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Discharge coefficient for bottom orifice of vortexchamberChyan-Deng Jan a & Quang-Truong Nguyen ba Department of Hydraulic and Ocean Engineering, National Cheng Kung University,Tainan, 70101, Taiwan, Republic of Chinab Department of Hydraulic and Ocean Engineering, National Cheng Kung University,Tainan, 70101, Taiwan, Republic of China E-mail:Version of record first published: 17 Jun 2011.

To cite this article: Chyan-Deng Jan & Quang-Truong Nguyen (2011): Discharge coefficient for bottom orifice of vortexchamber, Journal of Hydraulic Research, 49:3, 388-391

To link to this article: http://dx.doi.org/10.1080/00221686.2011.572442

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Technical note

Discharge coefficient for bottom orifice of vortex chamber

CHYAN-DENG JAN, Professor, Department of Hydraulic and Ocean Engineering, National Cheng KungUniversity, Tainan 70101, Taiwan, Republic of China.

Email: cdjan@mail.ncku.edu.tw (author for correspondence)

QUANG-TRUONG NGUYEN, PhD, Department of Hydraulic and Ocean Engineering, National Cheng KungUniversity, Tainan 70101, Taiwan, Republic of China.

Email: nqtruong79@gmail.com

ABSTRACTThis research presents investigations on the discharge coefficient of a circular orifice located at the apex of an inverted conical hopper attached to thebottom of a cylindrical vortex chamber. A circular jet inflow tangentially enters the vortex chamber at the top periphery of the conical hopper. Differentsizes of orifices and inflow jet discharges were applied in the experiments to investigate the variation of the discharge coefficient. The effect of overflowat the upper outlet on the discharge coefficient was also investigated. Based on the test data, empirical relations for the discharge coefficient are pro-posed. It is found that in the presence of tangential jet inflow, the discharge coefficient is considerably smaller than that without tangential jet inflow andthe presence of overflow significantly reduces it.

Keywords: Conical hopper, discharge coefficient, jet inflow, orifice, vortex chamber

1 Introduction

A vortex chamber-type sediment extractor is a fluidic device

using vortices to remove sediment from diverted water (Athar

et al. 2002, 2003). It mainly consists of a cylindrical chamber,

a bottom cone and a tangential inlet, designed for a liquid (or a

solid–liquid mixture) tangentially flowing into the cylindrical

chamber. The inflow raises the chamber water level, in which

it partially exits through the bottom orifice and partially

through the upper outlet near the chamber top if the water

level is higher than the outlet level. Recently, this type of

vortex chamber has been developed as a promising alternative

sediment removal device to avoid disadvantages of conventional

methods, especially for large dimensions and long residence

time. A vortex chamber is an economical, efficient and water-

conservation device without moving parts, and no chemical sub-

stance is required in sediment removal process.

The mechanism and sediment removal efficiency of a vortex

chamber were investigated by, for example, Cecen and Akman-

dor (1973), Mashauri (1986), Paul et al. (1991), Athar et al.(2002) or Keshavarzi and Gheisi (2006). However, their

works were limited to the shallow-depth-type vortex chamber,

i.e. using a flow depth smaller than the chamber diameter.

This type of vortex chamber is effective to extract bed-load

sediment. The works of, for example, Athar et al. (2002) or

Keshavarzi and Gheisi (2006) reveal that a vortex chamber

can also be utilized for partial removal of suspended sediment.

For improving the extraction capability of suspended sediment,

such as fine silt and clay, a deep-depth-type vortex chamber

(Fig. 1) was designed, in which the chamber depth is increased

for increasing the residence time of particles. The discharge

coefficient Cd of the bottom orifice of this vortex chamber is

investigated herein.

2 Laboratory experiments

As shown in Fig. 1, the vortex chamber system mainly con-

sists of a vortex chamber and a water tower. The vortex

chamber is a vertical, transparent cylindrical tank attached

with an inverted conical hopper of side angle 458 to the

bottom, a tangential inlet on the side wall near the top periph-

ery of the conical hopper, a circular orifice at its bottom and an

outlet at its upper part. A circular jet flows horizontally and

Journal of Hydraulic Research Vol. 49, No. 3 (2011), pp. 388–391

doi:10.1080/00221686.2011.572442

# 2011 International Association for Hydro-Environment Engineering and Research

Revision received 11 March 2011/Open for discussion until 31 December 2011.

ISSN 0022-1686 print/ISSN 1814-2079 onlinehttp://www.informaworld.com

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tangentially into the vortex chamber through the inlet. The

vortex chamber has a total height of H ¼ 110.0 cm, an internal

diameter of D ¼ 48.0 cm, a cone depth of Zh ¼ 24.5 cm, a

tangential inlet at distance Zi ¼ 28.0 cm above the orifice

and an upper outlet at Zo ¼ 95.7 cm above the orifice. The

diameters of the tangential inlet and the upper outlet were Di

¼ 3.0 cm and Do ¼ 4.2 cm, respectively. The orifice diameter

Du varied during experimentation.

The inflow system mainly consisted of the tangential inlet and

a water tower of 0.035 m3 capacity. A 458 circular pipe was

employed to connect the tangential inlet and the water tower.

The vertical distance of the jet summit point to the orifice is hm

¼ Zi + 0.5Di. The water tower was used to control the inflow

discharge. The pipe discharge Qi from the water tower was sup-

plied horizontally and tangentially into the inlet. Tap water was

used as an experimental liquid. The chamber outflows included

one through the bottom orifice as underflow discharge Qu and

the other through the upper outlet as overflow discharge Qo.

Under steady state, Qi ¼ Qu + Qo.

As the water horizontally flows into the vortex chamber

through its tangential inlet, vortex flow develops with an air

core at the chamber centre. For a given orifice diameter, the

chamber water level h is correlated with Qi. If Qi is small, h, hm with an unstable chamber water surface. If Qi is large

enough (h . hm), the inlet is fully submerged, resulting in a

stable chamber water surface. Only the latter case with the

inlet fully submerged is concerned below. Hence, tests were

conducted with various Du and Qi, resulting in different

water levels. If h ≤ Zo, there is no overflow from the upper

outlet, i.e. Qo ¼ 0. If, however, h . Zo, Qo depends on the

outlet diameter Do and the head over the outlet (h 2 Zo).

The values of Qu and Qo were measured in a steady state by

a volumetric method, and the values of h were measured by

a ruler attached on the side wall. For each test, the procedure

was repeated three times, and the average measured data were

employed for the analysis.

3 Effect of jet inflow on Cd

The discharge through a bottom orifice is a relevant parameter in

designing this type of device. The discharge was proved to be

closely related to the water head and a discharge coefficient Cd

(Afzalimehr and Bagheri 2009, Jan et al. 2009, Jan and

Nguyen 2010, Swamee and Swamee 2010). The orifice efflux

discharge Qu of liquid or solid–liquid mixtures from the

vortex chamber is estimated for an orifice so small compared

with that of the chamber as

Qu = CdAog

����2gh

√(1)

where Aog ¼ orifice face area, g ¼ gravitational acceleration and

h ¼ head on orifice (vertical distance from the free surface to the

orifice).

The discharge coefficient for water flow through a bottom

orifice of a conical hopper without a tangential inlet was investi-

gated by Jan and Nguyen (2010) for the same vortex chamber

geometry as used herein, except the inlet device. A vertical

inlet pipe was attached to the side wall at the upper part, while

herein a tangential jet inlet was horizontally added near the

base part. The discharge coefficient for the orifice with the

conical hopper is denoted by Cdo. According to Jan and

Nguyen (2010), Cdo then varies from 0.614 to 0.724, depending

on Du/D and h/D as

Cdo = 0.23Du

D

( )−0.29 h

D

( )−0.03

(2)

For water flow through a bottom orifice of a vortex chamber,

an air core is formed in the central chamber portion due to the

tangential jet inflow. The air core vertically connects the orifice

Figure 1 Schematic (a) side view and (b) top view of deep-depth-typevortex chamber used

Figure 2 Comparison of discharge coefficients Cd and Cdo versus h/D

Journal of Hydraulic Research Vol. 49, No. 3 (2011) Discharge coefficient for bottom orifice of vortex chamber 389

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and the free-surface and its size decreases as h increases. Tests

were conducted with Du ¼ 1.00, 1.25 and 1.50 cm. If there is

no overflow (h ≤ Zo), the inflow discharge varied in the range

of 111.5 ≤ Qi ≤ 333.5 cm3/s, corresponding to 0.021 ≤ Du/

D ≤ 0.031, 0.77 ≤ h/D ≤ 1.98 and 14,200 ≤ R ≤ 29,900,

respectively, where R ¼ VuDu/n is the orifice Reynolds

number with Vu as the orifice flow velocity and n as the liquid

kinematic viscosity. Since the above range of R is larger than

the lower limit value of R ≈ 1 × 104 (Rouse 1978), Cd is con-

sidered to be independent of R. By virtue of Eq. (1), the value

of Cd is determined if Du is given, and h and Qu are available.

Figure 2 shows that Cd increases proportionally with h/D but

decreases with Du/D. With a coefficient of determination r2 ¼

0.99, a regression relation of Cd for the orifice under the effect

of jet inflow is

Cd = 0.022Du

D

( )−0.84 h

D

( )0.15

(3)

A comparison of Eqs. (2) and (3) indicates that the discharge

coefficients for the vortex chamber and the conical hopper

both inversely depend on Du/D. However, the effect of Cd on

h/D for a vortex chamber is different from that for a conical

hopper. In the former case, Cd is proportional to h/D, while in

the latter case, it is negatively proportional to h/D (Fig. 2).

The reason for the difference is due to the vortex motion in the

vortex chamber. From Eqs. (2) and (3), one obtains the reduction

rate of discharge coefficient DCd/Cdo as

DCd

Cdo= Cdo − Cd

Cdo= 1 − 0.096

Du

D

( )−0.55 h

D

( )0.18

(4)

In the present tests, DCd/Cdo varies from 9.1 to 38.1%. Figure 3

shows that large Du/D and small h/D are related to large

DCd/Cdo.

4 Effect of overflow discharge on Cd

As h . Zo, the overflow occurs through the upper outlet. It is

well known that an air-core vortex is sensitive to disturbances

and perturbations of the free surface. Therefore, for no overflow,

the swirling strength of the air-core vortex increases and the air-

core vortex stabilizes, thereby increasing the turbulence strength

of orifice flow and Cd. Conversely, for overflow, the swirling

strength of air-core vortex is decreased, the air-core vortex

becomes less stable, thereby decreasing Cd in comparison to

no overflow (Fig. 4). Three test sets were conducted to study

the effect of overflow on Cd for 0.021 ≤ Du/D ≤ 0.031, 2.01

≤ h/D ≤ 2.08, 0.16 ≤ Qo/Qi ≤ 0.72 and 20,800 ≤ R ≤28,900. The regression relation between Cd and Qo/Qi is (r2 ¼

0.94)

Cd

CdZ0= 1.0 − 0.327

Qo

Qi

( )for 0.16 ≤ Qo

Qi≤ 0.72 (5)

Here, CdZo ¼ Cd(h ¼ Zo) from Eq. (3). The reduction rate of

Cd due to overflow DCd/CdZo ¼ 1 2(Cd/CdZo) varies from 7.4

to 23.2%. The larger Qo/Qi the higher is the reduction rate

of Cd.

5 Conclusions

The main results of this investigation are as follows.

. The discharge coefficient of a vortex chamber with a tangential

jet inflow is significantly smaller than that in a conical hopper

without jet inflow, due to the air core. The measured reduction

rate due to the tangential jet inflow is up to 38%.. For no overflow, the discharge coefficient depends on the rela-

tive orifice size and the relative water head. Small relative

orifice size and large relative water head result in a larger dis-

charge coefficient.. Overflow from the upper outlet makes the air-core vortex less

stable, thereby decreasing the discharge coefficient in com-

parison to no overflow. Its reduction rate due to overflow isFigure 3 Reduction rate of DCd/Cdo versus h/D for different orificesizes

Figure 4 Variation of Cd versus h/Zo for vortex chamber orifice withand without overflow

390 C.-D. Jan and Q.-T. Nguyen Journal of Hydraulic Research Vol. 49, No. 3 (2011)

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up to 23%. A high overflow is related to a large reduction rate

of the discharge coefficient.

Acknowledgement

The financial support from the National Science Council of

Taiwan (NSC 99-2625-M-006-002) is greatly acknowledged.

Notation

Aog ¼ orifice face area (m2)

Cd ¼ discharge coefficient for vortex chamber orifice (–)

Cdo ¼ discharge coefficient for conical hopper orifice (–)

CdZo ¼ Cd(h ¼ Zo) (–)

D ¼ diameter of vortex chamber (m)

Di ¼ diameter of jet inlet (m)

Do ¼ diameter of upper outlet (m)

Du ¼ diameter of orifice (m)

g ¼ gravitational acceleration (m/s2)

H ¼ height of vortex chamber (m)

h ¼ head on orifice (m)

hm ¼ distance of jet summit point to orifice (m)

Qi ¼ inflow discharge (m3/s)

Qo ¼ overflow discharge (m3/s)

Qu ¼ underflow discharge (m3/s)

R ¼ orifice Reynolds number (–)

Vu ¼ orifice flow velocity (m/s)

Zi ¼ inlet distance above orifice (m)

Zh ¼ cone depth (m)

Zo ¼ outlet distance above orifice (m)

n ¼ kinematic viscosity (m2/s)

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