Russian Journal of Applied Chemistry, 2010, Vol. 83, No. 9, pp. 1593−1597.
Pleiades Publishing, Ltd., 2010.
Original Russian Text
Yu.G. Chesnokov, 2010, Vol. 83, No. 9, pp. 1493−1498.
PROCESSES AND EQUIPMENT
OF CHEMICAL INDUSTRY
Computation of Some Characteristics
of Gas or Liquid Turbulent Flow in a Circular Pipe
Yu. G. Chesnokov
St. Petersburg State Technological Institute, St. Petersburg, Russia
Received May 13, 2010
Abstract—The dependence of the type of velocity proﬁ le in turbulent ﬂ ow of liquids and gases in a circular tube
outside the viscous sublayer and buffer area on the Reynolds number was examined. On this basis, the dependence
of the ratio of the velocity averaged over a pipe cross section to maximum velocity, as well as parameters in the
balance equation of mechanical energy and momentum on the Reynolds number were studied.
Ratios including turbulent ﬂ ow parameters averag-
ed relative to pipe cross-section characteristics are
frequently used in engineering calculations. For example,
for the experimental determination of the ﬂ ow a method
suggested in  can be used that consists of measuring
the velocity u
along a pipe line axis. Then, the ratio of
the velocity averaged over cross-section of the pipe to
the velocity on the axis was determined depending on
the Reynolds number calculated by the velocity on the
axis and the ﬂ ow was computed by a ﬂ ow equation. In
literature [1, 2], this dependence is usually presented as
graphs that leads to signiﬁ cant errors in calculations.
Computation of an energy spent on moving of liquid
or gas in pipe lines is based on use of the balance
equation of mechanical energy (Bernoulli’s equation
for real fluid). This equation includes the terms
in the form
where ρ is a liquid density,
, the velocity averaged over the pipe cross-
section of the liquid, S, an area of the cross-section of
the pipe, u, a local liquid velocity, that is the velocity at
a certain point of the cross-section.
As a rule it is assumed that in the enhanced turbulent
ﬂ ow regime the velocity proﬁ le differs little from ﬂ at
one and this term is approximately substituted by ρU
In order to account for a difference of the velocity
proﬁ le from the ﬂ at in this term a correction factor
a is introduced  and it is written as ρаU
correction factor depends on Reynolds number and is
reported in  for several values of this criterion. In the
case of laminar ﬂ ow а = 2.
Similarly, in the balance equation of momentum
appears a term. This term in the balance equation is
represented as ρa
, where a
is another correction
factor, which also depends on Reynolds number.
Indicative values of this factor are also reported in .
When laminar ﬂ ow a
For computation of the above characteristics of
turbulent ﬂ ow at different values of Reynolds number,
it is necessary to determine the dependence of the ﬂ uid
velocity u on the distance to the pipe axis. Recently new
experimental data were presented [5, 6] on the velocity
distribution over the pipe section in the turbulent ﬂ ow of
air in a pipe with smooth walls. In these studies failed to
reach very high values of Reynolds number Re = ρUd/μ,
where d was diameter of the pipe, μ, viscosity. In these
experiments, Reynolds number varied from 3.1 × 10
3.5 × 10
. The experimental data allowed, in particular, to
redetermine the coefﬁ cients in the so-called logarithmic
resistance law . With these experimental data for each
value of Reynolds number at which the experiments were
performed, one can numerically calculate the integrals
of the expressions for above noted parameters and as