Closure to “Hydraulic Characteristics of a Drop Square Manhole with a Downstream Control Gate” by Rita F. Carvalho and Jorge Leandroby Rita F. Carvalho, Jorge Leandro

Journal of Irrigation and Drainage Engineering

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Text

Discussions and Closures

Discussion of “Hydraulic Characteristics of a Drop Square Manhole with a Downstream

Control Gate” by Rita F. Carvalho and

Jorge Leandro

June 2012, Vol. 138, No. 6, pp. 569–576.

DOI: 10.1061/(ASCE)IR.1943-4774.0000437

F. Granata1; G. de Marinis2; R. Gargano3; and W. H. Hager, F.ASCE4 1Assistant Professor, Dipartimento di Ingegneria Civile e Meccanica,

Università degli Studi di Cassino e del Lazio Meridionale, Via G. Di

Biasio 43, 03043 Cassino (FR), Italy (corresponding author). E-mail: f.granata@unicas.it 2Full Professor, Dipartimento di Ingegneria Civile e Meccanica, Università degli Studi di Cassino e del Lazio Meridionale, Via G. Di Biasio 43, 03043 Cassino (FR), Italy. E-mail: demarinis@unicas.it 3Associate Professor, Dipartimento di Ingegneria Civile e Meccanica,

Università degli Studi di Cassino e del Lazio Meridionale, Via G. Di

Biasio 43, 03043 Cassino (FR), Italy. E-mail: gargano@unicas.it 4Professor, Laboratory of Hydraulics, Hydrology and Glaciology VAW,

ETH Zurich, CH-8092 Zürich, Switzerland. E-mail: hager@vaw .baug.ethz.ch

The discussers wish to stress some aspects of impact number I in relation to the results of this paper. The different experimental apparatuses of Granata et al. (2011) and the authors lead to different results, so that their direct comparison in Table 1 appears inappropriate. If the authors highlight only the different manhole sections, namely the authors’ square section and the circular section of

Granata et al. (2011), they overlook the effect of the jet takeoff angle α on the phenomena in addition to the shape of the downstream intake. Whereas α ¼ 0 (horizontal inflow jet) for all data of the discussers, the authors in the original paper assumed α ¼ −35°.

The impact number

I ¼  2 · s g  0.5 ·

Vo

DM ð1Þ represents the ratio between the jet range xr for α ¼ 0 and yðxÞ ¼−s from Eq. (2) and the manhole diameter DM, where Vo = approach flow velocity; and g = gravity acceleration. Because the discussers used α ≠ 0, I needs to be adjusted by means of the equation of the material point trajectory under gravity: yðxÞ ¼ tanðαÞx − g 2V2ocos2ðαÞ x2 ð2Þ

The discussers’ jet range results, by solving Eq. (2) and taking into account α ¼ −35° and yðxÞ ¼ −s, as xr ¼ tanð−35°Þ þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffitan2ð−35°Þ − 2gs=V2ocos2ð−35°Þp g=V2ocos2ð−35°Þ ð3Þ

The authors’ values of I according to Eq. (3) are stated in Table 1.

Regarding the limits of the regimes, the discussers wish to underline the following. The authors consider Eq. (2) describing the jet trajectory. Based on this assumption, they define precise values of I for the regime thresholds as • I ¼ 1 between R1 and R2; and • I ¼ 1.5 between R2 and R3 with the first limit I ¼ 1 if xr ¼ DM and yðxÞ ¼ −s. In addition, they suggest two other relations to classify the regimes in terms of ho ¼ approach flow depth, and hm ¼ manhole pool depth, namely

I ¼  2ðs − hoÞ g  0.5 ·

Vo

DM

I ¼  2ðs − hmÞ g  0.5 ·

Vo

DM ð4Þ

These account for the jet thickness and the pool height. Therefore, the authors specify the limits of the governing regimes by

Eq. (4), yet classify them based on Eq. (2), i.e., an approximate relation describing the material point under gravity force.

In addition, the authors attribute the aforementioned I limits to the discussers, whereas Granata et al. (2009, 2010, 2011, 2012) suggest • I ≅ 0.6 between R1 and R2; • I ≅ 0.95 ÷ 1 between R2 and R3; and • I ≅ 1.5 between R3a and R3b in which the third condition applies for the circular drop manhole, because it is impossible to distinguish regimes R3a and R3b for the square manhole.

Granata et al. (2009, 2010, 2011, 2012) suggested Eq. (2) only to detect the dimensionless parameter I describing the hydraulic phenomena, and to classify the regimes. Indeed, I appears to be an effective notion to describe circular drop shaft flow in relation to energy loss, pool height, and air entrainment (Granata et al. 2011). Therefore, it would be interesting to investigate the ability of I to describe the hydraulic phenomena for the square drop manhole.

To obtain a rigorous description of the jet profile, an improved usage of specific equations would be suggested, as proposed by

Clausnitzer and Hager (1997) y ho ¼ 1 3 x ho

F−0:8o þ 1 4 x ho ½F−0:8o 2 jet profile y he ¼ 1þ 0.06 x ho

F−0:8o jet thickness ð5Þ rather than Eq. (2), and rather than Eq. (4) to account for the jet thickness, where Fo = approach flow Froude number; and he = end outflow depth of pipe.

Finally, the discussers, unlike the authors in the original paper, would like to state that instead of Christodoulou (1991), they suggest the impact number [Eq. (1)] to classify the regimes and to analyze typical hydraulic flow phenomena in circular drop manholes.

Table 1. Impact Number for Jet Take-Off Angle α ¼ −35°

Vo (m=s) 0.97 1.06 1.12 1.17 1.21 1.28 1.32 1.38 1.4 1.41 1.47 1.48 1.52 1.53

I (–) 0.52 0.56 0.58 0.60 0.62 0.65 0.67 0.69 0.70 0.70 0.73 0.73 0.75 0.75

JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE / JULY 2013 / 593

References

Christodoulou, G. C. (1991). “Drop manholes in supercritical pipelines.”

J. Irrig. Drain. Eng., 117(1), 37–47.

Clausnitzer, B., and Hager, W. H. (1997). “Outflow characteristics from circular pipe.” J. Hydraul. Eng., 123(10), 914–917.

Granata, F., de Marinis, G., and Gargano, R. (2012). “Criteri per il dimensionamento dei pozzetti di salto circolari [Criteria for the design of circular drop manholes].” L’Acqua, 90(2), 9–20 (in Italian).

Granata, F., de Marinis, G., Gargano, R., and Hager, W. H. (2009). “Energy loss in circular drop manholes.” 33rd IAHR Congress (CDROM), International Association for Hydro-Environment Engineering and Research.