Answer to Question #121969 in Civil and Environmental Engineering for Ayush

Question

A rectangular plate 0f 7 ft by 3.5 ft at an angle 450 with the horizontal, and the 7 ft side is
horizontal. Calculate the magnitude of the force on one side of the plate and the depth of its centre
of its pressure when the top of edge is
(a) at free water surface
(b) 1.75 ft below the water surface.

Answer 1

the plane is symmetrical about y axis therefore

x=x_c=1.75ft

the depth of the centroid from free surface h_c=1.75sin45

=1.24ft therefore 1ft=0.3084m :1.24*0.3084=0.38m

F=pgh_cA=1000*9.81*0.38*2.134*1.07=8.512KN

l_x'x¹=bd³/12

=2.134*1.07/12

0.1903;y_c=0.38

y=lx^'x¹/y_cA+Y_C

Yc=0.38

=0.38+0.1903/(0.38*A)

A=2.134*1.07=2.2834m

=0.38+0.1903/0.38*2.2834

=0.38+0.22

=0.6m at free surface

b)depth below the water surface

depth of the centroid below =45+0.38=45.38

F=pghcA

F=1000*9.81*45.38*2.28=1015.01KN

Yc=45/sin45+0.5=64.14

y=0.1903/64.14*A+64.14

=0.1903/146.24+64.14

=0.0013+64.14 =64.1413

now we can say it's from the water surface=0.1413 is the magnitude from the upper edge of the plate.