Page 102 - Fluid Power Engineering

76 Cha pte r T h ree

Example 3.2 Find the transfer function relating the pressures and flow rates
at the two extremities of an open end line; the line end is open to atmosphere.

In the case of an open end line, P = 0
L
+
)
Q = Q and P = ( Is R Q L
L
o
o
or
Q 1
L =
+
P Is R
o
3.6 Exercises

1. Explain the different types of losses in the hydraulic transmission lines.
2. Explain in detail how to calculate the power losses due to friction in the
hydraulic transmission lines.

3. Discuss in detail the modeling of hydraulic transmission lines assuming
lumped parameters. State clearly your assumptions and derive the transfer
matrix relating the inlet and outlet pressures and flow rates.

4. Equation (3.19) describes the relation between pressures and flow rates
in a hydraulic pipe line, assuming lumped parameters. Give the expressions
for I, R, and C.

P s), and find
5. (a) Derive the transfer function of an open end line, Q /(
L o
the expressions for its parameters.
(b) A hydraulic line whose end is open to the atmosphere has the following
parameters:
3
Pipe length L = 3.5 m, pipe diameter D = 8 mm, oil density ρ = 850 kg/m ,
2
oil viscosity μ = 0.018 Ns/m , and oil bulk modulus B = 1.3 GPa.
Calculate the coefficients of the transfer function and plot in scale its
response to a step input pressure of 0.5 bar.
6. (a) Derive the transfer function of a closed end line, PP s/( ), and find
L o
the expressions for its parameters.
(b) A hydraulic line with a closed end has the following parameters.
L = 3 m, D = 10 mm, ρ = 867 kg/m , μ = 0.13 Ns/m , and B = 1 GPa.
3
2
Calculate the coefficients of the transfer function and plot in scale its
response to a step input pressure of 100 bar magnitude.