Problem $6.$ Figure below shows an open flow of a liquid with negligible viscosity on a flat plate. Between point $B$ and point $D$ of the plate, a uniform gas flow is injected into the bottom of the liquid through a sieve, converting the liquid with density ${}_L$ into a foamy liquid with density ${}_F.AB$ is a region of clear liquid with the mean velocity $\frac{?}{\text{b}\text{a}\text{r}}(u{)}_L$ and the mean height $h_L.$ The foaming begins at point $B$ and stabilizes at point $C.$ Stabilized foamy liquid region $(CD)$ has the mean velocity $\frac{?}{\text{b}\text{a}\text{r}}(u{)}_F$ and the mean height $\frac{?}{\text{b}\text{a}\text{r}}(h{)}_F.$The upper surface of the flow is exposed to air $(1[$atm$]).$ Gravitational acceleration is $9\mathrm{.}8[\frac{m}{s^2}].$ Provided that $h_L=0\mathrm{.}2[m],h_F=0\mathrm{.}3[m]$ and $u_L=0\mathrm{.}5[\frac{m}{s}],$ calculate the ratio of the density change $\frac{{}_F}{{}_{\text{I}}}$ and the ratio of the pressure change $\frac{p_F}{p_{\text{I}}}$ of the flow. Assume the flow is steady and disregard the vertical momentum transfer from the gas flow.