A SIMPLIFIED ANALYTICAL SOLUTION FOR THE DIVIDING MANIFOLD FLOW PROBLEM

L. AMARA, R.F. CARVALHO

Abstract


A simple analytical solution to the problem of dividing manifold flow has been developed in the present study. Based on simplifying hypotheses accepted in practice and using energy principle considerations, differential equations for pressure head variation over the manifold are derived for both turbulent and laminar flow regimes in the pipe and lateral port orifices. From that, simple analytical expressions are obtained for solving practical problems such as variations in the pressure head, residual flow, and lateral port flow distribution. A comparison with literature results related to an irrigation engineering problem shows excellent agreement despite the simplicity of the model. Additionally, a parametric analysis concerning the decay rate of the pressure head for both flow regimes is performed for illustration.


Keywords


Spatially varied flow, Manifold problem, Analytical solution

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References


ACRIVOS A., BABCOCK B.D., PIGFORD R.L. (1959). Flow distributions in manifolds, Chemical Engineering Science, Vol. 10, Issues 1-2, pp. 112-124.

BORUTZKY W., BARNARD B., THOMA J. (2002). An orifice flow model for laminar and turbulent conditions, Simulation modelling practice and theory, Vol. 10, Issues 3-4, pp. 141-152.

DARCY H. (1854). Sur les recherches expérimentales relatives au mouvement des eaux dans les tuyaux, Comptes rendus des séances de l’Académie des Sciences, On experimental research relating to the movement of water in pipes, Reports of the sessions of the French Academy of Sciences, No 38, pp. 1109-1121. In French.

HATHOOT H.M., AL-AMOUD A.I., MOHAMMAD F.S. (1993). Analysis and design of trickle-irrigation laterals, Journal of Irrigation and Drainage Engineering, Vol. 119, Issue 5, pp. 756-767.

LAROCK B.E., JEPPSON R.W., WATTERS G.Z. (2000). Hydraulics of Pipeline Systems, 1st Edition, CRC Press, Taylor and Francis Group, 552p.

LIU H., ZONG Q., LV H., JIN J. (2017). Analytical equation for outflow along the flow in a perforated fluid distribution pipe, PloS one, Vol. 12, Issue 1, e0185842.

NALLURI C., FEATHERSTONE R. (2016). Civil engineering hydraulics: Essential theory with worked examples, 6th Edition, Wiley-Blackwell, ISBN: 978-1-118-91563-9, 480p.

ROUSE H. (1938). Fluid Mechanics for Hydraulic Engineers, 1st Edition, McGraw-Hill Book Co., New York, USA.

SCALOPPI E.J., ALLEN R.G. (1993). Hydraulics of irrigation laterals: Comparative analysis, Journal of irrigation and drainage engineering, Vol. 119, Issue 1, pp. 91-115.

VALIANTZAS J.D. (1998). Analytical approach for direct drip lateral hydraulic calculation, Journal of irrigation and drainage engineering, Vol. 124, Issue 6, pp. 300-305.

VALIANTZAS J.D. (2002). Continuous outflow variation along irrigation laterals: Effect of the number of outlets, Journal of irrigation and drainage engineering, Vol. 128, Issue 1, pp. 34–42.

WARRICK A.W., YITAYEW M. (1987). An analytical solution for flow in a manifold, Advances in water resources, Vol. 10, Issue 2, pp. 58-63.

WARRICK A.W., YITAYEW M. (1988). Trickle lateral hydraulics, I: Analytical solution, Journal of Irrigation and Drainage Engineering, Vol. 114, Issue 2, pp. 281-288.

YILDIRIM G. (2007). Analytical relationships for designing multiple outlets pipelines, Journal of irrigation and drainage engineering, Vol. 133, Issue 2, pp. 140-154.


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