A $9$ m high, $8$ m wide rectangular gate is located at the end of an open freshwater tank $($see the figure below$).$

$9$ m

$5$ m

$3$ m

A $9$ m high rectangular gate is located on the right side of an open freshwater tank. The gate is hinged at the top and the bottom is allowed to swing upwards away from the water. A force F pushes the gate to the left, $5$ m below the hinge. A force Fwater pushes the gate to the right, $3$ m above the ground.

The gate is hinged at the top and held in place by a force F$.$ From the equation,

p$1=$ p$0+$gh$,$

the pressure is proportional to the depth of the water, and the average pressure pavg exerted on the gate by the water is

pavg $=$

$$p$2$

$,$

where $$p is the difference in pressure between the bottom of the gate $($p$1)$ and the surface $($p$0).$ The resulting force of the water on the gate is

Fwater $=$ pavgA,

where A is the area of the gate the water acts upon. The resulting force acts $3$ m from the bottom of the gate because the pressure increases with depth. Determine the force $($in N$)$ required to hold the gate in place. $($Enter the magnitude.$)$

N