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Abstract
The cross-sectional area of a surge tank (CAST) is a key factor for protecting pipelines from harm by hydraulic transients. However, for long-distance pipeline systems (LDPS), the water level fluctuations in the surge tank and valve closure water hammer normally share a coupling relationship. Traditionally, this coupling relationship renders difficulty in determining the CAST. This study focused on the influence of water level fluctuation and water hammer, and proposed a simplified approach for sizing surge tanks. First, a water hammer formula that considers the coupling effect was derived. Subsequently, formulae for sizing the CAST were deduced. Finally, a case study of an actual LDPS was conducted to verify the accuracy of the presented formulae. In addition, the calculation errors caused by the theoretical assumptions are discussed. The results indicate that the theoretical calculation values and time-domain simulation results match well, thereby demonstrating the great convenience of designing surge tanks.
Acknowledgements
Reviewer comments, feedback, and discussions from the Editor, Associate Editor, and multiple reviewers contributed to a much-improved article, which the authors greatly appreciate.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notation
| A, Apt, Atk | = | cross-sectional area of the pipe between the surge tank and valve, between the pump unit and surge tank, cross-sectional area of the surge tank (m2) |
| a, apt | = | pressure wave velocity of the pipe between the surge tank and valve, between the pump unit and surge tank (m s–1) |
| D | = | diameter of the pipe between the surge tank and valve (m) |
| f | = | Darcy–Weisbach coefficient (–) |
| g | = | acceleration of gravitational (m s–2) |
| H, Hd | = | piezometric head, pressure head in front of valve (m) |
| Hdown | = | water level in the downstream reservoir (m) |
| Hed, Hed 0.5, Hed 1 | = | pressure head in front of the valve at the moment of closure, of L/a seconds before closure, of 2L/a seconds before closure (m) |
| Hpump | = | pump head (m) |
| Hu | = | water level of surge tank (m) |
| Hud, Hud 0.5, Hud 1 | = | water level of the surge tank at the moment of closure, of L/a seconds before closure, of 2L/a seconds before closure (m) |
| Hu,min | = | minimum water level in the surge tank (m) |
| Hup | = | water level in the upstream reservoir (m) |
| h | = | dimensionless pressure head in front of valve (–) |
| hmax | = | maximum dimensionless pressure head in front of valve (–) |
| L, Lpt | = | length of the pipe between the surge tank and valve, between the pump unit and the surge tank (m) |
| m | = | fitting coefficient of discharge through valve (–) |
| Q, QT | = | discharge of pipe between the surge tank and valve, between the pump unit and the surge tank (m3 s–1) |
| Qmax | = | discharge when the valve fully opens (m3 s–1) |
| Qud 0.5 | = | discharge at the initial section of the pipeline at the moment of L/a seconds before closure (m3 s–1) |
| Tr | = | water hammer period (2L/a) (s) |
| Ts | = | valve closure time (s) |
| t | = | time (s) |
| = | water volume, water volume through surge tank, through valve (m3) | |
| x | = | distance of the pipeline (m) |
| ZP | = | bottom elevation of the surge tank (m) |
| ZV | = | elevation of valve (m) |
| α | = | head loss coefficient (–) |
| τ | = | dimensionless valve opening (–) |
Subscripts
| ap | = | approximate value |
| ex | = | exact value |
| r | = | rated value |
| 0 | = | initial steady state |