On the Hydraulics of the Rapid Acceleration Divider and Gauger

Abstract

This paper deals with the hydraulics of the rapid acceleration divider and gauger. lt is different fron the convensional theory in that the theoretical flow by Belanger's theorem is corrected with an experimental coefficient, and that the condition of free flow is shown on experimental foundation (see Fig. 2).
The overflow depth h₃ is from Bélanger's law,
h₂=3√Q²/b²g...(a)
whereQ, bandgare flow per unit time weir width and gravity acceleration respectively.
As for the free flow on the weir,
Q=mb (E-h_z) √2g (E-h_z)...(b)
wheremis the coefficient of overflow.
From (a) and (b)
h₃=3√Q²/c²b²g, C=3√3/2m...(c)
Then the height of the weirh_zbecomes
h_z=E₃-(c²/2+1) h₃...(d)
E₃is the specific energy on the weir.
The next problem is the condition of free flow, it is
k=h_u/E₃-h_z≤0.6...(e)
The loss head of hydraulic jump ΔEis given by
ΔE= (1-k) (E₃-h_z)-αv₀²/2g...(f)
α≅1.1
Henceh_dbecomes
h_d=E₃-(E₂+ΔE₂+ΔE)...(g)
Based on these equations, designing procedures are shown for the case in which whether the weir width or loss head is given, and for the case in which both the weir width and loss head are given.