Page 53 - Fluid Power Engineering

30 Cha pte r T w o

Q
v = (2.45)
A
ρ L dQ dQ
Then, ΔP = = I (2.46)
A dt dt

The hydraulic inertia, I, is given by

ρ L 4 ρ L
I = = (2.47)
A π D 2

where A = Line cross-sectional area, m 2
D = Line inner diameter, m
I = Line inertia, kg/m 4
L = Line length, m
The hydraulic inertia affects the transient response of the hydraulic
transmission lines, but it has no significant effect on its steady state
behavior.

2.2.3 Oil Compressibility

Definition
Liquids are of very low compressibility, while gases are highly com-
pressible. Therefore, liquids are usually assumed incompressible. But
this assumption is applied when the liquid compressibility has no
significant effect on the performance of the studied system.
The liquid compressibility is defined as the ability of liquid to
change its volume when its pressure varies. For pure liquid, the rela-
tion between the liquid volume and pressure variations is described
by the following formula:

Δ P dP
B =− =− or B =− dP =− dP dV (2.48)
Δ VV dV V V dV dt dt
/
/
where ΔP = Pressure variation, Pa
ΔV = Change in volume due to pressure variation, m 3
V = Initial liquid volume, m 3
B = Bulk modulus of liquid, typically B = 1 to 2 GPa for
mineral oils
The hydraulic oil compressibility has a direct impact on the tran-
sient behavior of the hydraulic system. Generally, the reduction of oil
volume by 1% requires an increase of its pressure by 10 to 20 MPa.
The bulk modulus of hydraulic oil is affected by the oil pressure
and temperature. Figures 2.15 and 2.16 illustrate the effect of the oil