Lesson 2 - Principles of Fluid Mechanics 1

We have now examined the pressure that a vertical height of fluid can exert. This concept is also used to directly refer to pressures by the height or, more commonly, head of fluid, i.e. instead of referring to a specific pressure, we often refer to an equivalent vertical head in metres of a fluid. This can be particularly useful when considering situations with tanks, where the vertical head in metres is more easily determined, but any pressure value can be referred to as an equivalent head, in metres, of fluid.

We need to ensure that the correct values of density are used to convert the metres of head value. Not all head values are metres of the same fluid, which is being processed, for example, a head of metres of water may be applied to a wort or beer processing plant. Wort and beer have differing values of density from water.!

Let us look at some worked examples to clarify this concept.

Example:

Convert an atmospheric head of 760 mm Hg (mm of mercury Hg, where the density is 13,600 kg/m³) to a pressure in kPa.

The first thing to notice is that this is the pressure of air in the atmosphere, expressed as a head of mercury, requiring conversion to kPa. We can see here how important it is for us to ensure we interpret the correct fluid.

Using our standard equation for pressure difference at the bottom of a column of, in this case, mercury, Hg:

You will notice we are using the density of mercury, as the head is in metres of mercury, not air.

It is a pretty simple conversion, as long as we take note of which fluid we are dealing with.