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16 Cha pte r T w o

2.2 Basic Properties of Hydraulic Oils

2.2.1 Viscosity

Definitions and Formulas
Viscosity is the name given to the characteristic of a fluid, and describes
the resistance to the laminar movement of two neighboring fluid layers
against each other. Simply, viscosity is the resistance to flow. It results
from the cohesion and interaction between molecules. Consider a fluid
between two infinite plates (see Fig. 2.1). The lower plate is fixed, while
the upper plate is moving at a steady speed v. The upper plate is sub-
jected to a friction force to the left since it is doing work trying to drag
the fluid along with it to the right. The fluid at the top of the channel
will be subjected to an equal and opposite force. Similarly, the lower
plate will be subjected to a friction force to the right since the fluid is
trying to pull the plate along with it to the right. The fluid is subjected
to shear stress, τ, given by Newton’s law of viscosity.

τ = μ du (2.1)
dy
The coefficient of dynamic viscosity, μ, is the shearing stress neces-
sary to induce a unit flow velocity gradient in a fluid. In actual mea-
surement, the viscosity coefficient of a fluid is obtained from the ratio
of shearing stress to shearing rate.

τ
μ = (2.2)
/
du dy
where τ = Shear stress, N/m 2
du/dy = Velocity gradient, s −1
u = Fluid velocity, m/s
y = Displacement perpendicular to the velocity vector, m
2
μ= Coefficient of dynamic viscosity, Ns/m ; μ is often
expressed in poise (P), where 1 P = 0.1 Ns/m 2

FIGURE 2.1 (at y = h, u = v)
Velocity variation v
for a fl uid between
two near parallel
plates.
h u(y)
y

x
(at y = 0, u = 0)