the plate within the boundary layer between sections at distances of $0\mathrm{.}1$ m and $0\mathrm{.}3$ m from the leading edge of the plate. Assume the velocity profile within the boundary layer to be given by $\frac{u}{U_{}}=\frac{3}{2}(\frac{y}{})-\frac{1}{2}(\frac{y}{}{)}^3,$ where $$ is the boundary layer thickness. For air, density is $1\mathrm{.}17k\frac{g}{m^3}$ and kinematic viscosity is $1\mathrm{.}85{10}^{-06}\frac{m^2}{s}.$