Author(s): John D. Fenton
Linked Author(s): John D. Fenton
Keywords: Energy; Momentum; Coriolis coefficient; Boussinesq coefficient; Pipes; Channels
Abstract: Expressions are obtained for discharge, momentum and energy conservation in pipes and channels that include the effects of boundary layers, secondary flows, and turbulence. The procedure is in the tradition of hydraulics, where the effects are not modelled exactly but approximately by generalised energy (Coriolis) and momentum (Boussinesq) correction factors. They are larger than the traditional definitions of those coefficients, that hydraulics teaching and practice has tended to ignore. It is suggested that they should be included in both the teaching and practice of pipe and channel hydraulics: (a) They are a better model of the physical situation and there can be a gain in accuracy of calculations of up to 5-10% ; (b) For pedagogical purposes they reveal the real nature of the complexity of hydraulic flows while approximating them simply; (c) As the numerical values of the correction factors are only approximately known, including them reminds that while one is improving accuracy, the calculations are approximate; and (d) They give a means of testing the sensitivity of solutions to uncertainty in their values. The momentum equation is presented in a generalised alternative form. It is suggested that most energy calculations in hydraulics actually use an integrated energy equation rather than Bernoulli’s equation, even if they do not acknowledge that. It would be better and simpler to introduce energy conservation to students using the integral form, then as shown here, it can be used to obtain Bernoulli’s equation for the cases where it is applicable, along a single streamline. Several problems of elementary hydraulics are solved using the energy or momentum correction factors, to show how they help accuracy and understanding in teaching. Their fundamental nature is demonstrated by an improved theory for the Venturi flow meter.
Year: 2005