Page 225 - Chemical engineering design

202
2
where P f D pressure drop, N/m ,
f D friction factor, CHEMICAL ENGINEERING
L D pipe length, m,
d i D pipe inside diameter, m,
3
D fluid density, kg/m ,
u D fluid velocity, m/s.
The friction factor is a dependent on the Reynolds number and pipe roughness. The
friction factor for use in equation 5.3 can be found from Figure 5.7.
The Renolds number is given by Re D ð u ð d i / 5.4

Values for the absolute surface roughness of commonly used pipes are given in Table 5.2.
The parameter to use with Figure 5.7 is the relative roughness, given by:

relative roughness,e D absolute roughness/pipe inside diameter
Note: the friction factor used in equation 5.3 is related to the shear stress at the pipe wall,
2
R, by the equation f D R/ u . Other workers use different relationships. Their charts
for friction factor will give values that are multiples of those given by Figure 5.7. So, it is
important to make sure that the pressure drop equation used matches the friction factor chart.

Table 5.2. Pipe roughness
Material Absolute roughness, mm
Drawn tubing 0.0015
Commercial steel pipe 0.046
Cast iron pipe 0.26
Concrete pipe 0.3 to 3.0

Non-Newtonian fluids
In equation 5.3, and when calculating the Reynolds number for use with Figure 5.7, the
fluid viscosity and density are taken to be constant. This will be true for Newtonian liquids
but not for non-Newtonian liquids, where the apparent viscosity will be a function of the
shear stress.
More complex methods are needed to determine the pressure drop of non-Newtonian
fluids in pipelines. Suitable methods are given in Volume 2, Chapter 4, and in Chabbra
and Richardson (1999); see also Darby (2001).

Gases
When a gas flows through a pipe the gas density is a function of the pressure and so is deter-
mined by the pressure drop. Equation 5.3 and Figure 5.7 can be used to estimate the pressure
drop, but it may be necessary to divide the pipeline into short sections and sum the results.
Miscellaneous pressure losses
Any obstruction to flow will generate turbulence and cause a pressure drop. So, pipe
fittings, such as: bends, elbows, reducing or enlargement sections, and tee junctions, will
increase the pressure drop in a pipeline.