Hydrostatics: Forces on Surfaces

When a surface is submerged in a fluid, hydrostatic pressure acts perpendicular to the surface.

Force on Plane Surfaces

For a plane surface of area $A$ inclined at an angle $\theta$, the total hydrostatic force $F$ is:

$F = \gamma \bar{h} A$

• $\bar{h}$ = Vertical depth to the centroid ($C$) of the area.
• $F$ acts at the Center of Pressure ($CP$), not the centroid.

Location of Center of Pressure ($y_p$): The distance measured along the inclined plane from the surface:

$y_p = \bar{y} + \frac{I_{xc}}{\bar{y}A}$

• $\bar{y}$ = Distance to centroid along the incline ($\bar{h} = \bar{y} \sin\theta$)
• $I_{xc}$ = Moment of inertia about the centroidal axis

Force on Curved Surfaces

The force is typically resolved into horizontal ($F_H$) and vertical ($F_V$) components.

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