1.3 Fluid Dynamics
19
1.3.9 Friction Losses
As air flows through a duct or gallery, it loses energy due to friction between fluid
layers, as well as friction between air and walls. In the particular case of mining,
they account for 70–90% of total mine losses. Figure 1.11 depicts the static pressure
losses suffered by a water pipe due to friction when circulating through a horizontal
pipe.
Velocity
head
Friction head
Static head
HGL
EGL,TH
Elevation head
Fig. 1.11 Energy gradients in a flow. HGL, Hydraulic Gradient Line; EGL, Energy Gradient Line
or Total Head (TH)
The total pressure losses by friction
8 ( f ) of a fluid with the walls of the duct
can be calculated using the Darcy–Weisbach equation (Eq. 1.21):
f = f
L
D h
ρ
V
2
2
(1.21)
where
• f : Pressure loss due to friction (Pa),
• f : Darcy friction factor (dimensionless),
• L: Length of the duct (m),
• D h : Hydraulic diameter of the pipe (m),
• v: Fluid velocity (m s
−1 ), and
• ρ: Density of the fluid (kg m
−3 ).
8 As a consequence of the continuity equation, if the cross section in a duct is the same, so is
the velocity. Thus, any pressure loss is total pressure loss if the duct has a constant cross section.
Therefore, as in this case there is no variation in the dynamic pressure, the total pressure loss
coincides with the static pressure loss.