A$.4$ A U$-$shape channel covered by a lid of $500mm$ long hinged at the top is depicted

in Fig. A$\mathrm{.}4.$ A horizontal water jet of $8mm$ diameter with velocity $10\frac{m}{s}$ strikes

at $250mm$ vertically below the hinge on the lid and the water is deflected

smoothly upward or downward along the lid. A force, F$,$ is applied normally at

the bottom of the lid causing it to a deflection of $30$ clockwise. Assuming that

the weight of the lid is negligible, determine the magnitude of the force, F$.$

$(10$ marks$)$

Shape of the channel lid

Fig. A$.4$