Page 74 - Fluid Power Engineering

Hydraulic Oils and Theor etical Backgr ound 51

5. Define the bulk modulus of oil and derive the equivalent bulk modulus
of an oil-air mixture.
6. Derive the expressions for the resultant hydraulic capacitance of two
hydraulic lines connected in series or in parallel.
7. Derive an expression for the pressure increment in a volume of liquid
trapped in a rigid container when subjected to a temperature increase ΔT.
8. Discuss briefly the effect of the saturated vapor pressure on the function
of hydraulic systems.
9. Calculate the percentage of variation in volume of liquid of bulk modulus
B = 1.4 GPa if its pressure is increased by 10 MPa.
10. A hydraulic pipe line has a diameter D, length L, wall thickness h, material
bulk modulus E, and oil bulk modulus B. Prove that the hydraulic capacitance
of the line is given by:
π DL
2
(a) C = , neglecting the pipe wall deformation
4 B
π DL ⎛ 1 D ⎞
2
(b) C = ⎜ + ⎟ , considering the radial deformation of pipe material
4 ⎝ B Eh⎠
π DL ⎛ 1 5 D ⎞
2
(c) C = ⎜ + ⎟ , considering both of the axial and radial deformations
4 ⎝ B 4 Eh⎠
11. Calculate the difference between the input and output flow rates of a line
if the rate of variation of pressure dP/dt = 13.4 MPa/s, given
D = 10 mm, L = 3 m, B = 1.3, wall thickness h = 1 mm GPa,
Modulus of elasticity of wall material E = 210 GPa
12. (a) Derive an expression for, and calculate, the viscous friction
coefficient for the given spool valve given: L = L = 10 mm, D = 8 mm, c =
2
1
2
2 μm, μ= 0.02 Ns/m .
(b) If the spool performs a rotary motion, derive an expression for the viscous
friction coefficient and calculate its value.

13. Calculate the radial clearance leakage, Q , and the resistance to leakage,
L
R , in the given spool valve if
L
D = 12 mm, c = 7 μm, L = 20 mm
2
μ= 0.018 Ns/m , P = 21 MPa, P = 0
T
P