LearnChemE

#### Submerged Gates: Screencasts

Determines the magnitude and location of the resultant force on a submerged gate.

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Explains and determines all of the forces acting on a rotating gate that levels a water reservoir on the other side.

We suggest you list the important points in this screencast as a way to increase retention.

##### Important Equations:

Hydrostatic force on a plane surface:

$F_R = \gamma h_c A$

where $$F_R$$ is the hydrostatic force
$$\gamma$$ is the specific weight
$$h_c$$ is the height of the centroid
$$A$$ is the area of the surface.

Location of the hydrostatic force on a plane surface: $$(y_R, x_R)$$

$y_R =\frac{I_{xc}}{y_c A} +y_c$

$x_R =\frac{I_{xc}}{y_c A} +x_c$

where $$I_{xc}$$ is the moment of inertia
$$y_c$$ is the y-coordinate of the centroid of area $$A$$
$$x_c$$ is the x-coordinate of the centroid of area $$A$$.

Calculation of moment of arms or hydrostatic forces:

$\sum M = 0$

$M = y_R F_R$