A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is $U_o$. The velocity profile at the inlet $a-b$ is uniform, while that at a downstream location $c-d$ is given by $u=U_o\left[2\displaystyle{\left(\frac{y}{\delta }\right)-\left(\frac{y}{\delta }\right)^2}\right]$.
The ratio of the mass flow rate, $\dot{m}_{bd}$ leaving through the horizontal section $b-d$ to that entering through the vertical section $a-b$ is ___________