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**Hydrostatic forces on a gate with no width??**

## Homework Statement

A gate is placed at the bottom of a dam wall at a distance of "H" below the surface (measured from the top of the gate). The gate is hinged so that there is 1.2m above the pivot point and 0.8m below the pivot. A stop is placed at the bottom of the gate to stop it from rotating. As the height of the water increases the force on the upper section of the gate will increase and eventually open the gate. Calculate the size of "H" in order for the gate to open.

*no gate width was given

*fluid in question is water

## Homework Equations

F(resultant)=γ.yc.A

F(position)=I/(yc.A)+yc

## The Attempt at a Solution

I know the solution for this question is 0.666m from the answers. So far I have used the resultant force equation to calculate the force for both the top and bottom section of the gate and then attempted to find the force position using the second equation before finally putting this information into a moment equation about the pivot point. My only problem is that the only examples i can find use a gate width and so far using this method I haven't been able to come to answer that matches. In both of the equations I have listed I have attempted to substitute length of the gate for area, however, obviously this doesn't work. Any help would be great, thanks!