Pipe Flow Head Losses for Sand-Water Mixtures

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME
45
EFFECT OF PIPE INCLINATION ON THE PIPE FLOW HEAD
LOSSES FOR DIFFERENT SAND CONCENTRATIONS
Mahmoud Ali Refaey Eltoukhy
Faculty of Engineering, Shobra, Banha University, Egypt
ABSTRACT
This paper presents results of an experimental study pertaining to the behavior of
sand-water (two-phase) flows in inclined pipes, a phenomenon that is generally witnessed at
the canal intakes which aligned at desert area, and dredging processes. The experiments were
conducted in a modern hydraulics laboratory to study the effect of sand concentration and
pipe inclination on the pipe flow head losses. The pipe inclination angle was varied from 0°
to 90° in upward and downward directions and the sand concentration in water was regulated
up to 15% by volume. It was concluded that the head losses of the downward sloping pipe
flow are always lower than the head losses of the horizontal flow and these are always lower
than the head losses of the upward sloping pipe flow, regardless of the concentration and
inclination angle. The experiment results were analyzed in the light of earlier published data
and useful empirical correlations have been developed to determine the head losses of
horizontal flow, alongwith upward and downward sloping pipe flows.
Keywords: head loss, sand - water mixture, inclined pipes, sand concentration
INTRODUCTION
Most of the applications of hydraulic transport in the past have been in the minerals
industries. Generally, such industrial facilities are located in remote areas with insufficient
road or rail infrastructure. Therefore, pipeline transport has been preferred and recognized as
the most cost effective method of transporting huge quantities of minerals over long
distances, across difficult terrain. The solid particles invariably being heavier than the
conveying liquid are transported in lower part of the channel. This unique pattern has been a
subject of special study and is presented in this paper. The effect of flow velocity, sand
concentration and the sloping pipe inclination angle on the head loss were investigated. The
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ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 4, Issue 3, May - June (2013), pp. 45-56
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46
head losses determined for the horizontal portion of the pipeline were compared with
correlations found in the literature. A pipe loop system was built, allowing variation of flow
velocity, sand concentration and pipe inclination.
OVERVIEW OF THE PRIOR PUBLISHED DATA
Wasp et al., (1999) found that the flow of solid-liquid slurries in pipes differs from the
flow of homogeneous liquids in a variety of ways. The complete range of velocities is
possible with liquids, whereas nature of the flow, i.e., laminar, transition, or turbulent, can be
characterized based on the knowledge of physical properties of the fluid and the pipe system.
The characterization of slurry flow is not as simple as for liquid flow mainly for two reasons:
firstly the properties of the solid particles to be accounted for are superimposed on the
properties of the liquid, and also the effect of the particles on the mixture properties;
secondly, depending on the particular conditions, a range of slurry behavior is possible.
Kaushal et al (2005), and Kaushal and Tomita (2007) carried out experimental study for
concentration of distributions in slurry pipeline by using γ- ray densitometer. Their
measurements show that, pressure gradient profiles of equivalent fluid for finer particles were
found to resemble with water data except for 50% concentration, however, more skewed
pressure gradient profiles of equivalent fluid were found for coarser particles. Experimental
results indicate absence of near-wall lift for finer particles due to submergence of particles in
the lowest layer into the viscous sub layer and presence of considerable near-wall lift for
coarser particles due to impact of viscous-turbulent interface on the bottom most layer of
particles and increased particle–particle interactions.
Richardson, et al., (1999) found that, in homogenous flow systems, the presence of
the solids can have a significant effect on the system properties, usually resulting in a sharp
increase in viscosity as compared to that of the carrier fluid. In heterogeneous flow systems,
solids are not evenly distributed and in horizontal flow, pronounced concentration gradient
exists along the vertical axis of the pipe, even at high velocities. Particle inertial effects are
significant, i.e., the fluid and solid phases to a large extent retain their separate identities, and
the increase in the system viscosity over that of the carrier liquid is usually quite small.
Heterogeneous slurries tend to be of lower solid concentrations and have larger particle sizes
than homogeneous slurries. Raudkivi, (1989), found that in vertical pipes the velocity of
solids for upward flow is less than the fluid velocity, but is greater for downward flow. The
difference is approximately the value of the settling velocity.
Coiado and Diniz, (2001), studied the solid-water flow in inclined pipes. Based on the
collected experimental data, the adopted methods and the experimental conditions, it was
concluded that the head losses values for the downward sloping pipes are always lower than
the head losses for the horizontal pipe, and these are always lower than the head losses for the
upward sloping pipes, regardless of the inclination angles and concentrations. Whereas, in
case of downward sloping length of water-sand slurry flow, the presence of sand decreases
the head losses values corresponding to the inclination angle and increasing concentration.
C. Kim et al, (2008), made an experimental study on the transport of sand-water
mixtures in circular and square pipelines, focusing on the economic transport of solid
particles. The measured data of the hydraulic gradient, solid effect, and deposition-limit
velocity for both circular pipe and square duct were compared and analyzed. The hydraulic
gradient of water in the circular pipe was found larger than that in the square duct because of
the secondary flow in the square duct. The hydraulic gradient of sand-water mixture in the

47
square duct was larger than that in the circular pipe. It was found that the hydraulic gradient
of the slurry flow in the circular and square pipelines increases with the volumetric delivered
concentration and Reynolds number.
D.R. Kaushal, et al, (2012), simulated Pipeline slurry flow of mono- dispersed fine
particles at high concentration numerically using Mixture and Eulerian two-phase models. It
was found that, pressure drop predictions by both MIxture and Eulerian two-phase models for
flow of water show good agreement with the experimental data. Whereas, in case of
comparison between measured and predicted pressure drops at different concentrations,
namely, 30%, 40% and 50%, the Mixture model fails to predict pressure drops correctly, the
amount of error increasing rapidly with the concentration. However, Eulerian model gives
fairly accurate predictions for pressure drop at all the efflux concentrations and for flow
velocities considered in the present study.
The published materials about two-phase (solid-liquid) flow are mostly related to
horizontal pipe flow. There are a limited number of studies concerning the effect of pipe
inclination on two-phase flow energy loss. In htis backdrop, this paper studies the effect of
the pipe inclination on the pipe flow head losses for different sand concentrations, and
presents its results in the forms of curves and equations to compute the head loss, given the
sand water mixture flow velocity, the pipe angle of inclination, and the sand concentration in
volume.
EXPERIMENTAL APPARATUS
The general layout of the apparatus is shown in Fig. 1. This apparatus is used to reach
the objectives proposed in this paper. It consists of a pipe loop system, and was fabricated in
the professional Hydraulics Laboratory. The sand water mixtures were prepared in the main
tank, which had dimensions of 0.80 m length, 0.70 m width, and 0.80 m depth. The mixture
was maintained homogeneous in the main tank by the use of an auxiliary pump. Then, the
homogeneous mixture was pumped, through a pipeline with diameter of 0.75 m. The pipeline
was made up of horizontal and inclined pipes. The head loss measurements for the sand-
water mixture flow were carried out in the pipelines. The sand used in the experiment was
uniform with median grain size d50 = 0.20 mm, and relative density of 2.67, with
concentrations 15 % up in volume. The pipe inclination angle used was varied from 0o
(horizontal position) to 90o
(vertical position), for each upward and downward inclinations.
During the sand water mixture flow through the pipeline, for different velocities and
concentrations of the mixture, the following parameters were measured: a) the head losses in
the horizontal, upward, and downward inclinations; b) the discharge; and c) the concentration
of the sand in water. The discharge was measured by dividing a volume of the outlet mixture
by the corresponding time. The concentration of the mixture was determined using a tank to
measure the volume and one balance. Whereas, the head losses in the horizontal, upward, and
downward sloping lengths were measured by differential manometer.
EXPERIMENTAL WORK
The experimental work consists of two main sets of experiments. The first set consists
of 126 runs, and it used to measure the head losses through the upward inclination pipeline at
different mixture velocities and for different sand concentrations. The angles of the pipeline
inclination were 5o
, 10o
, 25o
, 35o
, 45o
and

48
Rubber pipe
Tank auxiliary pump main pump
Fig. 1. The Apparatus Layout
90o
. The sand concentrations used for each angle of inclination are 5 %, 10 %, and 15 % in
volume. The second set of experiments consists of 118 runs, and the pipeline inclination
angles were as that of the first set except that, the pipeline inclination was downward. Fifty
runs were carried out to measure the head losses through the horizontal pipeline at three
different sand concentrations. The horizontal pipeline runs results, are analyzed with the
upward and downward pipeline inclination's results. In the light of above conclusions, the
sand water mixture velocity should be greater than the deposition limit (critical) velocity,
which is the mean mixture velocity at the limit of stationary deposition. From Durand (1953)
and Gibert (1960) for the used sand, the mixture velocity should be greater than 1.88 m/s in
all runs to maintain that the sand particles are always in suspension state.
RESULTS AND DISCUSSION
Two empirical equations were developed to calculate the head losses of the water-
sand mixture as a function of flow Froud's number, Fn, the sand concentration, C, and the
inclination angle, α, of upward and downward flows in inclined pipes. The equations were
developed by several curve fittings. First of all, the apparatus was calibrated through
comparison of the measured head losses in a horizontal pipeline with that measured by E. M.
Coiado, (2001), Fig. (2), which shows that the measured and Coiado results are almost
identical.
FLOW THROUGH UPWARD INCLINATION PIPELINE
For the first set of experiments, the sand water mixture was pumped through the
pipeline which was laid in upward inclination positions. The used pipeline inclination angles
are 0o
(horizontal position), 5o
, 10o
, 25o
, 35o
, 45o
, and 90o
(upward vertical position). The
head losses were measured in the pipeline in each inclination position for three sand
concentrations, i.e., 5%, 10%, and 15%.

49
The results of the flows through upward inclination Pipeline were analyzed. The
effect of each sand-water mixture velocity represented in Froude's number, Fn, the pipeline
angle of inclination, α, and the sand
Fig. 2. Apparatus Calibration, for C = 10%, and pipe inclination angle 10o
upward
concentration, C on the head losses in the pipeline was developed. It was found that the
hydraulic gradient increases with increasing sand water mixture velocity. For example, for C
= 10% and α = 35o
, if the sand water mixture velocity increases from 3.3 m/s to 5.2 m/s, the
hydraulic gradient increases from 0.27 to 0.37, meaning thereby that increase of 57.5% in the
mixture velocity results in increasing 37% in the hydraulic gradient, as indicated in Fig. (3).
Another runs of experiments were carried out through varying the sand
concentrations up to 15%, to study the effect of sand concentration on the head losses in
upward pipeline inclination. It was found that increase in the sand concentration results in
increasing hydraulic gradient. For example, for pipeline inclination angle of 25o
and sand
water mixture velocity of 3.75 m/s, changing sand concentration from 10% to 15%, the
hydraulic gradient changes from 0.21 to 0.265, thereby showing that 50% increase in sand
concentration yields 26% increase in the hydraulic gradient in the pipeline, as shown in Fig.
(4).
The effect of pipeline inclination angle was studied by changing α from 0o
(horizontal
pipeline) to 90o
(vertical pipeline). Experiments showed that the hydraulic gradient of the
pipeline increases as its upward angle of inclination increases, Fig. (5). For example, at sand
concentration C = 10 %, when the upward inclination angle increases from α =10o
to 45o
, the
hydraulic gradient increases from 0.199 to 0.296, implying that increase of 35% in upward
inclination angle of pipeline results into 49% increase in the hydraulic gradient.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
2 3 4 5 6 7
Froude's Number, Fn
HydraulicGradient,(i),
Present
Coiado, 2001

50
Fig. 3 Variation of the hydraulic gradient with the sand water mixture velocity for C=
10% and α = 35o
Fig. 4 Effect of sand concentration on the hydraulic gradient, for α = 25o
and v = 3.75
m/s (Upward)
0
0.1
0.2
0.3
0.4
0.5
0.6
2 2.5 3 3.5 4 4.5 5 5.5 6
Froude's Number, Fn
Hydraulicgradient(i), α = 0
Up 5
Up 10
Up 25
Up 35
Up 45
Up 90
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
2 2.5 3 3.5 4 4.5 5 5.5 6 6.5
Froude's Number, Fn
HydraulicGradient,(i),i
C = 5 %
C = 10 %
C = 15 %

51
Sin α
Fig. 5 Effect of the upward pipe inclination angle on the hydraulic gradient, i for C=
10%
With a view to accomplish the objectives set for this study, several curve fittings were
done and sound relationship was established between hydraulic gradient and the affecting
parameters, i.,e., the Froude's number, the pipeline inclination, and the sand concentration,
Fig. (6). With parameters factor UPI on the horizontal axis and the hydraulic gradient on the
vertical axis:
0779.025.0sin1091.00574.0 −−+= C
gD
v
IUP α (1)
Where:
v : sand water mixture flow velocity, (m/s)
α : pipeline angle of inclination
C: sand concentration in water (% in volume).
The hydraulic gradient, i , may be calculated for any UPI for a given sand water mixture
velocity, the pipeline inclination angle, and the sand concentration from Fig. (6). Through
curve fitting for data in Fig. (6), the following equation was obtained:
012.00669.1 −= UPIi (2)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.2 0.4 0.6 0.8 1 1.2

52
UPI
Fig. 6 Upward pipe flow hydraulic gradient variation with the affecting parameters
By substituting the value of UPI from Equation 1 into Equation 2, the hydraulic gradient can
be directly calculated as under:
0951.02667.0sin1164.00612.0 −−+= C
gD
v
i α (3)
FLOW THROUGH DOWNWARD INCLINATION PIPELINE
In the second set of experiments, the sand water mixture was pumped through
the pipeline which was laid in downward inclination positions. The study parameter
encompassed pipeline inclination angles 0o
(horizontal position), 5o
, 10o
, 25o
, 35o
, 45o
, and
90o
(downward vertical position). Whereas, all measurements of head losses in the pipeline
were carried out in each inclination position for the three sand concentrations, 5%, 10%, and
15%.
The results were analyzed to determine the effect of each of sand water mixture
velocity represented in Froude's number, Fn, the pipeline angle of inclination, α, and the sand
concentration, C on the head losses in the pipeline. The sand water mixture velocity effect on
the head loss is shown in Fig. (7). It was found that the hydraulic gradient increases as the
sand water mixture velocity increases. For example, for C = 10% and α = 35o
, if the sand
water mixture velocity increases from 3.28 m/s to 5.2 m/s the hydraulic gradient increases
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.1 0.2 0.3 0.4 0.5 0.6

53
Fig. 7 Variation of the hydraulic gradient with sand water mixture velocity for C= 10%
and α = 35o
from 0.024 to 0.175, showing that increase of 58.5% in the mixture velocity results in
increase of 629% in the hydraulic gradient.
Another set of experiments was undertaken to study the effect of sand
concentration on head losses in downward pipeline inclination by varying sand
concentrations up to 15%. The results showed that the sand concentration is inversely
proportional with the hydraulic gradient. For example, for pipeline inclination angle of 25o
and sand water mixture velocity of 3.75 m/s, changing sand concentration from 10% to 15%,
results in changing the hydraulic gradient from 0.0778 to 0.063, showing that 50% increase in
the sand concentration results in 19% decrease in the hydraulic gradient in the pipeline, Fig.
(8).
Also, the effect of the pipeline inclination angle on the pipeline hydraulic gradient
was studied by changing α from 0o
(horizontal pipeline) to 90o
(vertical pipeline).
Experiments showed that the hydraulic gradient of the pipeline decreases as its downward
angle of inclination increases, Fig. (9). For example, at sand concentration C = 10 %, when
the downward inclination angle increases from α =10o
to 45o
, the hydraulic gradient
decreases from 0.129 to 0.048, showing that with downward inclination angle of the pipeline
increasing by 35%, the hydraulic gradient decreases by 63%.
The curve fittings were done for this set of parameters as well to determine
relationship between the hydraulic gradient and the affecting parameters, i.e, the Froude's
number, the pipeline inclination, and the sand concentration, which yielded promising results
as shown in Fig. (10) and the underlying relationship, taking Parameters factor DwnI on the
horizontal axis and the hydraulic gradient on the vertical axis:
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
2 3 4 5 6 7
Froude's Number, Fn
α = 0
Dow 5
Dow 10
Dow 25
Dow 35
Dow 45
Dow 90

54
Fig. 8 Effect of sand concentration on the hydraulic gradient, for α = 25o
and v = 3.75
m/s (Downward)
Sin α
Fig. 9 Effect of the Downward pipe inclination angle on the hydraulic gradient, i for C=
10%
0
0.05
0.1
0.15
0.2
0.25
2 3 4 5 6 7
Froude's Number, Fn
HydraulicGradient,(i),i C = 5 %
C = 10 %
C = 15 %
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 0.2 0.4 0.6 0.8 1 1.2

55
DwnI
Fig. 10 Downward pipe flow hydraulic gradient variation with the affecting parameters
1346.015.0sin0675.00585.0 −+−= C
gD
v
IDwn α (4)
The hydraulic gradient, i may be calculated for any DwnI for a given sand water
mixture velocity, the downward pipeline inclination angle, and the sand concentration. The
relationship established by curve fitting for data in Fig. (10), is given as under:
0031.09848.0 += DwnIi (5)
The following relationship is obtained by combining Equations (4) and (5), to calculate the
hydraulic gradient given the values of sand water mixture velocity, the pipeline inclination,
and the sand concentration:
1295.0148.0sin0665.00576.0 −+−= C
gD
v
i α (6)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

56
CONCLUSIONS
This paper gives the results of an experimental study undertaken to determine the
effects of sand water mixture velocity, the pipeline inclination angle upward and downward,
and the sand concentration on the head loss in the pipeline. Based on the experimental data,
the results of curve fitting, and the resulting mathematical expressions, the following
conclusions are reached:
1. The head losses for the downward inclination of the pipeline are always lower than
the head losses for the horizontal pipe, and these are always lower than the head
losses for the upward sloping pipes, regardless of the inclination angles and
concentrations.
2. For the downward inclination of the pipeline, the presence of sand decreases the head
losses with increasing inclination angle and the sand concentration.
3. For the water-sand mixture flow in the horizontal pipe, the presence of sand increases
the head losses as the concentration increases.
4. For the upward inclination of the pipeline water-sand mixture flow, the presence of
sand increases the values of the head losses with increase in inclination angle and the
concentration.
5. The curve fitting results and the corresponding equations developed can be used for
calculating the head loss in the pipeline for given sand water mixture velocity, the
pipeline inclination angle, and the sand concentration.
REFERENCES
1. E. M. Coiado and M. G. Diniz, (2001), "Two-Phase (Solid-Liquid) Flow in Inclined
Pipes", J. Braz. Soc. Mech. Sci. vol.23 no.3 Rio de Janeiro.
2. D.R. Kaushal, T. Thinglas, Y. Tomita, S. Kuchii, and H. Tsukamoto, (2012), " CFD
modeling for pipeline flow of fine particles at high concentration", International Journal
of Multiphase Flow 43, 85–100
3. Durand, R. (1953), " Basic solids in pipes – Experimental Research", Proceedings
International Hydraulics Conference, Minneaplis, MN, pp. 89 – 103.
4. Gibert, R. (1960), "Transport Hydraulique et Refoulement des Mixtures en Conduit",
Anna1es des Pontes et Chaussees, 130e Annee, No. 12, et No. 17.
5. Kaushal D.R., Kimihiko Sato, Takeshi Toyota, Katsuya Funatsu, Yuji Tomita (2005),
"Effect of particle size distribution on pressure drop and concentration profile in
pipeline flow of highly concentrated slurry", International Journal of Multiphase Flow
Volume 31, Issue 7, July 2005, Pages 809–823
6. Kaushal, D.R., Tomita, Y., 2007, "Experimental investigation of near-wall lift of
coarser particles in slurry pipeline using γ-ray densitometer" Powder Tech nol. 172,
177–187.
7. Raudkivi, A. J., 1989 "Loose Boundary Hydraulics", Pergamon Press, New York
8. Richardson, J. F., Chhabra, R. P., Khan, A. R., 1999 "Multiphase flow ou non-
Nextonian fluids in horizontal pipes", Slurry Handling and Pipeline Transport.
Hidrotransport 14. Maastrich. Netherlands.
9. Wasp, E. J.; Kenny, J. P.; Gandhi, R. L. 1999. "Solid-Liquid Flow Slurry Pipeline
Transportation", Series on Bulk Materials Handling. International Standard Book
Number. Trans Tech Publications. Germany.

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