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and is defined by the Newtonian shear stress equation:
t
m = ---- (10.3)
dv
------
dy
where dv is the relative velocity between two parallel layers dy apart, and τ is the shear stress.
The kinematic viscosity is the ratio of the dynamic viscosity to the density of the fluid and is defined
using the following equation:

n = m (10.4)
---
r
In the SI system, the unit of dynamic viscosity is Pascal-seconds (Pa s), and the unit of kinematic viscosity
2
is square meter per second (m /s). Both the dynamic and kinematic vary strongly with temperature.
Bulk Modulus
Bulk modulus is a measure of the compressibility or the stiffness of a fluid. The basic definition of fluid
bulk modulus is the fractional reduction in fluid volume corresponding to unit increase of applied
pressure, expressed using the following equation (McCloy and Martin, 1973):


∂P
b = – V -------  (10.5)

∂V
The bulk modulus can either be defined as the isothermal tangent bulk modulus if the compressibility
is measured under a constant temperature or as the isentropic tangent bulk modulus if the compressibility
is measured under constant entropy.
In analyzing the dynamic behavior of a hydraulic system, the stiffness of the hydraulic container plays
, is often used to consider both the fluid’s com-
a very important role. An effective bulk modulus, b e
, at the same time (Watton, 1989).
pressibility, b f , and container stiffness, b c
1
1
1
---- = ---- + ---- (10.6)
b e b f b c
10.3 Hydraulic Control Valves

Principle of Valve Control

In a fluid power system, hydraulic control valves are used to control the pressure, flow rate, and flow
direction. There are many ways to define a hydraulic valve so that a given valve can be named differently
when it is used in different applications. Commonly, hydraulic valves can be classified based on their
functions, such as pressure, flow, and directional control valves, or based on their control mechanisms,
such as on-off, servo, and proportional electrohydraulic valves, or based on their structures, such as
spool, poppet, and needle valves.
A hydraulic valve controls a fluid power system by opening and closing the flow-passing area of the valve.
Such an adjustable flow-passing area is often described using an orifice area, A o , in engineering practice.
Physically, an orifice is a controllable hydraulic resistance, R h . Under steady-state conditions, a hydraulic
resistance can be defined as a ratio of pressure drop, ∆p, across the valve to the flow rate, q, through the valve.
d ∆p)
(
R h = --------------- (10.7)
dq
Control valves make use of many configurations of orifice to realize various hydraulic resistance char-
acteristics for different applications. Therefore, it is essential to determine the relationship between the

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