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A generalized mathematical theory and experimental verification of proportional notches

Keshava Murthy, K and Seshagiri, N (1968) A generalized mathematical theory and experimental verification of proportional notches. In: Journal of the Franklin Institute, 285 (5). pp. 347-363.

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Official URL: http://dx.doi.org/10.1016/0016-0032(68)90483-3


A theory and generalized synthesis procedure is advocated for the design of weir notches and orifice-notches having a base in any given shape, to a depth a, such that the discharge through it is proportional to any singular monotonically-increasing function of the depth of flow measured above a certain datum. The problem is reduced to finding an exact solution of a Volterra integral equation in Abel form. The maximization of the depth of the datum below the crest of the notch is investigated. Proof is given that for a weir notch made out of one continuous curve, and for a flow proportional to the mth power of the head, it is impossible to bring the datum lower than (2m − 1)a below the crest of the notch. A new concept of an orifice-notch, having discontinuity in the curve and a division of flow into two distinct portions, is presented. The division of flow is shown to have a beneficial effect in reducing the datum below (2m − 1)a from the crest of the weir and still maintaining the proportionality of the flow. Experimental proof with one such orifice-notch is found to have a constant coefficient of discharge of 0.625. The importance of this analysis in the design of grit chambers is emphasized.

Item Type: Journal Article
Publication: Journal of the Franklin Institute
Publisher: Elsevier Science
Additional Information: Copy right of this article belongs to Elsevier Science.
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 14 May 2010 05:09
Last Modified: 19 Sep 2010 06:06
URI: http://eprints.iisc.ac.in/id/eprint/27735

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