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.

82

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.

90

Plate 7 Flow Through Inclined Sluice Gate