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Flow distribution by depth

Flow is distributed according to the Chezy equation for resistance:

\[ Q = A \cdot C \cdot \sqrt{R \cdot S} \]

Equation: Chezy equation for resistance.

Where:

  • \(Q\) — flow.
  • \(A\) — area (\(= width \times depth = wh\)).
  • \(C\) — Chezy coefficient.
  • \(R\) — hydraulics radius (approx. depth = \(h\)).
  • \(S\) — slope of channel/river.

Rearranging the equation yields:

\[ Q = wh(Ch)^{0.5}S^{0.5} = h^{1.5}wCS^{0.5} \]

Equation: Chezy equation rearranged to isolate the water depth.

Thus, proportionality can be derived between flow and water depth \(h\)

\[ Q \sim h^{1.5} \]

Equation: Proportionality between flow and water depth.

Flow is then distributed across \(n\) surface element faces and for each one, the distributed flow \(Q_{i}\) is calculated from the total flow \(Q_{TOT}\).