Given the following expression for the mass flow rate across a surface: $m^{}={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}vec(V)*dvec(S)$

where $$ is the fluid density, vec$(V)$ is the fluid velocity, and dvec$(S)$ is the differential area

element:

a$.$ Compute the mass flow rate $($per unit depth$)$ across faces $1,2,$ and $3.$

b$.$ How is the sign of the mass flow rate related to the orientation of the velocity

vector and the surface?

c$.$ How would you determine the mass flow rate $($per unit depth$)$ along face $4?$

$A_1=2\frac{m}{ms}$

$A_2=4\frac{m}{s}$

$B_2=4\frac{m}{s}$

$A_3=5\frac{m}{m^2(s)}$