A dam has a parabolic shape $$\frac{z}{z_0} = \left( \frac {x}{x_0}\right)^2$$ as in shown in figure. with $$x_0 = 3 m$$ and $$z_0 = 7 m$$ The fluid is water (specific weight = 9810 N/m$$^3$$) and atmospheric pressure may be omitted. Compute the horizontal force $$F_H$$ and its line of action from surface of water ‘d’. Assume width of dam is 15 m.

A

$$F_H = 3605 kN, d = 1.16 m$$

B

$$F_H = 3605 kN, d = 4.66 m$$

C

$$F_H = 4300 kN, d = 4.66 m$$

D

$$F_H = 4300 kN, d = 1.16 m$$