Question #$2$

Consider a duct with height $H$ in which water enters at station $1$ and in which

water exits at station $2$ :

Knowing that the velocity of the water at station $1$ is:

vec$(v{)}_1=\frac{y{q}_{\text{r}\text{e}\text{f}}}{H}$vec$(i)+\frac{y^2{q}_{\text{r}\text{e}\text{f}}}{H^2}$vec$(j)$

determine, at steady$-$state, the mass flow rate of water exiting the duct $(\{$:$m_{\text{o}\text{u}\text{t}}^{}).$

Take the density of water as $1000k\frac{g}{m^3},$ the reference velocity $q_{\text{r}\text{e}\text{f}}$ as $20k\frac{m}{h}r$

and the duct height $H$ as $10$ cm $.$