Читать книгу Hydraulic Fluid Power - Andrea Vacca - Страница 54

The Pascal's law presented in Section 3.1 is related to the basic equation of fluid statics:

(3.3)

Equation (3.3) implies that for a liquid at rest, the pressure linearly increases with depth, due to the effect of gravity. The integration of the differential Eq. (3.3) provides an expression for the pressure difference between two points at different elevation:

(3.4)

The concept expressed by the above Eq. (3.4) is illustrated in Figure 3.2.

Many hydraulic machines are often referred to as “hydrostatic machines” because their basic functioning can be evaluated using only static equations (not involving fluid velocity), as described in Section 3.1. Indeed, in almost all hydraulic components, the effect of fluid pressure is significantly higher than that of fluid velocity, thus making the latter negligible.

Figure 3.2 Fluid pressure increases with depth.

Figure 3.3 Elevation difference in the hydraulic circuit of a mobile application.

Despite this, the basic law of fluid statics is almost always omitted from the analysis of a fluid power system¹. Neglecting elevation effects on fluid pressure is reasonable in all cases in which minimal variation of fluid pressure does not affect the operation of the systems. To better explain this concept, Figure 3.3 shows an example of a circuit of a mobile machine.

A reasonable value for h can be 3 m. Considering a fluid density of 870 kg/m³, which is typical for a hydraulic oil, the pressure difference between two points with the maximum elevation difference is

(3.5)

which is considerably lower than the typical operating pressure of the system, which is easily above 100 bar.

The elevation difference in typical hydrostatic circuits can be neglected when calculating the system pressures. The effects of elevation become critical only when in parts of the system the pressure is close to the saturation conditions, such as at the suction of hydraulic pumps.