In open-channel flow, if y is the flow depth at a section, an accepted empirical relation for the mean velocity V (m/s) is V = k * y, where k is approximately which of the following?

Introduction:
Velocity distribution in open channels is non-uniform: it is zero at the boundary and maximum near the surface, with the depth-averaged (mean) velocity occurring below the surface. Field practice often uses empirical depth–velocity relations for quick checks.

Given Data / Assumptions:

• y is the flow depth.
• An empirical proportionality V ≈ k * y is referenced.

Concept / Approach:
For many steady, uniform flows in rough channels, the depth of mean velocity occurs at about 0.6 y below the free surface; equivalently, the velocity measured at 0.6 y is close to the depth-average. Hence a shorthand rule uses the 0.6-depth velocity (or coefficient 0.6 in simple proportionalities).

Step-by-Step Solution:
Recall common field rule: V_mean ≈ V at 0.6 y below surface.Translate to proportional form: coefficient closest to 0.6.Select option “0.6 y”.

Verification / Alternative check:
USGS and standard hydraulics references use the two-point (0.2 y and 0.8 y) or single-point (0.6 y) method; the 0.6-point is the accepted single-point estimate for mean velocity.

Why Other Options Are Wrong:

• 0.1–0.5 y: Do not match the observed location/estimate of mean velocity in typical natural channels.

Common Pitfalls:

• Confusing the depth where mean velocity occurs (0.6 y below surface) with the location of maximum velocity (near surface).

Final Answer:
0.6 y.