Q$2.$ Air, density $\backslash (1\mathrm{.}23\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ flows past a solid object in a pipe of $2$ m diameter and exits as a free jet as shown. The velocity and pressure upstream are uniform at $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and $50$ Pa $.$ At the exit from the pipe the velocity is non$-$uniform as shown. The shear stress along the wall is negligible. Determine:

$($a$)$ the head loss associated with a fluid particle as it moves from upstream to a position within the wake at the exit plane, and

$($b$)$ the force that the air puts on the object.

You should also check for continuity of the flow.

$[$Ans: $($a$)8\mathrm{.}43$ m $,($b$)\backslash (\backslash$mathbf$\{110.7$ ~ N $]$ ~$\}\backslash )$