$($Show work and steps. Circle$/$box final answers$)$ Problem $3^{\text{'}}$

A steady airflow enters a duct $($shown in the figure below$)$ at $50\frac{m}{s}$ with a density of $1\mathrm{.}2k\frac{g}{m^3}$

through an area of $0\mathrm{.}35m^2.$ The duct has two outlets, one outlet is $0\mathrm{.}2m^2$ and has air leaving at

a density of $1\mathrm{.}1k\frac{g}{m^3}$ at a velocity of $40\frac{m}{s}.$ The other outlet is also $0\mathrm{.}2m^2$ in area and based

on the outlet pressure and temperature the density of the flow is $1\mathrm{.}15k\frac{g}{m^3}$ Compute the velocity

$V_3.$

$($You may use $C_p=1\mathrm{.}005k\frac{J}{k{g}^0(K)},C_v=0\mathrm{.}718k\frac{J}{k{g}^0(K)},R=287\frac{J}{k{g}^0(K)},$ and $7=1\mathrm{.}4)$