Density of liquids and gases

Both gases and liquids have a certain density ρ. As with viscosity or surface tension, this is a specific rheological value. The density of liquids depends primarily on the fluid temperature. Fluid pressure plays only a minor role here.

This does not apply to gases! In addition to the temperature, the pressure p must always be taken into account here, because gases are compressible.

The density - limiting factor for the flow velocity

The liquid density ρ is especially important for pressure nozzles. This is due to the fact that in these nozzle types a pressure difference Δp is used to allow the liquid to escape at a certain velocity v from the nozzle orifice.

This velocity is relevant for the disintegration of a liquid jet or a lamella to drops. The maximum flow velocity vmax can be easily calculated with the formula shown for the frictionless case.

In this context, friction-free means that the viscosity of the liquid should not play a role. In this respect, this is a limit value estimate and a theoretical consideration. In reality, the flow velocity is lower than that calculated using the formula above. And thus, of course, also the actual flow rate at a given pressure differential Δp.

These "friction losses" depend on the one hand on the Reynolds number and on the other hand on the geometric design of the nozzle itself. It is obvious that additional fluid diversions inside the nozzle or installed turbulence bodies cause an additional loss of pressure. Of course, such fluidic installations can result in a significantly lower flow rate than calculated on the basis of friction-free theory. At the same time, however, they promote the breaking up of liquid jets and thus generally ensure finer atomisation.

A calculation example:

Water with a density of ρ = 998 kg/m3  under a differential pressure of 5 bar flows out of a nozzle orifice. The maximum flow velocity is then:

Density of air and gases

The density of gases can be calculated in good approximation with the formula shown. M is the molar mass, R is the universal gas constant and T is the temperature in Kelvin; "ideal gas law".

The density of gases is significantly lower than that of liquids.

As a result, the flow velocity of gases exhibit higher values even at relatively low pressure differences! This effect is used by two-substance nozzles! For example, the flow velocity of air at a gas pressure difference of slightly more than one bar already reaches the speed of sound!

In order to achieve such high velocities for a liquid with a density of almost 1000 times that of air, extremely high pressure differences would be necessary.

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