An equation ascribed to the Swiss mathematician Daniel Bernoulli (1700–1782), based on the principle of the conservation of energy (that is, ‘energy cannot be destroyed’) can be applied, inter alia, to parallel or gradually varied flow in an open channel with a small bed slope. It is probable that the equation was formulated first by Leonard Euler (1707–1783) and popularized later by Julius Weisbach in the middle of the nineteenth century. Considering flow through an open channel cross-section, the total energy upstream and downstream of that cross section is a constant value, although the component energy values may be different upstream from those downstream. The total energy components are ‘position’ energy (the elevation of the channel bed, above a horizontal datum), the pressure head and the velocity head, and the equation is:
where z is the bed elevation above the horizontal datum in meters, d is the depth of water (m), 
is the mean velocity of the water through a cross-section...
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Bibliography
BS 3680, Part 1, 1991. Glossary of Terms, British Standards Institution, London.
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© 1998 Kluwer Academic Publishers
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Holland, P.G. (1998). Bernoulli energy equation . In: Hydrology and Lakes. Encyclopedia of Earth Science. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4513-1_29
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