QUESTION $6$

$3\mathrm{.}50$ Points

Force on curved area

A curved gate depicted in Figure is retaining a $6-m$ depth of water in a storage tank. Determine the magnitude and direction of the total hydrostatic force on the gate.

Gate length $L=10\mathrm{.}5m$;

Finish the following calculations:

$1.)$ Unit weight of water is $q,k\frac{N}{m^3}$

$2.)$ The horizontal component of the final force:

a$.$ it is equal to the hydrostatic pressure force on the $q,$ projection plane:

b$.$ the projection plane ares is $A=q,m^2.$

c$.$ Location of the centroid point of the projection plan is $y=q,$ m

d$.$ hence the magnitude of forizontal force component is $F_H=q,$ kN $.$

e$.$ location of horizontal force component from water ssurface is $y_p={?}_m$

$3.)$ The vertical component of the final force

a$.$ it is equal to the weight of the water with direction pointing $q,.q,$ kN ;

b$.$ Magnitude of the vertical force is $F_V=$

$.$ Final resultant force:

a$.$ Magnitude $R=q,$ kN ;

b$.$ Direction is $=q,0$