Oxygen $(\backslash$rho $=2\mathrm{.}5$ kg$/$m$3)$ and methane $(\backslash$rho $=1\mathrm{.}5$ kg$/$m$3)$ are mixed in a tank at as shown in the figure.

The velocity of the gases into the mixer is $7$ m$/$s$.$ Where A$1=1$ cm$2,$ A$2=3$ cm$2,$ A$3=3$ cm$2.$Part A:

Oxygen $(=2\mathrm{.}5\frac{kg}{m^3})$ and methane $(=1\mathrm{.}5\frac{kg}{m^3})$ are mixed in a tank at as shown in the figure.

The velocity of the gases into the mixer is $7\frac{m}{s}.$ Where $A_1=1c{m}^2,A2=3c{m}^2,A_3=3c{m}^2.$

If the velocity of the exiting gas is $9\frac{m}{s}$ determine:

$($i$)$ The mass flow rate into the system.

$($ii$)$ The exit density of the gas mixture.