Question $3.$

$[15$ Marks$]$

A pipe which is carrying water turns through $50$ in the horizontal plane, at the same time it reduces diameter from $0\mathrm{.}6$ m at the entrance to the bend to $0\mathrm{.}3$ m at the exit. The water is measured as flowing at the rate of $300$ litres$/$s with a pressure at the entrance of $1\mathrm{.}2$ bar.

Neglecting any head loss due to friction, calculate the force exerted by the water on the bend, and its direction of application.