Shallow-Water Theory and Channel Flow with Hydraulic Jump: Non-Steady Consideration

Asuquo Essien Eyo

Abstract


We examine the classical hydraulic jump in an open channel flow and show that it can be qualitatively understood using the model, namely, equation of shallow-water type.  Based on this model the relation for the speed of propagation of the jump in terms of depth ratio is obtained.  We employ the method of characteristics and the Riemann invariants to determine the precise location and time of the onset of the hydraulic jump.  Our analysis reveals that the location xand time tJ of the jump formation are influenced by the initial acceleration of the fluid.  Specializations are later made to the cases where the initial acceleration is positive and finite, negative, infinite.  Results are obtained in each of these cases.

Full Text: PDF DOI: 10.5539/mas.v6n1p50

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Modern Applied Science   ISSN 1913-1844 (Print)   ISSN 1913-1852 (Online)

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