$6$ HW$.$ A hydrocarbon liquid enters a simple flow system shown in Fig. $3$ at an average velocity of $1\mathrm{.}282\frac{m}{s},$ where $A_1=4\mathrm{.}33{10}^{-3}{m}^2$ and $=902k\frac{g}{m^3}.$ The liquid is heated in the process and the exit density is $875k\frac{g}{m^3}.$ The cross$-$ sectional area at point $2$ is $5\mathrm{.}26{10}^{-3}{m}^2.$ The process is steady state.

a$.$ Calculate the mass flow rate $(m)$ at the exit and the entrance.

b$.$ Calculate the average velocity $G$ in $1.$