Page 61 - Fluid Power Engineering

38 Cha pte r T w o

the thermal expansion of the cylinder is negligible with respect to that
of the oil. Therefore, the oil volume remains constant, even when its
temperature increases, due to the combined effect of the oil compress-
ibility and its thermal expansion. The change in pressure (ΔP) due to
temperature variation (ΔT) is deduced as follows. Assuming that the
total volume of oil is constant, then ΔV = 0.

ΔV = ΔV + ΔV = 0 (2.82)
T C

ΔV =− V Δp (2.83)
C B

αVT − V Δ P = 0 (2.84)
Δ
B
or ΔP =α B ΔT (2.85)

where ΔV = Variation of volume due to oil compressibility, m 3
C
Example 2.2 A liquid of (α= 0.0007) and (B = 1 GPa), trapped in a rigid vessel, is
subjected to an increase in temperature of 50°C. Assuming that the vessel is of
negligible thermal expansion, the oil pressure increases by 35 MPa.

2.2.5 Vapor Pressure
All liquids tend to evaporate by projecting molecules into the space
above their surface. If this is a confined space, the partial pressure ex-
erted by the molecules increases until the rate at which molecules reen-
ter the liquid is equal to the rate at which they leave. In this equilibrium
condition, the vapor pressure is the saturated vapor pressure (SVP).
The molecular activity increases with temperature. Also, the reduction
of pressure to values less than SVP induces a rapid rate of evaporation:
boiling. Higher-saturated vapor pressure leads to a higher rate of
evaporation. The vapor pressure is defined as the pressure at which a
liquid will boil. It increases with the increase of oil temperature.
The reduction of the liquid pressure to the SVP leads to cavitation
in a hydraulic system. The term cavitation refers to the formation and
collapse of vapor-filled cavities in the liquid. The collapse of vapor
cavities leads to very great local oil velocities. In the case of displace-
ment pumps, the cavitation occurs when the suction pressure de-
creases below the vapor pressure of oil. The vapor cavities that form
in the suction line of the pump collapse as they travel through the
pump to its high-pressure zones. The collapse, under the action of
high pressure, results in very high local velocities and great impact
forces and pressures (up to 7000 bar), which cause the erosion of the
pump elements. (See Sec. 4.4.)