On the Seddon speed formula |
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| Authors: | SURENDRA KUMAR MISHRA VIJAY P SINGH |
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| Institution: | 1. National Institute of Hydrology , Jal Vigyan Bhawan, Roorkee, 247 667, Uttar Pradesh, India;2. Department of Civil and Environmental Engineering , Louisiana State University , Baton Rouge, Louisiana, 70803-6405, USA |
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| Abstract: | Abstract The Seddon speed formula expressed mathematically as c = dQ/dA (or alternatively, as c = (1 + m)uo; where Q is the discharge, A is the area of cross-section, c is the wave speed, uo is the normal flow velocity, and m is a dimensionless parameter) is revisited in the context of elasticity and thermodynamics. Its link with the linearized solution of St Venant's equations for wave celerity, which does not appear to have been reported in the hydrological literature, is established. The rating exponent m is shown to be equivalent to the dimensionless relative celerity and is found to be the ratio of two specific heats, viz. cp and cv which are the specific heats at constant pressure and volume, respectively. The use of the parameter m as a complex variable helps describe shallow wave characteristics, the damping capacity of a wave, and the mechanism of occurrence of the hysteretic phenomenon. The damping capacity is found to describe the magnitude of wave subsidence, whereas the hysteresis also describes the speed of subsidence. |
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| Keywords: | Seddon formula wave celerity attenuation kinematic wave diffusion wave steady-dynamic wave dynamic wave loop rating curve hysteresis |
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