The quarter$-$circular gate $1\mathrm{.}2$ m wide and hinged at A seals off the end of a fresh water $($density $=1000k\frac{g}{m^3})$ channel as shown Figure $4.$ Neglect the weight of the gate.

$($a$)$ Calculate the hydrostatic force acting on the gate.

$($b$)$ Calculate the force F required to hold the gate in a closed position against the hydrostatic force of the water.

Answer $(20377$ N$)$