Force on flat surface

A circular gate is installed on a vertical wall as shown in Figure. Detennine the horizontal force $P$

necessary to hold the gate closed.

Gate diameter D $=3\mathrm{.}6$ft;

Gate height $h=7\mathrm{.}2ft$;

Neglect friction at the pivot.

Finish the following calculations:

$1.)$ Set the origin $O$ at the location of

$2.)$ Unit weight of water takes

pcf

$3.)$ Area of the gate $A=$

$f{t}^2.$

$4.)$ Location of the centroid of the gate to the $O$ is $y=$

$5.)$ Magnitude of the resultant force on the gate is

Ibf.

$6.)$ Moment of inertia of the gate is $I=$

$f{t}^4.$

$7.)$ Thus location of the equivalent single resultant force is

ft $.$

$,$

$8.)$ To figure out the required supporting force $P,$ take the ft from $O.$

$9.)$ So the required force $P$ is

Ibf.