Two numbers, both called velocity, differing by a substantial factor at exactly the place armor is placed. It is the most consequential input error in this field and the easiest to make.
What each one is
Depth-averaged velocity is the mean through the water column at a point, and a one-dimensional model typically reports something coarser still: the mean through the whole cross-section. It is what discharge divided by area gives you.
Local velocity is the actual velocity at a specific location, at a specific height above the bed, in the disturbed flow field around whatever is there.
Why they differ
Velocity varies across a section. The thread of fastest flow sits in the deepest, smoothest part. Near banks and near the bed it is slower through friction. A section average is an average over that whole distribution, including the slow parts.
Structures accelerate flow around them. Water diverted around a pier, an abutment, or a projecting structure moves faster past it than it did approaching it.
Bends redistribute it. On a meander, the fastest flow moves to the outside and plunges down the outer bank. The section average does not represent the outer bank at all. See outer bend erosion.
Turbulence is not in the average. The downflow and horseshoe vortex at a pier are what excavate the bed, and neither is captured by a mean velocity. See bridge pier scour.
Contractions accelerate everything. Through a bridge opening narrower than the natural flood width, the whole section speeds up. See contraction, local, and degradation scour.
The result is that armor sits precisely where the local condition most exceeds the average.
How the difference is handled
Three approaches, in ascending order of effort:
A velocity multiplier applied to the section average, chosen for the location — outer bank of a bend, at a pier, in a contraction. Standard practice, quick, and only as good as the multiplier. FHWA’s HEC-23 covers this for countermeasure design, and HEC-18 covers the equivalent for scour evaluation. See HEC-18 and bagged armor design.
A two-dimensional model, which resolves the velocity distribution across the section directly rather than reporting a mean. More work, and the right answer where the geometry is complex or the consequence of getting it wrong is high.
Measurement, where it is feasible and where the flow of interest actually occurs. Rarely available for a design flood, which is the condition that matters.
What to ask about a velocity you have been given
- Is this depth-averaged, section-average, or local? If nobody knows, that is the answer.
- Where in the section was it taken?
- What model produced it, and was it calibrated?
- At what discharge and return period?
- Has a location multiplier been applied, and what was it?
- Does it account for the structure, or is it the approach condition?
A velocity supplied without those attributes is a number, not an input.
The bend and the pier, specifically
Two cases worth naming because they recur:
On a bend, the outer bank sees substantially more than the section average, and the maximum is typically downstream of the apex rather than at it. Protection centred on the apex can be centred in the wrong place.
At a pier, the relevant condition includes the downflow and the horseshoe vortex, not just the accelerated approach flow. Effective pier width and flow alignment drive it strongly, and a debris raft against the upstream face makes the pier hydraulically much wider than the drawings say.
Where this leaves the sizing
Armor sizing is sensitive to velocity, so an error in this input propagates directly into the selected size and into the protection’s performance.
The rated conditions for each size are published on product specifications, and the calculator applies them. What this article is about is making sure the number you put in describes the condition at the structure rather than the average through the reach.
FES is a supplier, not the engineer of record. Establishing the design velocity at the structure is the engineer’s work, and where our data does not support a case, when not to use rock bags says so.