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mity coefficient should be done by conducting field experiments

in future.

References

Capra, A., and Scicolone, B. 2004. Emitter and filter test for waste-

water reuse by drip irrigation. Agric. Water Manage., 682, 135

149.

Christiansen, J. E. 1942. Hydraulics of sprinkler systems for irriga-

tion. Trans. Am. Soc. Civ. Eng., 107, 221239.Duran-Ros, M., Puig-Barques, J., Arbat, G., Barragan, J., and de

Cartagena, F. R. 2009. Effect of filter, emitter and location on clog-

ging when using effluents. Agric. Water Manage., 961, 6779.

ISO.2003. ISO/TC 23/SC 18/WG5 N4: Clogging test methods for emit-

ters, International Organization for Standardization, Geneva.

Li, G. Y., Wang, J. D., Alam, M., and Zhao, Y. F. 2006. Influence of

geometrical parameters of labyrinth flow path of drip emitters on hy-

draulic and anticlogging performance. Trans. ASABE, 493, 637

643.

Nakayama, F. S., and Bucks, D. A. 1986. Trickle irrigation for crop

productionDesign, operation, and management developments in ag-

ricultural engineering, 9 , Elsevier, New York.

Wei, Q. S., et al. 2008a. Evaluations of emitter clogging by two-phase

flow simulations and laboratorial experiments. Comput. Electr. Eng.,

632, 294303.Wei, Q. S., Shi, Y. S., Dong, W. C., and Huang, S. H.2006a. Advanced

methods to develop drip emitters with new channel types.Appl. Eng.

Agric., 222, 243249.

Wei, Q. S., Shi, Y. S., Dong, W. C., Lu, G., and Huang, S. H. 2006b.

Study on hydraulic performance of drip emitters by computational

fluid dynamics. Agric. Water Manage., 8412, 130136.

Wei, Q. S., Shi, Y. S., Lu, G., Dong, W. C., and Huang, S. H. 2008b.

Rapid evaluations of anticlogging performance of drip emitters by

laboratorial short-cycle tests. J. Irrig. Drain. Eng., 1343, 298304.

Wu, I. P. 1997. An assessment of hydraulic design of micro-irrigation

systems. Agric. Water Manage., 323, 275284.

Wu, I. P., Lin, B. Y., and Lau, L. S. 1991. Plugging evaluation in the

reuse of sewage effluent by drip irrigation. Proc., ASCE National

Conf., Honolulu.

Discussion of Method of Solution ofNonuniform Flow with the Presence ofRectangular Side Weir byMaurizio Venutelli

November/December 2008, Vol. 134, No. 6, pp. 840846.

DOI: 10.1061/ASCE0733-94372008134:6840

Ali R. Vatankhah1

and M. Bijankhan2

1Asst. Prof., Irrigation and Reclamation Eng. Dept., Univ. College of

Agriculture and Natural Resources, Univ. of Tehran, P.O. Box 4111,Karaj, Iran 31587-77871. E-mail: arvatan@ut.ac.ir

2M.Sc. Student, Irrigation and Reclamation Eng. Dept., Univ. College of

Agriculture and Natural Resources, Univ. of Tehran, P.O. Box 4111,

Karaj, Iran 31587-77871. E-mail: bijankhan@ut.ac.ir

The discussers would like to thank the author for presenting an

iterative step method for solving the spatially varied flow equa-

tion with decreasing discharge. The discussers, however, would

like to add a few points.

The proposed iterative step method incorporates the variations

along the side weir, of the specific energy due to the bottom and

friction slope, of the weir coefficient, and of the velocity distri-

bution coefficient. The results, in comparison with experimental

data and with the solutions obtained assuming constant specific

energy, are also presented.

To improve the solution, the author incorporates the variations

along the side weir for different parameters, but for achieving a

direct integration of the spatially varied flow equation, these pa-

rameters have been assumed constant for the computational weir

segmentsx. In this case, the accuracy of the proposed analyti-cal solution is influenced. Considering constant energy along the

computational weir segment causes c1 =0. Thus, this parameter

can be omitted in the proposed analytical solution. In such a case,

the solution reduced to the solution proposed by De Marchi

1934. Also since x0 the application of Eq. 22 or Eq. 23

in the original paper requires a tedious trial and error procedure.

Suitable Governing Equation

For a short weir, the hypothesis of constant specific energy along

the side weir is acceptable Sf= S0. Considering this assumption

and assuming

=1, the nonlinear ordinary differential equationgoverning spatially varied flow with decreasing discharge takes

the form

dy

dx=

4CW

3WEyyp3

3y 2E1

Muslu 2001 derived the weir coefficient for subcritical flow

conditions in the case ofx= 0

CW= 0.611

31 0.036

2E

/

y 1y/

E 2 2

An analytical solution of Eq. 1 is not possible for variable weir

coefficient. In this case, Eq. 1 can be numerically integratedwith the aid of any mathematical software such as MathCad,

Maple, or Mathematica.

To verify Eq. 1, it is referred to the experimental observa-tions carried out by Hager1982and mentioned by the author. Incurrent research, specific energy at the control section is consid-

ered a constant for numerical integration of Eq. 1. The com-puted and measured values are given in Table 1 together with

computed values by Muslu 2001. In comparison with the au-

thors solution, the numerical integration method gives better re-

sults as indicated by the standard error values. Discharges and

flow depths calculated in the current study are also shown in Fig.1. As seen, the predicted values are in good agreement with the

measured ones.

Alternative Governing Equation

Considering =1, subcritical depth in a rectangular canal can be

determined by the inversion of the specific energy equation as

Chanson 1999

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y=E13

+2

3cos1

3cos11 27Q2

4gw2E3 3

Using Eq. 8 of the original paper

dx= 3

2CW2gy p3/2dQ 4

Substituting Eqs. 2 and 3 in Eq. 4 yields

dx= fQ,w,p,EdQ 5

where ffunction ofQ,w, p , and E. For a given problem,w and

pconstant. Assuming constant specific energy along the side

weir, this nonlinear ordinary differential equation can be numeri-

cally solved for Q. As seen, in such a case, S0 and Sf does not

appear in the differential equation. After determining Q, y can be

calculated by Eq. 3. It should be noted that predicted values byEq. 3 are the same as those by Eq. 1.

Conclusion

Considering a variable weir coefficient, the classical hypothesis

about constant specific energy is still acceptable for a short side

weir and for subcritical flow conditions. In this case, there is not

an analytical solution for the governing equation, and numericalintegration methods can be used for solving the equation. It

should be noted that considering the term ofSf-S0 in the govern-

ing equation reduces the accuracy of the predicted values in the

case of constant specific energy. As shown, S0 and Sf can be

omitted from the governing equation. Also predicted values

Table 1 show =1 is acceptable in the computations.

Table 1. Experimental Verification of Simple Numerical Solution E=Cons. and = 1 Using Data of Hager 1998

Distance from upstream

end of the weir m

Depth of flow cm Rate of flowl/s

Measured

Computed by

Muslu 2001

Computed by

discussers Measured

Computed by

Muslu 2001

Computed by

discussers

Run E

0.0 19.20 19.30 19.16 38.87 36.93 37.88

0.2 19.31 19.64 19.54 35.49 34.38 35.20

0.4 19.88 19.98 19.91 31.97 31.36 32.04

0.6 20.50 20.30 20.27 28.44 27.97 28.37

0.8 20.78 20.61 20.59 24.23 23.95 24.191.0 20.88 20.88 20.88 19.52 19.52 19.52

ry =0.19890 ry =0.16994 rQ =1.06462 rQ =0.46381

Run F

0.0 24.36 24.59 24.49 39.79 40.12 41.21

0.2 24.48 24.83 24.76 35.79 37.1 38.01

0.4 24.92 25.06 25.02 32.40 33.86 34.45

0.6 25.32 25.29 25.27 28.70 30.13 30.54

0.8 25.55 25.50 25.49 25.67 26.12 26.28

1.0 25.69 25.69 25.69 21.70 21.7 21.7

ry =0.19920 ry =0.14926 rQ =1.11391 rQ =1.72656

Run G

0.0 17.72 18.12 17.95 39.06 39.20 40.07

0.2 17.43 18.36 18.23 38.82 37.88 38.61

0.4 18.61 18.63 18.53 36.40 36.22 36.86

0.6 18.27 18.90 18.84 34.46 34.35 34.80

0.8 18.95 19.18 19.15 31.92 32.14 32.39

1.0 19.46 19.46 19.46 29.60 29.60 29.60

ry =0.54316 ry =0.46135 rQ =0.44634 rQ =0.56786

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References

Chanson, H. 1999. The hydraulics of open channel flows: An introduc-

tion, 1st Ed., Edward Arnold, London.De Marchi, G. 1934. Saggio di teoria del funzionamento degli stra-

mazzi laterali. Energ. Elettr., 1111, 849860 in Italian.

Hager, W. H. 1982. Die hydraulik von verteilkanlen. Teil 12, Mit-

teilungen der Versuchsanstalt fr Wasserbau, Hydrologie und Glazi-

ologie, No. 5556, Zurich, Switzerland.

Muslu, Y. 2001. Numerical analysis for lateral weir flow. J. Irrig.

Drain. Eng., 1274, 246253.

Fig. 1. Depths of flow and discharges computed and observed along the side weir using data of Hager 1998

814 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING ASCE / NOVEMBER/DECEMBER 2009

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Closure to Method of Solutionof Nonuniform Flow with the Presenceof Rectangular Side Weir by MaurizioVenutelli

November/December 2008, Vol. 134, No. 6 , pp. 840846.

DOI: 10.1061/ASCE0733-94372008134:6840

Maurizio Venutelli1

1Dipartimento di Ingegneria Civile, Universit di Pisa, Via Gabba 22,

I-56126 PISA. E-mail: m.venutelli@ing.unipi.it

The author would like to thank the discussers for their interest

in the paper. The writer is of an opinion that it is practically

impossible incorporate all the parameters in the general integral

of Eq.15. Therefore, has proposed an method in which the weir

coefficient Cw and the velocity distribution coefficient are as-

sumed constant in the step weir segment x. At contrary, the

bottom slope So and the energy slope Sfare integrated explicitly.

However, it is important to notice the better results obtained by

the discussers with Cwvariable, from the numerical integration of

the basic ordinary differential equation of the De Marchis theory.

On the other hand, as it can be verified, for all test cases pre-

sented, on side weir with a length of 1 m, we have a Froudenumber Fr0.6. The results obtained by the discussers confirm,

as indicate theoretically by De Marchi 1934and experimentally

by Gentilini 1938 and Collinge 1957, that for short side weir

and for subcritical flow conditions, the validity of constant energy

and of the coefficient of velocity distribution equal to 1. But if

these hypotheses are not verified, De Marchis theory show seri-

ous disagreement from the experimental results Hager and

Volkart 1986. For a reasonable accuracy, the friction gradient

and, for any weir segment an appropriate value of distribution

velocity and weir coefficients are take into account in the pro-

posed model.

Energy losses, in particular for supercritical flow, produce pro-

files above the De Marchis solution and in good agreement with

the observed values as shown in Fig. 6. Under this flow condi-

tions, in accordance with the recent study of Durga Rao and Pillai

2008on several test cases, the values of the differences from the

bottom and the energy slopetermc1in the paperare significant.Moreover, as been observed by El-Khashab and Smith 1976forsubcritical flow the value of, as a consequence of the nonuni-

form velocity distribution, becomes very high towards the end of

the weir. This aspects, as can be see from Fig. 4, is evaluated inthe paper by Hagers model for rectangular channel of Eq. 7.

The effects of the variations of along the side weir are exam-

ined in details in the works of Lee and Holley 2002 and Mayet al. 2003.

In conclusion, the versatility of Eq. 22 or 23 allows tocompute, for wholly subcritical and wholly supercritical flow pro-

files, the longitudinal variations of the bottom and energy slope,

and the longitudinal variations of the weir coefficient and of the

velocity distribution coefficient continuously and step by step,

respectively.

References

Durga Rao, K. H. V., and Pillai, C. R. S. 2008. Study of flow over side

weirs under supercritical conditions. Water Resour. Manage., 22,

131143.

El-Khashab, A., and Smith, K. V. H. 1976. Experimental investigations

of flow over side weirs. J. Hydr. Div., 1029, 12551268.

Lee, K.-L., and Holley, E. R. 2002. Physical modeling for side-channel

weirs. CRWR Online Rep. 02-2, Center for Research in Water Re-

sources, Univ. of Texas, Austin, Tex.

May, R. W. P., Bromwich, B. C., Gasowski, Y., and Rickard, C. E.

2003. Hydraulic design of side weirs, Thomas Telford, London.

JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING ASCE / NOVEMBER/DECEMBER 2009 /815

Downloaded 10 Nov 2010 to 217 218 49 8 Redistribution subject to ASCE license or copyright Visithttp://www ascelibrary org