 Submarines are subject to Hydrostatic Pressure (Photo: ref.)

Hydrostatic pressure is the pressure a fluid exerts onto an underwater structure (be it a pool wall, a container wall, a ship, etc.). Pressure is equal to force per unit area \left(\frac{F}{A}\right) and has the following behaviors:

• Pressure is linearly related to the vertical depth of the object
• Pressure is independent of the size and shape of the container that holds it (only depth and density factors into determining the hydrostatic pressure acting on an object)
• A pressure at any given point will have the same magnitude in all directions (this is referred to as Pascal's Law).
• Since fluids are not capable of supporting any shear stress, the pressure exerted on a submerged object will always be normal to the object's surface (See Figure 1)
 Fluid Statics

### Fluid Pressure

Liquids can be assumed to have constant density over fairly large vertical distances. The same can be said of gases although only over small distances. Given that the pressure of the fluid body is zero at its surface, the pressure at any point below the surface is easily calculated as:

p = \gamma h
p_{psi} = \frac{\gamma h}{144}

where:

p = pressure (lb/ft2)
γ = specific weight of the fluid (lb/ft3)
h = height of water above point (ft)

### Forces on Submerged Planar Surfaces

The resultant force of fluid on a submerged planar surface is defined by its magnitude, direction, and location as shown on the following summary diagram: Figure 1: Forces act normal to a submerged plane

#### Direction

For planar surfaces in a fluid, the pressure direction is always normal to the surface it contacts.

#### Magnitude

The magnitude of the force acting on the planar surface is the volume under the pressure prism: the product of the pressure at its centroid and the area of the plane.

F = \gamma h_c A

where:

γ = specific weight of the fluid (lb/ft3)
hc = height of water above the centroid of area of the planar surface (ft)
A = area of the planar surface (ft2)

#### Location

The location of the force acting on a planar surface is the center of gravity of the pressure prism and is also called the center of pressure (yp).

y_p = \frac{I_o}{y_c A}
I_o = y_c^2 A + I_{cg}
y_p = y_c + \frac{I_{cg}}{y_c A}

where:

yp = distance from origin to center of pressure (ft)
yc = distance from origin to centroid of area (ft)
Io = moment of inertia (in4, ft4)
Icg = moment of inertia about the centroid

Main