Discussion
According to Lacey's theory, the bed slope is given by :
Answer: D
Lacey's bed slope is \(\frac{F^{5/3}}{3340\ Q^{1/6}}\).
Lacey's regime theory for alluvial channels gives the slope in terms of the silt factor \(f\) and the discharge \(Q\) in cumecs:
\[ S = \frac{f^{5/3}}{3340\,Q^{1/6}} \]
A coarser silt (larger \(f\)) needs a steeper slope to keep it moving, and a larger channel can carry it at a flatter slope, which is why \(f\) is in the numerator and \(Q\) in the denominator. The exponents 1/3, 4/3 and 2/3 on \(f\), and 1/2 and 1/4 on \(Q\), do not belong to the regime equations.
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