1. For a rectangular gate having its width b, thr force acting on the gate, Fg, is:

Fg = P * b = (ρg/2)(2h1+h2)*h2*b

where,
ρ: fluid (or water) density (kg/m^3)
g : gravity acceleration (m/s^2)
h1, h2, b : water depth, height abd width of gate, respectively (m)

따라서, 계산되는 힘의 단위는 N이 된다.

Acting point of Fg is where the resultant force of forces P1*h2 and  (1/2)*(P2-P1)*h2 acts and the moment from the center of the gate is zero.

At the center of the gate, the moment by P1*h2 is zero. Letting the distance between the center of gate and the point of action og the force as d,

P*d = (1/2)*(P2-P1)*h2*(h2/6)

d = (1/2)*(P2-P1)*h2*(h2/6) / ((1/2)*(P1+P2)*h2) = (h2/6)*(P2-P1)/(P1+P2)

P2-P1 = ρg(h1+h2) - ρgh1 = ρgh2
P1+P2 = ρgh1 + ρg(h1+h2) = ρg(2h1+h2)

d = (h2/6)*(h2/(2h1+h2)) = h2^2 / (6*(2h1+h2)) 가 된다.

2. Location of the point of action of the force, hc (from water surface)

※ Conversion of the force unit into tons