Hydrostatic Pressure


What Does a Hydrostatic Pressure Do?

Applying a Hydrostatic Pressure:

If you have surfaces selected, you can right click in the display area and select the "Add" pull-out menu. Select the "Surface Hydrostatic Pressure..." command.

 

Specify the weight density of the fluid that will cause the hydrostatic pressure in the "Fluid Density" field.

 

The hydrostatic pressure can increase along any direction. First specify a point on the top of the fluid in the "X", "Y" and "Z" fields in the "Point on Fluid Surface" section. Then specify a vector that is normal to the surface of the fluid and points into the fluid using the "Surface Normal of Fluid" section. See Figure 1.

 

Cross-section View (Shell elements shown)

Point P is the global coordinate where the pressure is 0, entered in the "Point on Fluid Surface" fields. The vector V is the direction of the fluid, entered as vector components in "Surface Normal of Fluid" fields.

Figure 1: Hydrostatic Pressure

 

Shell and membrane elements also include a selection for the "Pressure Type". The options are as follows:

  1. "Normal to the surface": The magnitude of the hydrostatic pressure = (fluid density) x (depth below fluid surface), and the direction is normal to the surface of each shell or membrane element. See Figure 2(a).

  2. "Full pressure in horizontal": The magnitude of the hydrostatic pressure will be calculated as usual, but applied in the “horizontal” plane. There is no force parallel to the vector defined by "Surface Normal of Fluid". In other words, the direction is in the plane normal to the “Surface Normal of Fluid” and perpendicular to each shell or membrane element. See Figure 2(b).

  3. "Horizontal component only": This indicates that only the horizontal component of the hydrostatic pressure will be applied. The magnitude of the pressure = (fluid density)x(depth below fluid surface) x sin(angle between element normal and “Surface Normal of Fluid”). The direction is in the plane normal to the “Surface Normal of Fluid” and perpendicular to each shell or membrane element. See Figure 2(c).

Note

If the shell or membrane element is “horizontal”, then the horizontal direction for applying the pressure is not uniquely defined. (That is, the normal direction for the shell and the fluid normal direction are parallel, so the horizontal component of the hydrostatic pressure cannot be defined.) In this situation, the hydrostatic pressure will be 0 for "Pressure Type" of "Full pressure in horizontal" (and "Horizontal component only".) This may cause convergence difficulties as the element wobbles around the horizontal direction. Be aware that the element can become horizontal in a large displacement analysis even if it does not start out horizontal.

 

(a) "Normal to the surface"

(b) "Full pressure in horizontal"

(c) "Horizontal component only"

Figure 2: Types of Hydrostatic Pressure on Shell and Membrane Elements

 

Specify the load curve that will be used to multiply the pressure in the "Load Case / Load Curve" field. If you want to have an additional multiplier applied to this load, specify this value in the "Multiplier" field.

 

If you want the load to maintain the same orientation with respect to the model as it deforms, activate the "Follows Displacement" checkbox.

 

If you are applying the hydrostatic pressure to General shell elements, select the side that you want it to be applied to in the "Side" drop-down box. You can choose between "Top", "Bottom", "Both Sides" or "Neither".

 

Note

The General shell element takes the thickness of the element into account for the pressure loading. (The other planar elements – membrane, Co-rotational and thin shell – consider the pressure to be applied at the midplane. The type of shell element is set in the "Element Defintion" dialog) Thus, the General shell element has options to apply the hydrostatic pressure to the "Top" side, "Bottom" side, "Both Sides", or "Neither" side. The bottom side of the element is the side facing the element normal point defined in the "Element Definition" dialog. A positive pressure points into the element regardless of which side it is applied to.

 

Although the area of the top side of the element equals the area of the bottom side of the element in the stress-free condition, large displacement effects can stretch the two surfaces differently. Thus, although a pressure of -1000 on the top and 1000 on the bottom may appear to be identical graphically, the results can be different. See the figures below. A similar situation occurs with hydrostatic load.

(a) General shell element, one with a negative pressure applied to the top side of the element (left side of figure) and one with a positive pressure applied to the bottom side of the element (right side of figure). In the stress-free condition, the area of the top side and bottom side are the same. (The element normal point is indicated by the "X".)

(b) As the elements stretch, the area of the top and bottom sides also stretch. Thus, the total force due the same pressure on the top as on the bottom may be different. In this example, the top side stretches more than the bottom side, so the force in the model with the pressure on the top is higher than the force in the model with the pressure on the bottom.

 

 

Tip

A common occurrence is the combination of a constant pressure P and a hydrostatic pressure. For example, a tank partially filled with water and pressurized with air on top. Since each surface can have only one pressure applied – either a constant pressure or hydrostatic pressure – how to enter this may not be obvious. With the aid of the following diagram, it can be seen that this combination is identical to a hydrostatic pressure with a higher "free surface".

 

At the top of the water, the pressure is P = (coordinate of higher free surface - coordinate of water surface)*(fluid density). All values are known except for the "coordinate of higher free surface", so calculate this value and enter it for the hydrostatic pressure.

constant pressure + hydrostatic pressure = hydrostatic pressure of greater depth

 

Naturally, the surface number of the model may need to be adjusted so that the hydrostatic pressure is only applied where needed (below the water level) and not in the dotted region of the figure (above the water leve). A constant pressure is applied to the surface above the water level.