Estimating in a stream’s cross-section the depth-averaged velocity,
V, from the free-surface velocity,
vsurf, is an efficient, non-invasive hydrometric method. The ratio
fv =
V/
vsurf is typically assumed constant at
fv = 0.86 in field
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Estimating in a stream’s cross-section the depth-averaged velocity,
V, from the free-surface velocity,
vsurf, is an efficient, non-invasive hydrometric method. The ratio
fv =
V/
vsurf is typically assumed constant at
fv = 0.86 in field applications, despite observations to the contrary. Guidance is, therefore, needed in estimating actual
fv-ratios when velocity profile data are absent. This work provides field-verified guidance based on the hydromechanics of the logarithmic velocity law, which shows that
fv depends on the scaled resistance measure ‘friction length/depth’,
yo/
h, with the
yo(
k) function of the equivalent sand grain roughness,
k. The mean-to-surface-velocity ratio in rough-bed streams is estimated from the bed roughness and stream morphology by modifying
Nikuradze’s equation,
yo =
k/30, to
yo =
ck, with
c(
h/
k) ≥ 1/30, and
k ≈
D84—data fit:
c ≈ 8.61(
h/
k)
−1.821, ~5 ≤
h/
k < ~30. Field-verification of the ratio’s modified hydromechanics,
fv =
f with
yo(
h/
k) evaluated from bed roughness estimated by inspection or sieve analysis shows this ratio holding within ~|10|% error for shallow streamflow over a coarse bed of gravels and rocks, giving submergences of ~5 ≤
h/
D84 ≤ ~30;
yo =
k/30 suits large streams with smooth beds (
h/
k ≥ ~30,
fv ≥ ~0.86). Variable roughness-estimated
fv-ratios appear to be more reliable than the fixed default,
fv(
h/
yo ≈ 1000) = 0.86. This flow-gauging concept is based on observable physical characteristics of a monitoring cross-section and facilitates the rating of hard-to-access streams draining small basins in ragged upland terrain.
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