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Discussion of “Self-Cleansing Sewer Design Based on Sediment Transport

Principles” by David Butler, Richard May, and John Ackers

Article  in  Journal of Hydraulic Engineering · July 2004

DOI: 10.1061/(ASCE)0733-9429(2004)130:7(722)

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 can be directly applied to suspensions of wide particle size distri-
Discussion of ‘‘Self-Cleansing Sewer bution.
Design Based on Sediment Transport Karabelas 共1977兲 obtained the general solution of the system
Principles’’ by David Butler, Richard May, of Eq. 共1兲 proposed by Hunt 共1954兲 for the flow of multisized
and John Ackers particles in pipelines and channels. On the basis of extensive
analysis of experimental data for multisized particles in closed
April 2003, Vol. 129, No. 4, pp. 276 –282. ducts and open channels collected by Kaushal 共1995兲 in the range
DOI: 10.1061/共ASCE兲0733-9429共2003兲129:4共276兲 of a volumetric efflux concentration from 0.001 to 26% and a
particle size from a few microns to 750 microns, Kaushal et al.
D. R. Kaushal1 and Cyril Clement2 共2002a兲 observed discrepancies in the prediction of composite
1
Senior Lecturer, Civil Engineering Dept., Visvesvaraya National Insti- concentration profiles by Karabelas’ 共1977兲 solution at higher ef-
tute of Technology, Nagpur—440011, Maharashtra, India. E-mail: flux concentrations. Kaushal et al. 共2002a兲 modified the Kara-
Downloaded from ascelibrary.org by Indian Institute of Technology, Delhi on 09/28/15. Copyright ASCE. For personal use only; all rights reserved.

dkaushal@vnitnagpur.ac.in
2 belas 共1977兲 model by considering the effect of efflux concentra-
Post Graduate Student, Civil Engineering Dept., Visvesvaraya National
tion on particle diffusivity (␧ s ) and settling velocity. On the basis
Institute of Technology, Nagpur—440011, Maharashtra, India.
of a comparison with experimental data, Kaushal et al. 共2002a兲
observed that the modified Karabelas model also shows good
The writers acknowledge the authors’ excellent contribution to
agreements at higher efflux concentrations. Kaushal and Tomita
develop a new design methodology for sewers based mainly on
共2002c兲 compared the solids concentration profiles based on the
sediment mobility data from laboratory pipe-flume experiments
modified Karabelas model with experimental data and observed
using single-sized sediment. The authors have also considered the that the model predicts more asymmetric profiles for larger par-
effects of sediment deposition on the hydraulic performance of ticles and less asymmetric profiles for finer particles. Kaushal and
sewers in the design methodology. This discussion stems from the Tomita 共2002d兲 modified their previous model for composite and
main limitation of the design methodology that it is based mainly solids concentration profiles by considering the effect of particle
on single-sized sediment. The writers also attempted to comple- size and efflux concentration on particle diffusivity. The modified
ment some less addressed, yet relevant, aspects of sewer design method is compared with experimental data and shows good
with deposited beds. agreement for composite as well as solids concentration profiles.
O’Brien 共1933兲 and Rouse 共1937兲 presented an advection/ From the modified Karabelas model, Kaushal et al. 共2002a兲 ob-
diffusion method to predict the variation of particle concentration tained the overall concentration profile across the cross section at
with depth in sediment-laden open channel flow. According to the measured deposition velocity. From the analysis of predicted
this method, the rate of upward transfer of suspended particles concentration profiles, it is concluded that the ratio of concentra-
due to turbulence (⫺␧ s dC/dy) is in equilibrium with the down- tion at the bottom to the static settled concentration can be used
ward exchange due to gravitational forces (wC), where effectively as a tool to evaluate the deposition velocity. Deposi-
w⫽settling velocity; C⫽concentration; ␧ s ⫽particle diffusivity; tion occurs when the solid concentration at the bottom reaches
and (dC/dy)⫽concentration gradient. The value ␧ s is defined as approximately three times the product of efflux concentration and
(␤␧ 1 ), where ␤ is dimensionless particle diffusivity and ␧ 1 is static settled concentration by volume. This methodology can be
liquid diffusivity or eddy viscosity of liquid. This method is at- used for finding the minimum design velocity for multisized par-
tractive in that the only parameter that is not very well quantified ticles transport in sewers by considering its hydraulic diameter.
is the dimensionless particle diffusivity 共␤兲. This model of par- The writers are of the same opinion as the authors that a small
ticle suspension may be traced back to the work of O’Brien amount of deposition may be advantageous in terms of sediment
共1933兲, through Rouse 共1937兲, Ismail 共1952兲, Hunt 共1954兲, Kara- mobility. The sewer pipeline with a deposited bed will behave
belas 共1977兲, Walton 共1995兲, Kaushal 共1995兲, Kaushal et al. like a duct having a flat bottom. Kaushal and Tomita 共2003兲 com-
共2002a,b兲, and Kaushal and Tomita 共2002c,d兲 to the lucid ac- pared pressure drop data for multisized sediment transport in a
counts given in many textbooks 共Wasp et al. 1977; Raudkivi rectangular duct having an aspect ratio of 4.0 and in a pipeline. It
1990; Govier and Aziz 1982兲. was felt that not only the larger bed area but also the secondary
The completeness of the basic advection/diffusion model has flows inside a rectangular duct is a factor for head loss reduction.
been questioned by Hunt 共1954兲. He has shown that the main Kaushal and Tomita 共2003兲 observed that particle diffusivity in-
deficiency of this model lies in the fact that the law of mass creases exponentially with efflux concentration in both rectangu-
conservation has been essentially disregarded by not taking into lar ducts and pipes. They also observed that particle diffusivity in
account the volume of particles in suspension. Hunt 共1954兲 has a rectangular duct is more than in a pipe for all the efflux con-
developed a more complete set of diffusion equations, in which centrations. Thus the solid distribution across the pipe cross sec-
he has taken into account the liquid volume displaced upwards by tion will be more asymmetric than in a rectangular duct according
an equal volume of particles moving in the lower strata of a to the basic diffusion equation, which is also borne out from
Kaushal and Tomita’s 共2003兲 experimental observations. Less
horizontal flow field as given below
asymmetric solids concentration profiles will lead to larger sedi-
⳵C j ment mobility in the rectangular duct. Similar observations have
␧s ⫹C j 关 w j ⫺ v y 兴 ⫽0, j⫽1,2,...,n (1) been made by the authors while comparing the hydraulic perfor-
⳵y
mance of a sewer with and without a deposited bed.
where v y ⫽ 兺 i⫽1
n
w i c i ⫽liquid velocity in the vertical direction;
C j ⫽concentration of jth particle size; and w j ⫽settling velocity of
jth particle size. References
Obviously, Eq. 共1兲 proposed by Hunt 共1954兲 is more suitable
than the basic equation for studies of relatively concentrated sus- Govier, G. W., and Aziz, K. 共1982兲. The flow of complex mixtures in
pensions. Another major advantage of Hunt’s equation is that it pipes, Krieger, Malabar, Fla.

722 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JULY 2004

J. Hydraul. Eng. 2004.130:722-723.

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