When we’re performing finite element analysis, we’re always looking for ways to idealize and simplify loading. This both increases the confidence in our results and reduces the overall computational expense required to solve the problem. A great example of this is the ability to estimate the pressure at the bottom of a liquid filled tank, for example, without the need to actually model the fluid. In this blog post, we’ll talk about the method used to estimate this pressure and then how to utilize a define hydrostatic pressure in Abaqus.

## What Is Hydrostatic Pressure

Hydrostatic pressure is the force exerted per unit area, based on the gravity acceleration of a liquid in an enclosure. The deeper the liquid is, the more pressure that it exerts onto the surface of the container – as well as everything in it. Pressure increases linearly from the surface of the liquid to the bottom of the container. Imagine if you are in a pool, think about how much heavier the water feels when you dive deep into the water compared to just swimming at the surface level.

Hydrostatic pressure is a function of the density and depth of the liquid as well as the constant for gravity as shown below the schematic above. Ensure that your units remain consistent either in metric or imperial. Remember that the height value is measured from the surface of the liquid downwards.

It is worth noting that neither the shape nor the mass of the liquid are part of this calculation. This is because, unlike a solid, liquids take the shape of their containers. This is easy to visualize for a column of liquid, but less so when it comes to oddly shaped containers. A cone, for example, will contain less liquid than a cylinder. However, the hydrostatic pressure at the bottom of it will be the same given the same depth of liquid. This stands for both an upright and an inverted cone (and all other container shapes) as shown below – only density and depth are considered for the calculation:

## Why Does Hydrostatic Pressure Matter

Hydrostatic pressure is extremely important for safety measures when structures are in space or deep water. We want to design parts that can be safely subjected to liquid loading that they are expected to see in service. Piping inside a house or other building is a particularly good example. If plumbing is unable to hold its liquid load (as well as any additional applied pressure), the piping will simply burst. Using FEA, we need hydrostatic pressure calculations to validate the amount of stress and displacement a structure will undergo from this liquid loading.

Unfortunately, this hydrostatic pressure estimation method does have some limitations. For example, these calculations cannot be used when the structure properties may absorb some of the liquid, such as sand or gravel. It also fails if the liquid has a non-constant density value.

## Using Hydrostatic Pressure In Abaqus

First, ensure that the hydrostatic pressure loading will vary with respect to z axis. In Abaqus, you may need to adjust the orientation of your model to account for this restriction.

In the load module, select Load > Create (remember that loading cannot occur in the initial step):

Select pressure loading & highlight the surfaces that will be subjected to the liquid loading:

A pressure vessel, for example, will have water filled inside the container. Thus, the hydrostatic pressure loading needs to be applied to all inner surfaces of the structure, as highlighted above:

Abaqus has the hydrostatic distribution option already built in:

Finally, input the magnitude of the hydrostatic pressure for any (non-zero) reference point. Specify the Z coordinate value for the surface of the liquid (where it is zero pressure) and the Z coordinate value for the reference magnitude input above.

After running the FEA, this is what the results should look like. The stress on the model will increase the deeper the liquid sits in the container, as outlined earlier in this post. Regardless of the actual values for hydrostatic pressure, all models should visually generate similar results.

## Final Thoughts

In conclusion, hydrostatic pressure is simple yet reliably accurate way to represent liquid loading when performing engineering calculations. It works regardless of the structure’s shape. There are, however, some limitations as to when you can use it, depending on type of container material and liquid density. Additionally, when using Abaqus, the structure needs to be correctly oriented. Despite these restrictions, hydrostatic pressure is considered a highly reliable method for simulating liquid behavior (without the liquid) and has been validated thoroughly via field testing.

If you have a project where you think this methodology in Abaqus might come in useful, don’t hesitate to ,**reach out to our team**! We’re here for all your FEA engineering