$($Flowrate$)$ Water flows through the rectangular channel shown in the figure below with a uniform velocity. Directly integrate equations for $B_{\text{o}\text{u}\text{t}}^{}$ and $B_{in}^{}$ with $b=1$ to determine $($a$)$ the mass flowrate $)$ across and $A-B$ of the control volume. $($b$)$ Repeat for $C-$ D$.$

$B_{\text{o}\text{u}\text{t}}^{}={\displaystyle \underset{c{s}_{\text{o}\text{u}\text{t}}}{\overset{\phantom{}}{}}}bV*hat(n)dA$

$B_{in}^{}={\displaystyle \underset{C{s}_{in}}{\overset{\phantom{}}{}}}bVcosdA=-{\displaystyle \underset{c{s}_{in}}{\overset{\phantom{}}{}}}bV*hat(n)dA$

$($a$)k\frac{g}{s}$

$($b$)$ kg$/$s