This article was downloaded by: [UGR-BTCA Gral Universitaria]On: 12 March 2015, At: 08:46Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,UK

ISH Journal of HydraulicEngineeringPublication details, including instructions for authorsand subscription information:http://www.tandfonline.com/loi/tish20

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

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all theinformation (the Content) contained in the publications on our platform.However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness,or suitability for any purpose of the Content. Any opinions and viewsexpressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of theContent should not be relied upon and should be independently verified withprimary sources of information. Taylor and Francis shall not be liable for anylosses, actions, claims, proceedings, demands, costs, expenses, damages,and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of theContent.

This article may be used for research, teaching, and private study purposes.Any substantial or systematic reproduction, redistribution, reselling, loan,sub-licensing, systematic supply, or distribution in any form to anyone isexpressly forbidden. Terms & Conditions of access and use can be found athttp://www.tandfonline.com/page/terms-and-conditions

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015

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.

ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. IJ. 2007. NO. 2

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015

(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.

ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. 13. 2007. NO.2

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015

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)

ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. 13. 2007. NO.2

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015

(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

ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. 13. 2007. NO.2

t X

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015

\'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

ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. 13. 2007. NO. 2

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015

(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

ISH JOURNAL OF HYDRAULIC ENOINEERINO, VOL 13. 211. NO.2

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015

(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

ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. 13. 2007. NO.2

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015

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

ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. 13. 2007. NO.2

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015

(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

ISH JOURNAL OF HYDRAULIC ENGINEERING. VOL. l.l 2007. NO.2

Dow

nloa

ded

by [U

GR-B

TCA

Gral

Unive

rsitar

ia] at

08:46

12 M

arch 2

015