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ANALYSIS OF FLOW OVERHORIZONTAL TRANSVERSEBOTTOM RACKSC. S.P.
Ojha F.ISH a , Vijay Shankar b & N. S. Chauhanc
a Civil Engineering Department , IIT Roorkee ,Roorkeeb Civil
Engineering Department , IIT Roorkee ,Roorkeec Satluj Jal Vidyut
Nigam , Shimla , H.P.Published online: 07 Jun 2012.
To cite this article: C. S.P. Ojha F.ISH , Vijay Shankar &
N. S. Chauhan (2007) ANALYSISOF FLOW OVER HORIZONTAL TRANSVERSE
BOTTOM RACKS, ISH Journal of HydraulicEngineering, 13:2, 41-52,
DOI: 10.1080/09715010.2007.10514870
To link to this article:
http://dx.doi.org/10.1080/09715010.2007.10514870
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VOL.I~.I2)
THE INDIAN SOCIETY FOR HYDRAULICS JOURNAL OF HYDRAULIC
ENGINEERING
ANALYSIS OF FLOW OVER HORIZONTAL TRANSVERSE BOTTOM RACKS
by
Ojha C.S.P.'. F.ISH, Vijay Shankar2 and Chauhan N. S.3
ABSTRACT
(41)
A rack set in the bottom of a channel is often used as a
hydraulic structure for intake or an outlet for flow. The flow
through the bottom racks is a typical case of spatially varied flow
with decreasing discharge. In the present work, experiments have
been conducted to study flow diversion from transverse bar bottom
rack under varying flow conditions i.e. Froude number ranging from
0.1 to 1.5 and ratio of transverse bar spadng to rack length
ranging from 0.041 to 0.1 02. To study discharge characteristics,
invariant specific energy assumption is utilized. The variation of
Mostkow's discharge coefficient, which is based on invariance of
specific energy along the bottom rack, is investigated with Froude
number as well as bottom rack parameters. Existing functional fonns
of discharge coefficient variation in case of longitudinal bar
bottom racks have been utilized to develop relationships for
discharge (Oefficient variation in case of transverse bar bottom
racks. Observed and computed values of discharges based on theses
new functional relationships show good agreement. In some cases,
where specific energy loss has been significant, these
relationships do not work well.
KEY WORDS : Bottom rack, Spatially varied Flow, Specific energy.
Discharge.
INTRODUCTION Bottom racks find applications as intakes in
mountainous regions, to divert water
from mainstream for different purposes. The structure
essentially consists of a transverse trench in channel bed covered
with metal racks to prevent transport of unwanted solid material
through the opening of the racks. Broadly the bottom racks are
classified into longitudinal bars, transverse bars, perforated
plates and bottom slots (Subramanya, 1997). The flow through bottom
racks is a typical case of spatially varied flow with decreasing
discharge. Mostkow ( 1957) derived expressions for the
I. Professor, Civil Engineering Department, liT Roorkee.
Roorkee. 2. Research Scholar, Civil Engineering Department,
IITRoorkee, Roorkee. 3. Asst. Engineer, Satluj Jal Vidyut Nigam,
Shimla, H.P.
Note: Written discussion of this paper will be open until 31st
December 2007.
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(42) ANALYSIS OF FLOW OVER HORIZONTAL TRANSVERSE BOTTOM
RACKS
VOL. 13. (2)
water surface profiles for flow over the racks, by making
assumptions that specific energy over the rack remains constant
along the length of bars. Chow ( 1959) classified the flow through
bottom racks into vertical and inclined flows. To date, most of the
studies related to flow through bottom racks are based on the
concept of invariant specific energy.
Most of work in this area have been confined to rectangular
prismatic channel of mild or zero slopes. Bauvard ( 1953}, Kunzmann
and Bouvard ( 1954 ), and Mostkow ( 1957) have evolved various
theories and formulae giving the relationship between quantity,
depth of flow and length of racks. Jain et al. (1975}, in their
work on inclined bottom racks, studied the variation of ratio of
diverted flow to upstream flow with respect to 8 (inclination of
bars with horizontal) and upstream Froude number for different bars
with semicircular and triangular tops. Detailed studies on
horizontal transverse bottom racks are limited in literature.
Rangaraju et al. ( 1977) observed that the specific energy along
the transverse bottom rack is not constant, but decreases along the
rack. Subramanya ( 1990 and 1994) and Subramanya and Shukla (1988},
proposed equations for coefficient of discharge for approach flow
conditions and characteristics of the rack. Subramanya and Sengupta
( 1981 ), in their work on flow over transverse bottom rack made of
rectangular section flats, observed that the values of discharge
coefficient C, is not constant, but varied with the flow and rack
geometry parameters viz.; Froude No.(F1), opening area ratio (E),
and the ratio of the width of bars to length of rack (aiL). They
observed that for supercritical flow, C, varies from 0.11 to 0.45
for horizontal parallel bar rack and for subcritical flow C, varies
from 0.36 to 0.85.
In the present study, experimental data on flow over transverse
bottom rack, as given in Chauhan (2000}, are used to (I) check the
dependency ofC 1 on various flow and rack geometry parameters; (2)
test the applicability of existing functional relationships for
discharge coefficient of longitudinal bar bottom racks to
transverse bar bottom racks; and (3) to develop new relationships
for computation of discharge coefficient in case of transverse bar
bottom rack.
THEORETICAL BACKGROUND
For a flow Q with a depth y in a rectangular channel of width B,
the specific energy E can be expressed as
(I)
In Eq. (I), g is acceleration due to gravity. Let the flow
depths at the beginning and end of bottom racks be y 1 and y 2,
as
shown in Fig. I.
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VOL. 13. (2) ANALYSIS OF FLOW OVER HORIZONTAL TRANSVERSE BOTTOM
RACKS
(43)
Corresponding to these depths, the specific energy E 1 and E2
can be expressed as 1
E = + Q~-1 y I 2 B 1 (2) g Y1
E - + (QI -QJ2 1- Y2
2 B 2 1 (3) g Y2
Where Q 1= total discharge at the beginning of the rack, and Qw=
total discharge passing through the rack. In figure I, Q2 = Q 1-Qw
=discharge downstream of main channel, a =width of rack bar, s
=clear spacing of bars in bottom rack, and L =length of bottom
rack.
ENERGY LINE _1 _______ --------
.H.:.~'-:'-1\.-'--"~:J. t=:x --1 Ow (D L (!>
L-SECTION
PLAN
FIG. 1 DEFINITION SKETCH OF BOTTOM RACK FLOW
Following expressions, for water surface profile in case of
spatially varied flow over the bottom racks, assuming that channel
is rectangular and prismatic, kinetic energy correction factor is
unity and specific energy is constant along the bottom rack were
obtained by Mostkow ( 1957) as
(4)
Mostkow ( 1957) also assumed that the gradient of flow with
distance x can be expressed as:
-dQ ~ --=EC 1Bv2gE dx (5)
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(44) ANALYSIS OF FLOW OVER HORIZONTAL TRANSVERSE BOTIOM
RACKS
VOL. 13. !21
where, C 1 =coefficient of discharge and e =ratio of the opening
area to total rack area
(porosity). E being constant, the discharge at any section is
given by
Q = By~2g(E- y) (6) Substituting Eqs. (5). and (6) in Eq.
(4)
dy 2EC 1 ~E(E- y) =
dx 3y-2E (7)
Integrating Eq. (7) and using boundary conditions y = y 1 at x =
0, gives
X= ~[1..!_~1- y, _1._~1- y l (8) EC 1 E E E E
Thus, one can note that at x = L, y = y 2 and eqn. 8 can be used
to compute C 1
DETAILS OF EXPERIMENTAL SETUP AND DATA The schematic view of the
experimental set-up used by Chauhan (2000) is given
in Fig. 2.
INLE T PIPE cF>
t X
MOVABLE POINTER GAUGE
c ITo ______ _ 0 c
~ 0GRILL IJALL 0 0
, . ..
SECTIONAL VIEW ... 1 ___ _
f------I REC. VEIR F-REe-:-wEiR" BRANCH CHAN~EL )[
II CHANNEL III
39.1 ~M
' --II II t MAIN CHANNEL TAIL GATE
-. 60 CM-ii ii 35.5 CM iiiT T
PLAN
FIG. 2 EXPERIMENTAL SET-UP
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\'OL. 13. C! I ANALYSIS OF FLOW OVER HORIZONTAL TRANSVERSE
BOTTOM RACKS
(45)
Main channel is I 0.0 m long, 0.355 m wide (B), 0.6 m deep, and
has a horizontal slope of I in I 000. The bottom rack wao;; located
5.30 m downstream of the main channel. The rectangular bars cut out
of mild steel plates of length 0.355 m, width 0.02 m and thickness
0.005 m, were used for bottom rack set up. Photographs of
experimental set up in hydraulic engineering lab at liT Roorkee are
shown in figures 3a and 3b. Flow depths y 1 and y 1 at upstream and
downstream end of bottom rack were measured at the centre line of
main channel with a point gauge having least count ofO.OOOI m.
Geometry of bottom racks, i.e., length (L), width of bar( a),
spacing between bars (s), and porosity (ratio of opening area to
total area of the rack) (E), were varied with the experiments.
FIG. 3 (a) MEASUREMENT OF FLOW DEPTH
Fig. 3 (b) BOTTOM RACKS WITH SPACING 0.028 m
In the present study, a set of 219 runs have been obtained. The
range of various variables involved in the experimental program is
given in Table 1.
TABLE-t RANGE OF EXPERIMENTAL DATA (Chauhan, 2000)
S. No. Variables Unit Minimum Maximum
I. Q m3/s 0.010 0.076 2. Qw m-1/s 0.008091 0.062971 3. aiL
dimensionless 0.041 0.102 4. Spacing between bars (s) (m) 0.004
0.028 5. Porosity (E) dimensionless 0.173 0.627 6. Froude No. (f1)
dimensionless 0.1 1.5
ANALYSIS OF THE EXPERIMENTAL DATA
The first objective of the study has been to analyse the
variation of discharge coefficient C1_ By adopting Mostkow's
equation (Eq. (8)) and applying boundary
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(46) ANALYSIS OF FLOW OVER HORIZONTAL TRANSVERSE BOTTOM
RACKS
conditions. the expressions for C 1 can be written as
C~=E~[~~~-~ _Y~~~-y~l
VOL. n. 1:!1
(9)
Let, the diverted flow through bottom rack is Qw. Thus for known
initial conditions i.e.
-
VOL. 13. (21 ANALYSIS OF FLOW OVER HORIZONTAL TRANSVERSE 801TOM
RACKS
FUNCTIONAL RELATIONSHIPS
(47)
Based upon the flow characteristics, Subrdmanya and Shukla (
1988) proposed a classification of the flow over bottom mcks into
five types. Table 2 shows the characteristic features of the types
of flow over bottom racks. In present work, 57 o/c runs
corresponded to 82 type, 35% runs A3 type and only 8% as B I type.
Subramanya ( 1997) gave functional relationships for the variation
of discharge coefficient, in various types of flows for inclined
and horizontal. longitudinal bar bottom rdcks. These functional
relationships take into account important rack geometry and flow
parameters. A typical relationship for A3 type flow over
longitudinal bar bottom racks was proposed by Subramanya ( 1990)
as,
C1 = 0.752+0.281og(D/ s}-0.5651],; (13) In Eq. ( 13 ). D is the
diameter of the rack bar, and 11 E is defined ali a flow
parameter
TABLE-2 TYPES OF FLOW OVER BOTfOM RACKS
Type Approach Flow over the rack Downstream state AI Subcritical
Supercritical May beajump A2 Subcritical Partially Supercritical
Subcritical A3 Subcritical Subcritical Subcritical 81 Supercritical
Supercritical May be a jump 82 Supercritical Partially
Supercritical Subcritical
To obtain a regression relationship for variation of discharge
coefficient in case of transverse bar bottom mcks. similar
functional form of Eq. ( 13) has been considered in the present
work, i.e.
(14) where, a1, b 1 and c 1 are regression coefficients. a is
width of the rack bar, and s is clear spacing of the bars in the
rack. To obtain a1, b1 and c 1 an error term AAPE (Average Absolute
Percentage Error) is defined as
IOOx i: ObservedC1 -ComputedC1 AAPE = ___ i=_; ___
o_b_se_rv_e_d_C_1 __ ~ (15}
n
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(48) ANALYSIS OF FLOW OVER HORIZONTAL TRANSVERSE BOTIOM
RACKS
where, n is the number of observations.
VOL. 13, (2)
To obtain a 1, b1 and c1, trials have been performed to minimize
AAPE and the best fitting values for different types of flows over
transverse bottom racks have been obtained. Using these values of
a1, b1 and c1 for each type of flow, the following relationships
are obtained:
A3 Type flow: C 1 = 0.484 +0.181og(a/s) -0.518TlE Bl Type flow:
C 1 = 0.536+0.241og(a/s)-0.912TlE B2 Type flow: C 1 = 0.726 +
0.241og(a Is) -l.274TlE
(16) (17) (18)
C 1 values for different runs obtained using Eqs. (16), ( 17)
and ( 18) have been found to be in very good agreement with C 1
calculated using experimental data. The AAPE values have been found
to be 4.38 %, 6.28% and 7.67% for A3, B I and B2, type of flows
respectively. Agreement diagram between observed. and computed
discharge through bottom racks, using C1 values obtained from Eqs.
(16), (17) and ( 18), for A3, B I and B2 type of flow is shown in
figures (5), (6) and (7) respectively. Lack of good agreement for
some of the values is possibly due to specific energy loss in the
direction of flow, which needs to be investigated further. Good
agreement of computed values with observed ones indicates that Eqs.
(16), (17) and ( 18) can be used for the computation of C 1
0.01
----Moooooooo--oMoooooooooooo--oo---------------oooooooooooooo-oooooooooooooooo
0.06 Ill G) u E 0.05 ::l (.)
~0.04 G) ~
~0.03 0 (.) -o.o2 0
0.01
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Ow (Observed) (C umecs)
FIG. 5 AGREEMENT DIAGRAM BETWEEN OBSERVED AND COMPUTED DISCHARGE
THROUGH BOTTOM RACK FOR A3 TYPE FLOW
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VOL 13. 121
0.035
rn 0.028 0 Q) E ::J
(.) 0.021 "0
~ ::J Cl. E0.014 0
(.)
~ 0 0.007
0 0
ANALYSIS OF FLOW OVER HORIZONTAL TRANSVERSE BOlTOM RACKS
0.007 0.014 0.021 0.028 Qw (Observed) (Cumecs)
(49)
0.035
FIG. 6 AGREEMENT DIAGRAM BETWEEN OBSERVED AND COMPUTED DISCHARGE
THROUGH BOTTOM RACK FOR B1 TYPE FLOW
0.05
...............................................................
.
~ 0.04
- (50) ANALYSIS OF FLOW OVF.R 1101
-
\ OL U. 121
REFERENCES
ANALYSIS OF rLOW OVER HORIZONTAL TRANSVERSE ROTTOI\1 RACKS
(51)
Bouvard. M. ( 1953). Discharge Passing through a Bottom Grid. La
Houille Blanche. No. 2, pp. 290-291.
Chauhan. N. S. (2000). Analysis of Flow through Bottom Racks.
M.E. Thesis. Civil Engineering Department, UOR, Roorkee, pp.
56.
Chow, V. T. ( 1959). Open Channel Hydraulics. McGraw Hill Book
Company, New York, pp. 337-340.
Jain, A. K .. Asawa. G. L. and Mehrotra, A. K. ( 1975). Bottom
Racks-An Experimellfal Studv. Journal of Irrigation & Power,
Vol. 3( I), pp. 219-222.
Kuntzmann, J. and Bouvard, M. (1954). Theoretical Study of
Bottom Type Water /make Grids. La Houille Blanche, No. 3, pp.
569-574.
Mostkow, M.A. ( 1957).A Theoretical Study of Bottom Type
Wt-uerlntake. La Houille Blanche, No. 4, pp. 570-580.
Rangaraju, K. G., Asawa, G. L. and Setharamaiah, R. (
l977).Analysis of Flow through Bottom Racks in Open Channels. 61h
Australasian Hydraulics and Fluid Mechanics Conference, Adelaide,
Australia, pp. 237-240.
Suhramanya, K. ( 1990). Trench Weir Intake for Mini Hydro
Projects. Proc. Hydromech and Water Resources Conference. liSe
Bangalore, pp. 33-41 .
Subramanya, K. ( 1994). Hydraulic Characteristics of Inclined
Bottom Racks. National Symposium on Design of Hydraulic Structures.
Department of Civil Engineering. UOR Roorkee, pp. 3-9.
Subramanya. K. ( 1997). Flow in Open Channels. McGraw Hill
Publishing Company Ltd., New Delhi, pp. 283-288.
Subramanya, K. and Sengupta, D. ( 1981 ). Flow through Bottom
Racks. Indian Journal of Technology, Vol. 19. No. 2, pp. 64-67.
Subramanya, K. and Shukla, S. K. (1988). Discharge Diversion
Characteristics of Trench Weir. Journal of Civil Engineering
Division, Institute of Engineers (India). Vol. 69, pp. 163-168.
NOTATIONS a = width of rack bar a 1, b 1 & c 1 = regression
coefficients B = width of bottom rack C 1 = Mostkow's discharge
coefficient, when effective head is equal to
specific energy E = specific energy
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(52)
El = E, = Fl = g = L = Ql = Q\1 = s =
VI = X = y = yl = Yc = f.:
TIE =
ANALYSIS OF R.OW OVER HORIZONTAL TRANSVERSE BCJ"ffi)M RACKS
specific energy at the inlet of the rack specific energy at the
th.Jtlet of the rack Froude number of the flow .tt the beginning of
the rack acceleration due to gravity length of the bottom rack
total discharge at the beginning of the rack total discharge
passing through the rack clear spacing of the bars in the rack flow
velocity at inlet of rack
VOL U. 12
distance along the rack measured from the beginning of the rack
depth at any section depth at the beginning: of the rack depth at
the end of the rack ratio of the opening area of rack to the total
rack area a flow parameter
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