Читать книгу Hydraulic Fluid Power - Andrea Vacca - Страница 40

In the field of hydraulics, it is very common to express flow rates as volumetric flow rates. As it will be discussed in the next chapter, there are two main reasons for that. First, it is straightforward to evaluate the motion velocity of a hydraulic actuator if the volumetric flow through it is known. Second, it is quite common to use volumetric flow meters for the measurement of the flow rate.

This example describes what is the effect of fluid compressibility on the volumetric flow rate.

A hydraulic pump supplies flow to a hydraulic cylinder that lifts a certain load. Due to this load, the pump outlet is pressurized at 100 bar. The inlet flow, from a tank open to atmosphere, is 100 l/min. Determine the volumetric flow exiting the pump. The density of the fluid is 870 kg/m³; bulk modulus of the fluid is 18 000 bar.

Consider the following cases:

1 The pump inlet pressure is the same as the tank pressure.

2 The pump inlet pressure is −0.3 bar gauge pressure.

The Bunsen coefficient for the oil is 9%.

Given:

The pump inlet flow, Q₁ = 100 l/min; the pump outlet pressure p₂ = 100 bar (gauge pressure); the Bunsen coefficient of the oil, α_a = 9 % ; the density of the fluid, ρ = 870 [kg/m³]; the bulk modulus of the fluid B = 18 000 bar.

The inlet pump pressure in two cases: (a) p₁ = p_T = 1 bar (absolute pressure); (b) p₁ = 0.7 bar (absolute pressure).

Find:

The outlet pump flow rate, Q₂, for the two cases (a) and (b).