Lesson 2 - Principles of Fluid Mechanics 1

There are times when we wish to relate a pressure value to two differing benchmarks. These are:

• A pressure relative to atmospheric pressure, i.e. we want to know how much the pressure is above atmospheric pressure. This is called gauge pressure and will be the pressure we would read with a pressure gauge on, for example, a bottle of compressed gas. When the bottle is empty, the gauge will read zero.

We designate gauge pressures with a small g, sometimes in brackets, or as a subscript after the symbol P, e.g. bar g, bar (g) or P_g.

• A pressure which includes atmospheric pressure – called absolute pressure. In the example above of the gauge on the compressed gas bottle, when the bottle was full, and the gauge perhaps showed 10 bar, then the absolute pressure would be 10 + atmospheric pressure. So, if atmospheric pressure was 1 bar, then the absolute pressure would be 10 + 1, so 11 bar absolute.

We designate absolute pressures with a small a, sometimes in brackets, or as a subscript after the symbol P, e.g. bar a, bar (a) or Pₐ.

Mathematically, gauge and absolute pressure are related as follows:

Let us have a look at a worked example to understand better how to apply these concepts.

Example:

We are responsible for the management of fermenters at two breweries: one at sea level, where the atmospheric pressure is 100 kPa, and another which is located at altitude, where the atmospheric pressure is 80 kPa. For product consistency reasons, we have been asked to ensure that both sets of fermenters operate at the same maximum absolute pressure of 120 kPa. What would be the maximum gauge pressures on the fermenters at both breweries?

We know that gauge, absolute and atmospheric pressures are related by:

Rearranging this equation to make P_Gauge the subject gives:

For the sea level brewery, the gauge pressure is determined by:

And likewise, for the brewery at altitude:

The fermenters at altitude would have double the maximum gauge pressure operating limit.

We have explored pressure as a parameter in some detail. Let us now look at how the value of pressure can be influenced by vertical differences of height, such as that found at the bottom of a fermenter.