Experimental and Numerical Investigations on the Effect of Rectangular Openings’ Aspect Ratio on Outflow Discharge

Document Type: Research Paper

Authors

1 Ph.D. Student, Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran 19537, Iran

2 Associate Professor, Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran 19537, Iran

3 Assistant Professor, Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES),Tehran 19537, Iran

4 Assistant Professor, Civil, Water and Environmental Engineering Department, Shahid Beheshti University, Tehran 1658953571, Iran

Abstract

Up to now, a few formulas have been suggested by scholars for the amount of discharge from openings, however, the effect of opening's geometry on the amount of discharge has not addressed thoroughly. In this study, to assess the effect of rectangular openings’ aspect ratio on the discharge amount, experimental and numerical investigations have been conducted on the discharge amount from rectangular openings at the bottom of tanks. In the experimental part of the study different water depths have been considered and the amounts of discharge have been measured for openings with identical area, but different aspect ratios. In the numerical part of the study the test results have been compared to those obtained from finite-volume-based numerical simulation. The experimental and numerical results are in good agreement, and both show that there is a trend of increase in the amount of discharge with increase of the opening’s aspect ratio. The amount of this increase is from 13% to 21% for hydraulic head varying between 0.3 to 0.6 meters. On this basis, the conventional orifice formula for calculation of the rectangular opening discharge needs modification.

Keywords

Main Subjects

[1] Schussler, H., The water supply of San Francisco, California, before, during and after the earthquake of April 18th, 1906: and the subsequent conflagration. MB Brown Press, 1906.

[2] Manson, M., Harris De Haven, C., Ransom, T.W., Robinson, W.C., Reports on an auxilary water supply system for fire protection for San Francisco, California. Britton & Rey, 1908.

[3] Lawson, A.C., Reid, H.F., The California Earthquake of April 18, 1906: Report of the State Earthquake Investigation Commission. No. 87. Carnegie institution of Washington, 1908.

[4] Scawthorn, C., O’Rourke, T.D., Blackburn, F.T., The 1906 San Francisco earthquake and fire—Enduring lessons for fire protection and water supply, Earthquake Spectra, 22(S2) (2006) 135-158.

[5] Steinbrugge, K.V., Schader, E.E., Bigglestone, H.C., Weers, C.A., San Fernando earthquake, February 9, Pacific Fire Rating Bureau, San Francisco, California, 1971.

[6] Jennings, P.C., Housner, G.W., Earthquake Damage to Water and Sewerage Facilities, San Fernando, California Earthquake of February 9, 1971, U.S. Department of Commerce, N.O.A.A., Washington, D.C., 2 (1973) 75-1973.

[7] Eguchi, R.T., Earthquake performance of water supply components during the 1971 San Fernando Earthquake, Prepared for the National Science Foundation. Redondo Beach, CA: JH Wiggins Company, 1982.

[8] Lund, L., Cooper, T., Water system." Northridge Earthquake: Lifeline Performance and Post-earthquake Response, Technical Council on Lifeline Earthquake Engineering Monograph No 8, (1995) 96-131.

[9] Hall, J.F., Northridge earthquake of January 17, 1994: reconnaissance report, Eeri, 1995.

[10] Eguchi, R.T., Chung, R.M., Performance of lifelines during the January 17, 1994 Northridge Earthquake. No. CONF-9508226, American Society of Civil Engineers, New York, NY (United States), 1995.

[11] O'Rourke, T.D., Stewart, H.E., Jeon, S.S., Geotechnical aspects of lifeline engineering, Proceedings of the Institution of Civil Engineers-Geotechnical Engineering, 149(1) (2001) 13-26.

[12] Shi, P., O'Rourke, T.D., Seismic response modeling of water supply systems, Technical Report MCEER-08-0016. May 5, 2006.

[13] Makar, J.M., Desnoyers, R., McDonald, S.E., Failure modes and mechanisms in gray cast iron pipe, International conference, Underground Infrastructure research: municipal, industrial and environmental applications; Kitchener, Canada, (2001) 303-312.

[14] Neville, J., Hydraulic tables, coefficients, and formulae for finding the discharge of water from orifices, notches, weirs, pipes, and rivers, Lockwood & Co., London, 1875.

[15] Bovey, H.T., A treatise on hydraulics, New York, Wiley, 1909.

[16] Greyvenstein, B., Van Zyl, J.E., An experimental investigation into the pressure-leakage relationship of some failed water pipes, Journal of Water Supply: Research and Technology-AQUA, 56(2) (2007) 117-124.

[17] White, F.M., Fluid Mechanics fourth edition, McGraw and Hill, International Edition, Singapore, 1994.

[18] Greyvenstein, B., An experimental investigation into the pressure-leakage relationship of some failed water pipes in Johannesburg, Eng. Final Year Project Report, 2004.

[19] Cassa, A.M., Van Zyl, J.E., Laubscher, R.F., A numerical investigation into the behaviour of leak openings in uPVC pipes under pressure, CCWI2005 Water Management for the 21st Century (2005) 155-160.

[20] Cassa, A.M., Van Zyl, J.E., Laubscher, R.F., A numerical investigation into the effect of pressure on holes and cracks in water supply pipes, Urban Water Journal, 7(2) (2010) 109-120.

[21] Cassa, A.M., Van Zyl, J.E., Laubscher, R.F., A numerical investigation into the effect of pressure on holes and cracks in water supply pipes, Urban Water Journal, 7(2) (2010) 109-120.

[30] Almohammadi, K.M., Ingham, D.B., Ma, L., Pourkashan, M., Computational fluid dynamics (CFD) mesh independency techniques for a straight blade vertical axis wind turbine, Energy, 58 (2013) 483-493.

[22] Cassa, A.M., A numerical investigation into the behaviour of leak openings in pipes under pressure, PhD diss., University of Johannesburg, 2008.

[23] Brater, E.F., King, H.W., Handbook of hydraulics for the solution of hydraulic engineering problems, 1976.

[24] Michelotti, F.D., Sperimenti idraulici principalmente diretti a confermare la teorica e facilitare la pratica del misurare le acque correnti, Stamperia Reale, Turin, Italy, 1767.

[25] Groulx, D., Numerical study of nano-enhanced PCMs: are they worth it, In Proceedings of the 1st Thermal and Fluid Engineering Summer Conference, TFESC, New York City, USA, 2015.

[26] Shahangian, S.A., Experimental and numerical investigation on the leakage head-discharge relationship in the water distribution networks, M.Sc. Thesis, University of Tehran, 2015.

[27] Shahangian, S.A., Numerical study of leakage of submerged steel pipes in water based on laboratory results of non-submerged pipes, Iranian Journal of Water and Wastewater, 11(4) (2017) 100-120 (In Persian).

[28] Temam, R., Navier-stokes equations, Amsterdam: North-Holland, 1984.

[29] Feistauer, M., Theory and Numerics for Problems of Fluid Dynamics, Charles University Prague, Faculty of Mathematics and Physics, 2006.

[30] Ondřej, S., Mohelníková, J., Plášek, J., Thermal CFD analysis of tubular light guides, Energies, 6(12) (2013) 6304-6321.

[31] Almohammadi, K.M., Ingham, D.B., Ma, L., Pourkashan, M., Computational fluid dynamics (CFD) mesh independency techniques for a straight blade vertical axis wind turbine, Energy, 58 (2013) 483-493.

[32] Soroushian, A., Pseudo convergence and its implementation in engineering approximate computations, In Proceedings of 4th international conference from scientific computing to computational engineering (IC-SCCE 2010), Athens, Greece. 2010.

[33] Soroushian, A., Equivalence between convergence and pseudo convergence when algorithmic parameters do not change geometrically, In Proceedings of 6th international conference from scientific computing to computational engineering (IC-SCCE 2014), Athens, Greece. 2014.

[34] Liu, S., Valkó, P.P., Optimization of Spacing and Penetration Ratio for Infinite-Conductivity Fractures in Unconventional Reservoirs: A Section-Based Approach, SPE Journal, 22(6) (2017) 1-16.

[35] Soroushian, A., Proper convergence, a concept new in science and important in engineering, In Proceedings of 4th international conference from scientific computing to computational engineering (IC-SCCE 2010), Athens, Greece. 2010.

[36] Matthews, R.J., Liggett, J.A., Flow in a sharp corner, Journal of the Hydraulics Division, 93(6) (1961) 387-410.