The flexible shape Palmer-Bowlus flume is a simple device for flow measurement in free-surface flow circular channels and conduits. In this study, the discharge-stage relation for Palmer-Bowlus flumes is determined based on the Bernoulli theorem. The proposed analytical method is able to account for geometric peculiarities and shape deformation of the flume for adaptation to pipes of different diameters, without need of experimental calibration. Experimental tests on different conduits demonstrate the robustness of the theoretical formulation for reliable free-surface flow measurement. Empirical criteria are also provided for assessing the limit of the proposed discharge-stage relation. The research will further encourage and support the use of these flexible and versatile flumes for hydraulic engineering applications.
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