CHAPTER 8
Discharge Equation For Inclined Sluice Gate 8.1 A b s t r a c t
General ly, sluice gates are used to regulate flow in open channels .
The discharge coefficient of a sluice gate is a function of geometric and
hydraulic propert ies . For free flow condit ions; the discharge coefficient is
related to upstream flow depth and gate opening, whereas for submerged
flow, it also depends on tail water depth. Flow through the gnle opening
has been the subject of investigation for many academicians and
researchers . The main objective of this chapter is to report an
investigation done on flow through inclined sluice gate and establish
relat ionships for the discharge through the gate for free-flow and
submerged-flow conditions independently. For free-flow condition, the
discharge is expressed as a function of head causing flow, gate opening
and inclination of the gate. For submerged-flow condit ion, the discharge is
expressed as a function of head cuiising flow, inclinatiun of the gate, gate
opening and tail water depth. Experiments were carried on different gate
inclinations such as 0" (normal to flow), 15", 30", and 45" with respect to
the vertical plane on upstream side for different gate openings.
8.2 I n t r o d u c t i o n
Flow metering is an integral part of water management especially in
the field of irrigation and environmental engineering. Due to the increased
pressure on demand from every phase of human activity, the water is being
treated as scarce commodity; it needs proper regulation and restricted
usage so that the ecological balance is maintained. The water is being
supplied for irrigation through canals . In canals , a sluice gate is often used
as a flow-controll ing and measuring device.
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The conventional sluice gate discharge equation is written in the form
Q^C.ab^l^ (8-1)
In which Q is the sluice gate discharge; a is the sluice gate opening; b is
the sluice gate length or width of rectangular channel; y is the upstream
water depth; g is gravitational acceleration; and Cj is the discharge
coefficient of the gate.
Many investigators have studied flow below vertical sluice gates
located across the full width in rectangular channel. Henry [65] derived a
plot showing variation of discharge coefficient with y/a under free-flow,
and with y/a and y,/a for submerged-flow conditions, where y, is the tail
water depth. Later, Rajaratnam and Subramanya [40] confirmed Henry's
investigations. Ramamurthy, et. al. [43] have carried out experimental
investigation on flow past gate with cylindrical lip for submerged-flow
condition and reported a higher discharge coefficient for such gates. Using
the concept of elementary discharge coefficient, C«, Swamee, et. al. [65]
proposed equation for free-flow in terms oi y/a and for submerged flow in
terms of>'/a for different ^ /̂a ratios.
Available literature mainly pertains to flow through normal sluice
gate with bottom edge sharp or cylindrical. Literature on inclined sluice
gates was not available. Thus, there is a need to analyse the discharge
characteristics of these types of gates and exploit the advantages of these
gates for the best use of sluice gates in practical conditions. In this
direction, it is an attempt to experimentally obtain the data on flow
conditions below the inclined sluice gates and analyse the same.
In the present investigation, the flow through the inclined sluice
gates is studied. Independent expressions for discharge for free-flow and
submerged-flow conditions are obtained for the inclined gates by
conducting experiments on normal. 15°, 30° and 45° inclinations of sluice
gules with respect to the vertical plane (normal to the bed of the
rectangular channel). Most of the researchers have used weir to calibrate
the sluice gate (or measure actual discharge) in a channel, which limits the
accuracy of the results. In the present work, the discharge was measured
by volumetric measurement.
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8.3 Formulation of the Problem
The discharge cocrficicnt of a sluice gate depends on the conditions
of flow through the gate such as free flow and submerged flow. Hence, an
explicit equation for discharge coefficient has to be obtained as a function
of y & 'a' for free-flow condition, and 'y', 'a' and 'y,' for submerged-
flow condition. The expression for discharge coefficient for the normal
gate can be obtained for free-flow and submerged-flow conditions as
For free flow,
C,=Aa.y) (8-2)
For submerged flow,
C, = / ( a .y ,y . ) (8.3)
The discharge coefficient is a function of various factors such as
head causing flow, gate shape, surface tension, viscosity, Froude's
number, Reynold's number and inclination of gate with free water surface
in channel. In the present experimental work, as the gates are inclined to
the bed of the channel, the uniform flow condition does not exist and the
streamlines converge more rapidly for higher inclinations as compared to
streamlines in case of (conventional) normal gate. Hence, the inclined
gates are likely to improve their discharging capacity. The pattern of
streamline flow lines near the gates is as shown in Fig. 8.1. Therefore, a
new parameter '^' as a function of gate inclination with respect to the
normal ' a ' (in radians) has been introduced in the equation as
For free flow,
C, = (1+J^)f(a,y) (8.4)
For submerged flow,
C,'-(l-^/f)f(a,y.y,) (8.5)
The schematic definition sketch for submerged flow is as shown in Fig.
8.2.
K.<
(a) Vertical gate (b) Upstream Inclined gate
Fig.8.1 Strcani-Flow patterns Tor Sluice gates
f-
B >
J S l u l t t <Jc*.ltf
M ff f
%
•rrrrrrrrr7
I Tftllgrvit
^:xm^~^ /'//f »f/*f*//f**f^
Fig.8.2 Definition Slcetclt for submerged flow
8.4 Experiments
The sluice gate was of 5mm thick MS s\i&eX. The lower edge was
chamfered at 45° downslrcam in upward direction, with 1mm flat edge.
The gates were raised or lowered in the slot provided in the channel to a
desired gate height opening. Experiments were carried out on sluice gates
fixed normal to the flow direction, 15°, 30°, and 45° inclinations with
vertical plane for 10 to SQ mm gate openings with a step of 10 mm
increment in opening. Experiments were conducted for the range ol
variables shown in Table 8.1.
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8.5 Analysis of Experimental Data
The actual discharge is plotted against the head for the gate opening
(a = 40 mm) for all the positions of sluice gate (free-flow condition)
(Fig.8.3). This indicates that, there is a relative increase in discharge for a
particular head, with the increase in the gate inclination. It can be
concluded that unlike the conventional sluice gates, smooth convergence
of flow lines for flow under the inclined sluice gate increases the sluice
discharge coefficient.
Retaining the functional form of C^ as given by Swamee [65] for normal
gale, a general expression for C^ fur inclined sluice gate is obtained
through regression analysis as follows.
For free-flow conditions
( \0.072
y + 15aj (8.6)
where a is the gate inclination with respect to the (conventional) normal
gate.
0.020
0.018
:^ 0.016 ^
\ 0.014 g) 0.012 I o.oioH t3
^
0.008
0.006-
0.004-
0.002
O.(XX)
o . % • .0 * • *
° *
%i
<fi
0*»
f f
• Nomal
« 15 degree inclination
A 30 degree inclination
o 45 degree inclination
0 0.1 0.2 0.3 0.4 0.5
Head (m)
Fig. 8.3 Actual discliargc Vs Mead (For a =40 mm)
0.6 0.7
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Table 8.1: Range of variables studied
Variable Normal Gate Inclination
Variable «r-0* a-15* a-30* a-45*
1 a) Free flow
Gate liciglil opening 'a' (in) O.OI-
0.05
0.01-0.05 0.01-
0.05
0.01-
0.05
Flow cIcptU on u/s of sluice
gate y (m)
0.0692 -
0.6117
0.054 -
0.6029
0.0589 -
0.5549
0.0511 -
0.4514
Actual discharge 'Q'" (mVs) 0.0016 -
0.02036
0.00131 -
0.0200
0.00164
-0.02029
0,00148
-0.01988
Number of runs 75 59 65 71
(b) Submerged flow
Gate height opening ' a ' (m) 0.01- 0.01-0.05 0.01- 0.01-
0.05 0.05 0.05
Flow depth on u/s of sluice 0.1065 - 0.0519 - 0.0711 - 0.0606 -
gate y (m) 0.6352 0.6211 0.5725 0.4775
Tail water depth y (m) 0.0329 - 0.0434 - 0.052 - 0.05 -
0.5554 0.5427 0.5305 0.461
Actual discharge 'Q' (mVs) 0.00183- 0.00162 - 0.00227 0.00171
0.0126 .008164 -.008458 -.009332
Number of runs 177 143 188 193
For submerged flow conditions:
An additional factor y,/y' is introduced as a third parameter along with
'a ' and 'y' as
C, =0.645(i + 0 . I 5 2 a " j - ^ ^ ^ ^ ^ V + 15a
\0,07J
-0.9052U^ + 0.3781 <y.
\
+ 0.8394 (8.7)
The Variation of /^ with a for inclined sluice gates for both the cases
are as shown in Fig 8.4.
The discharge values are computed, for the measured head, gate
opening, upstream flow depth and tail water depth for the corresponding
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flow conditions using Eqs. 8.1, 8.6 and 8.7. Figs. 8.5 and 8.6 show plot of
computed discharge versus actual discharge for free-flow and submerged
flow conditions respectively.
0.18
0,16
0.14
0.12
0.10
'̂ O.OS
0.06
0.04
0.02
0.00
y^ _.ik
Free Flow ti' P =0.224 a '•" , •
..••' • - — "
,.-^,^ Submerged Flow ^ /3 =0.152 a"'
0.0 0.2 0.4 0.6 0.8 l.O
a FiB.8.4 /J VM. a
The computed discharges are well within ±10% of actual discharge for
free-flow condition. Fig. 8.5 indicates a good agreement of established
0.025
0.000 0.005 0.010 0.015 0.020 Actual Discharge (rt?/s)
fig. 8.5 Actual Discliarge Vs Cbiipjlcd Discliarge (Free flow)
0.025
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Eq. 8.6 except at very low discharge values. This may be due to the effect
of viscosity and surface tensior\ properties of fluid and further, for small
head, the sluice gate acts as a large orifice.
From Fig. 8.6, it can be observed that, majority of discharge values
(except very few points) lie within ±10% error line. For smaller discharges
with small gate opening, the computed discharges are closer to -10% error
line, whereas for higher discharges and higher gate openings, the majority
of estimated values are within ±10% error line for all the inclined gate
positions.
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
Actual cliscliargc (m /s)
Fig. 8.6 Actual discharge Vs Computed discharge (Submerged flow)
The percentage increase in discharge with inclinations when
compared to normal sluice gate is shown in Table 8.2.
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Tabic 8.2: Variation in relative Increase In % discharge with '•oi • «»
Inclination with the
vertical plane a=15* a-30* a-45*
For free-flow condition 4.19 9.98 16.56
For submerged-flow
condition 2.85 6.77 11.24
8.6 Practical Applications
The conventional sluice gate can be fixed inclined in a rectangular
channel to improve its discharge capacity. The arrangement will also help
to reduce afflux especially for higher discharges in an existing channel as
it can discharge at a relatively quicker rate. The property of inclined
sluice gates can be used in designing canal most economically because
inclined gates requires lesser free board in the channel.
8.7 Conclusions
Equations Eqs. 8.6 and 8.7 can be used to compute discharge. The
computed discharges as obtained by these equations are within 10% error.
The property of improvement in discharge capacity of gates with
inclination may be effectively used, in economical design of the channels
by reducing the free board requirements, as the afflux magnitude is
reduced.
It is possible to fix the gate in any desired inclination even under
general field conditions. Mcnce they find applications in various fields of
engineering such as irrigation, chemical and environmental for flow
measurement and control.
Following conclusions are drawn based on the analysis of experimental
data.
1. The variation of computed discharge using the equations derived
here (Eqs. 8.6 & 8.7) with the actual discharge is observed to be
within ±10 % error. However, majority of points lies on 45° line
indicating the accuracy of the equation.
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2. Higher discharge is possible for the same head, with the increase in
gate-inclination towards upstream side. The inclination will also
help in reducing afflux in a pre-designed canal, thereby higher
discharge may be allowed in the canal.
3. With the reduction of afflux, the requirement of free board for the
channel is reduced and hence sections can be designed more
economically.
4. It is possible to fix gate in any desired inclination even under
general field conditions. Hence it finds use in various fields of
engineering such as irrigation, chemical and environmental for flow
measurement and control.
A paper based on the content of above chapter has been presented at
the international seminar on earth resources management held at Kuvempu
University, Shimoga ,28-30, Jan 2004.
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Plate 7 Flow Through Inclined Sluice Gate