Textbook Problem

Hydraulics In Exercises 43-46. determine the location of the horizontal axis $y_a$ at which a vertical gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading (see figure). The model for $y_a$ is

$y_a=\bar{y}-\frac{I_{\bar{y}}}{hA}$

where $\bar{y}$ is the y-coordinate of the centroid of the gale, $I_y$ is the moment of inertia of the gate about the line $y=\bar{y},h$, h is the depth of the centroid below the surface, and A is the area of the gate.