d$)$ A pipe is bent in the horizontal plane so that the angle between the inlet and the outlet sections of the pipe is $45.$ The inlet dianteter of the pipe is $0\mathrm{.}3$ m and the outlet diameter is $0\mathrm{.}15$ m $.$ The mas flow rate of air through the pipe is $4k\frac{g}{s}$ and air density remains constant throughout at $1\mathrm{.}2k\frac{g}{m^3}.$ Calculate the force on the pipe bend exerted by the air $($in magnitude and direction$)$ if the upstream static pressure of the air is ${10}^5\frac{N}{m^2}.$

$[9$ marks$]$