Contribution to the Analytical Equation Resolution Using Charts for Analysis and Design of Cylindrical and Conical Open Surge Tanks
Affiliation(s)
1 Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, 2500 Chemin de Polytechnique, Montreal, QC, Canada. 2 Department of CGEM, Polytechnique Montréal, Succursale Centre, Montréal, Canada.
1 Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, 2500 Chemin de Polytechnique, Montreal, QC, Canada. 2 Department of CGEM, Polytechnique Montréal, Succursale Centre, Montréal, Canada.
ABSTRACT
In the event of an instantaneous valve closure, the pressure transmitted to a surge tank induces the mass fluctuations that can cause high amplitude of water-level fluctuation in the surge tank for a reasonable cross-sectional area. The height of the surge tank is then designed using this high water level mark generated by the completely closed penstock valve. Using a conical surge tank with a non-constant cross-sectional area can resolve the problems of space and height. When addressing issues in designing open surge tanks, key parameters are usually calculated by using complex equations, which may become cumbersome when multiple iterations are required. A more effective alternative in obtaining these values is the use of simple charts. Firstly, this paper presents and describes the equations used to design open conical surge tanks. Secondly, it introduces user-friendly charts that can be used in the design of cylindrical and conical open surge tanks. The contribution can be a benefit for practicing engineers in this field. A case study is also presented to illustrate the use of these design charts. The case study’s results show that key parameters obtained via successive approximation method required 26 iterations or complex calculations, whereas these values can be obtained by simple reading of the proposed chart. The use of charts to help surge tanks designing, in the case of preliminary designs, can save time and increase design efficiency, while reducing calculation errors.
In the event of an instantaneous valve closure, the pressure transmitted to a surge tank induces the mass fluctuations that can cause high amplitude of water-level fluctuation in the surge tank for a reasonable cross-sectional area. The height of the surge tank is then designed using this high water level mark generated by the completely closed penstock valve. Using a conical surge tank with a non-constant cross-sectional area can resolve the problems of space and height. When addressing issues in designing open surge tanks, key parameters are usually calculated by using complex equations, which may become cumbersome when multiple iterations are required. A more effective alternative in obtaining these values is the use of simple charts. Firstly, this paper presents and describes the equations used to design open conical surge tanks. Secondly, it introduces user-friendly charts that can be used in the design of cylindrical and conical open surge tanks. The contribution can be a benefit for practicing engineers in this field. A case study is also presented to illustrate the use of these design charts. The case study’s results show that key parameters obtained via successive approximation method required 26 iterations or complex calculations, whereas these values can be obtained by simple reading of the proposed chart. The use of charts to help surge tanks designing, in the case of preliminary designs, can save time and increase design efficiency, while reducing calculation errors.
KEYWORDS
Hydraulic Transients, Surge Tank, Water Hammer, First-Order Non-Homogeneous Differential Equation with Variables Coefficients, Friendly Charts
Hydraulic Transients, Surge Tank, Water Hammer, First-Order Non-Homogeneous Differential Equation with Variables Coefficients, Friendly Charts
Cite this paper
Seck, A. and Fuamba, M. (2015) Contribution to the Analytical Equation Resolution Using Charts for Analysis and Design of Cylindrical and Conical Open Surge Tanks. Journal of Water Resource and Protection, 7, 1242-1256. doi: 10.4236/jwarp.2015.715101.
Seck, A. and Fuamba, M. (2015) Contribution to the Analytical Equation Resolution Using Charts for Analysis and Design of Cylindrical and Conical Open Surge Tanks. Journal of Water Resource and Protection, 7, 1242-1256. doi: 10.4236/jwarp.2015.715101.
References
[1] Streeter, V.L. and Wylie, E.B. (1993) Fluid Transients in Systems. Prentice-Hall, Upper Saddle River. [2] Menabrea, L.F. (1858) Note sur les effets du choc de l’eau dans les conduites. Mallet-Bachelier, Paris. [3] Anderson, A. (1976) Menabrea’s Note on Waterhammer: 1858. Journal of the Hydraulics Division, 102, 29-39. [4] Michaud, J. (1878) Coups de bélier dans les conduites. étude des moyens employés pour en atteneur les effects. Bulletin de la Société vaudoise des ingénieurs et des architectes, 4, 4. [5] Michaud, J. (1903) Intensité des coups de bélier dans les conduites d’eau (Intensity of Water Hammer in Water Pipelines). Bulletin Technique de la Suisse Romande, 29, 35-38; 29, 49-51. [6] Allievi, L. (1903) Teoria generale del moto perturbato dell’acqua nei tubi in pressione (colpo d’ariete). Annali della Società degli ingegneri e degli architetti italiani, 17, 285-325. [7] Allievi, L. (1913) Teoria del colpo d’ariete. Atti dell’Associazione elettrotecnica italiana, 17, 127-150, 861-900, 127-1145, 1235-1253. [8] Allievi, L. (1932) Il colpo d’ariete e la regolazione delle turbine. Industrie Grafiche Italiane Stucchi, Milano. [9] Schnyder, O. (1932) Uber Druckstosse in Rohrleitungen. Wasserkraft und Wasserwirtschaft, 27, 49-54, 64-70. [10] Jaeger, C. (1933) Théorie générale du coup de bélier. Doctoral dissertation. Edition Dunod, Paris. [11] Lescovich, J.E. (1967) The Control of Water Hammer by Automatic Valves. Journal (American Water Works Association), 59, 632-644. [12] Roche, E. (1975) Assainissement rural: Protection des conduites de refoulement. TSM l’Eau, Août-Sept, 365-378. [13] Chaudhry, M. (1987) Applied Hydraulic Transients. Van Nostrana Reinhold Co., New York. [14] Jaeger, C. (1958) Contribution to the Stability Theory of Systems of Surge Tanks. English Electric Company Limited, London. [15] Jaeger, C. (1960) A Review of Surge-Tank Stability Criteria. Journal of Basic Engineering, 82, 765-775.
http://dx.doi.org/10.1115/1.3662744 [16] Guinot, V. (2003) Godunov-Type Schemes: An Introduction for Engineers. Elsevier, Amsterdam. [17] Brunone, B., Golia, U. and Greco, M. (1991) Modelling of Fast Transients by Numerical Methods. Proceedings of the International Conference on Hydraulic Transients with Water Column Separation, Valencia, 4-6 September 1991, 273-280. [18] Bergant, A., Simpson, A.R. and Vìtkovsk, J. (2001) Developments in Unsteady Pipe Flow Friction Modelling. Journal of Hydraulic Research, 39, 249-257.
http://dx.doi.org/10.1080/00221680109499828 [19] Chaudhry, M.H., Sabbah, M.A. and Fowler, J.E. (1985) Analysis and Stability of Closed Surge Tanks. Journal of Hydraulic Engineering, 111, 1079-1096.
http://dx.doi.org/10.1061/(ASCE)0733-9429(1985)111:7(1079) [20] Finnemore, E. and Franzini, J. (2002) Fluid Mechanics with Engineering Applications. 10th Edition, McGraw-Hill, Boston. [21] Moghaddam, M.A. (2004) Analysis and Design of a Simple Surge Tank (Research Note). International Journal of Engineering-Transactions A: Basics, 17, 339-345. [22] Chaudhry, M.H. and Silvaaraya, W.F. (1992) Stability Diagrams for Closed Surge Tanks. HR Wallingford and International Association for Hydraulic Research. [23] Kim, S.-H. (2010) Design of Surge Tank for Water Supply Systems Using the Impulse Response Method with the GA Algorithm. Journal of Mechanical Science and Technology, 24, 629-636. [24] Ramadan, A. and Mustafa, H. (2013) Surge Tank Design Considerations for Controlling Water Hammer Effects at Hydro-Electric Power Plants. University Bulletin, 3, 147-160. [25] Hildebrand, F.B. (1962) Advanced Calculus for Applications. Volume 63, Prentice-Hall, Englewood Cliffs.
[1] Streeter, V.L. and Wylie, E.B. (1993) Fluid Transients in Systems. Prentice-Hall, Upper Saddle River. [2] Menabrea, L.F. (1858) Note sur les effets du choc de l’eau dans les conduites. Mallet-Bachelier, Paris. [3] Anderson, A. (1976) Menabrea’s Note on Waterhammer: 1858. Journal of the Hydraulics Division, 102, 29-39. [4] Michaud, J. (1878) Coups de bélier dans les conduites. étude des moyens employés pour en atteneur les effects. Bulletin de la Société vaudoise des ingénieurs et des architectes, 4, 4. [5] Michaud, J. (1903) Intensité des coups de bélier dans les conduites d’eau (Intensity of Water Hammer in Water Pipelines). Bulletin Technique de la Suisse Romande, 29, 35-38; 29, 49-51. [6] Allievi, L. (1903) Teoria generale del moto perturbato dell’acqua nei tubi in pressione (colpo d’ariete). Annali della Società degli ingegneri e degli architetti italiani, 17, 285-325. [7] Allievi, L. (1913) Teoria del colpo d’ariete. Atti dell’Associazione elettrotecnica italiana, 17, 127-150, 861-900, 127-1145, 1235-1253. [8] Allievi, L. (1932) Il colpo d’ariete e la regolazione delle turbine. Industrie Grafiche Italiane Stucchi, Milano. [9] Schnyder, O. (1932) Uber Druckstosse in Rohrleitungen. Wasserkraft und Wasserwirtschaft, 27, 49-54, 64-70. [10] Jaeger, C. (1933) Théorie générale du coup de bélier. Doctoral dissertation. Edition Dunod, Paris. [11] Lescovich, J.E. (1967) The Control of Water Hammer by Automatic Valves. Journal (American Water Works Association), 59, 632-644. [12] Roche, E. (1975) Assainissement rural: Protection des conduites de refoulement. TSM l’Eau, Août-Sept, 365-378. [13] Chaudhry, M. (1987) Applied Hydraulic Transients. Van Nostrana Reinhold Co., New York. [14] Jaeger, C. (1958) Contribution to the Stability Theory of Systems of Surge Tanks. English Electric Company Limited, London. [15] Jaeger, C. (1960) A Review of Surge-Tank Stability Criteria. Journal of Basic Engineering, 82, 765-775.
http://dx.doi.org/10.1115/1.3662744 [16] Guinot, V. (2003) Godunov-Type Schemes: An Introduction for Engineers. Elsevier, Amsterdam. [17] Brunone, B., Golia, U. and Greco, M. (1991) Modelling of Fast Transients by Numerical Methods. Proceedings of the International Conference on Hydraulic Transients with Water Column Separation, Valencia, 4-6 September 1991, 273-280. [18] Bergant, A., Simpson, A.R. and Vìtkovsk, J. (2001) Developments in Unsteady Pipe Flow Friction Modelling. Journal of Hydraulic Research, 39, 249-257.
http://dx.doi.org/10.1080/00221680109499828 [19] Chaudhry, M.H., Sabbah, M.A. and Fowler, J.E. (1985) Analysis and Stability of Closed Surge Tanks. Journal of Hydraulic Engineering, 111, 1079-1096.
http://dx.doi.org/10.1061/(ASCE)0733-9429(1985)111:7(1079) [20] Finnemore, E. and Franzini, J. (2002) Fluid Mechanics with Engineering Applications. 10th Edition, McGraw-Hill, Boston. [21] Moghaddam, M.A. (2004) Analysis and Design of a Simple Surge Tank (Research Note). International Journal of Engineering-Transactions A: Basics, 17, 339-345. [22] Chaudhry, M.H. and Silvaaraya, W.F. (1992) Stability Diagrams for Closed Surge Tanks. HR Wallingford and International Association for Hydraulic Research. [23] Kim, S.-H. (2010) Design of Surge Tank for Water Supply Systems Using the Impulse Response Method with the GA Algorithm. Journal of Mechanical Science and Technology, 24, 629-636. [24] Ramadan, A. and Mustafa, H. (2013) Surge Tank Design Considerations for Controlling Water Hammer Effects at Hydro-Electric Power Plants. University Bulletin, 3, 147-160. [25] Hildebrand, F.B. (1962) Advanced Calculus for Applications. Volume 63, Prentice-Hall, Englewood Cliffs.