Slurry Critical Deposition Velocity Calculator (Durand–Condolios)

Returns the critical deposition velocity V_D = F_L·√(2·g·D_i·(s−1)) from the Durand–Condolios form, the actual line velocity V = 0.4085·Q/d² from your flow rate and bore, and the ratio between them with a PASS/FAIL verdict. The Durand limiting-velocity coefficient F_L — read from the published chart against particle size and concentration — stays a user input.

Method last updated 2026-07-30 (calculation changelog) · fixture-verified on every build — most recently 2026-07-31.

A settling slurry has a speed below which it stops being a slurry. Drop under it and the solids leave suspension, build a stationary bed along the invert, and the line's effective bore starts shrinking; the velocity in what is left rises, which can restabilise things for a while, right up until it does not. The failure mode is not gradual wear — it is a plugged pipeline and a shutdown to clear it. The critical deposition velocity is the floor that has to be cleared, and clearing it at the design flow is the easy half of the problem.

The Durand–Condolios correlation is the classic form for heterogeneous, settling slurries in water-like carriers, and it remains the screening method most slurry pipeline work starts from. Its structure is intuitive once you see it: the velocity needed scales with the square root of the bore — bigger pipe needs more velocity, not less — and with the square root of the buoyant density difference, so heavy solids in a light carrier are the demanding combination. Everything not captured by geometry and density is pushed into a single empirical coefficient F_L, which is where particle size distribution and delivered concentration enter.

That coefficient is the part that deserves care, and it is deliberately your input here rather than something this tool selects. F_L is read from the published Durand chart against the particle d₅₀ and the volumetric concentration, and it is not a constant of nature — it is a curve fit to a specific body of experimental data on specific materials. Two engineers reading the same chart for the same slurry can reasonably land a few percent apart, and that spread propagates straight into V_D. The calculator does the arithmetic exactly and repeatably; selecting a defensible F_L is the engineering.

A note on which code governs, because it is a common source of confusion: ASME B31.11 was the slurry transportation piping code, and recent editions of ASME B31.4 have absorbed slurry service into their scope. Either way, the codes require operation above the deposition velocity but leave the hydraulics to the designer — they do not publish a method. That is why this is a hydraulics correlation with a code-adjacent citation rather than a code equation, and why the result is a design screen rather than a code compliance verdict.

Method

Two velocities are computed and compared.

Critical deposition velocity, Durand–Condolios form, with the bore converted from inches to feet and g = 32.174 ft/s²:

s = SG_solids / SG_carrier

V_D = F_L · √( 2 · g · (D_i/12) · (s − 1) )

Actual line velocity from volumetric flow and inside diameter, in the standard gpm/inch form (0.4085 is the unit constant for gpm and inches → ft/s, not a code value):

V = 0.4085 · Q / d²

ratio = V / V_D → PASS when ratio ≥ 1

The specific gravity term is a ratio, s = SG_solids/SG_carrier, not a difference — which matters whenever the carrier is not water. Running sand in a dense medium rather than water lowers s, lowers the buoyant driving force, and genuinely reduces the velocity needed to keep solids up; that is the physical basis of dense-medium transport. The engine rejects SG_solids ≤ SG_carrier outright, because a solid no denser than its carrier is not a settling slurry and this correlation does not describe it.

Entering Q = 0 puts the card in deposition-velocity-only mode: it returns V_D and suppresses the operating check and the verdict, which is what you want when you are sizing a line rather than checking one. With a flow entered, the verdict is a hard comparison at that flow, and a second warning fires when the margin is under 10% — a line that only clears deposition at full rate is a line that silts up the first time it is turned down.

Limitations — what this calculator is not

• Heterogeneous settling slurries only. The Durand form describes solids that want to settle out of a water-like carrier. It does not describe homogeneous or non-Newtonian slurries (fine tailings, thickened paste, high-concentration clays), where the governing concern is rheology and laminar-to-turbulent transition rather than deposition, and where applying this equation will mislead you.
• F_L carries all the empiricism and is your input. Particle size distribution, delivered concentration, and particle shape enter only through that one coefficient. A slurry with a wide or bimodal size distribution is poorly represented by a single chart read, and a coarse fraction can govern deposition even when the d₅₀ suggests otherwise.
• Horizontal, straight, full-bore pipe is assumed. Inclined runs change the deposition condition — upward-sloping sections are more prone to sliding-bed behaviour — and the correlation says nothing about vertical legs, where deposition in this sense does not apply but particle slip does.
• It is a floor, not a design velocity. Clearing V_D does not size the line: pressure gradient, pump power, and erosive wear all rise steeply with velocity, and wear on slurry lines commonly scales near the cube of velocity. The economic design sits above the deposition floor with margin, not far above it.
• Single operating point only. The card checks the flow you enter. Real lines run at turndown, during startup, and during shutdown settling, and the deposition check that matters is usually at minimum flow with the heaviest expected solids loading — not at the design point.
• No code verdict. ASME B31.11 and the slurry provisions of recent B31.4 editions require operation above the deposition velocity but do not prescribe how to determine it. A PASS here means this correlation is satisfied at this operating point with your chosen coefficient; it is not a statement of code compliance, and it does not replace pipeline hydraulic design or a wear assessment.

Quick reference — reading the velocity ratio

The ratio V/V_D is more informative than the PASS/FAIL flag, because the interesting question is never whether the design point clears — it is how much of the operating envelope clears. Bands below are engineering practice, not code values:

The single most common way a slurry line gets designed wrong is to check the ratio only at the design flow. Check it at the flow the line will actually see on its worst day, which is nearly always the lowest one.

Worked example — fixture-verified

A sand-water slurry in an NPS 12 line with a 12.0 in bore. The solids are silica sand at specific gravity 2.65 in a water carrier at 1.0, and the design flow is 5,000 gpm. The Durand coefficient read from the chart for this particle size and concentration is 1.34.

Step by step

1. Specific gravity ratio: s = SG_solids/SG_carrier = 2.65/1.0 = 2.65, so the buoyant term (s − 1) = 1.65.
2. Convert the bore to feet: D_i = 12/12 = 1.0 ft.
3. Inside the radical: 2·g·D_i·(s − 1) = 2·32.174·1.0·1.65 = 106.1742; √106.1742 = 10.30409 ft/s.
4. Critical deposition velocity: V_D = F_L·10.30409 = 1.34·10.30409 = 13.807 ft/s.
5. Actual velocity: V = 0.4085·Q/d² = 0.4085·5,000/12² = 2,042.5/144 = 14.184 ft/s.
6. Margin: ratio = 14.184/13.807 = 1.02727 → V exceeds V_D, so the card returns PASS — but by under 3%.

A PASS worth arguing with. The line clears deposition at design flow by 0.377 ft/s — under 3% — which puts it in the band where the engine raises its margin warning. Any reduction in throughput, any batch of coarser sand, or any conservative re-read of F_L puts this line under the deposition velocity. Read this result as "the design flow works and nothing else has been demonstrated," and go check the turndown case before signing it.

Worked example 2 — the same line at 20% turndown fails

The identical line, sand and carrier — nothing about the pipe or the solids has changed. The only difference is throughput: the plant runs at 4,000 gpm instead of 5,000. This is the check the main example said to go and do.

Step by step

1. Deposition velocity is unchanged — it depends on bore, densities and F_L, none of which moved: V_D = 13.807 ft/s.
2. Actual velocity at the reduced flow: V = 0.4085·4,000/144 = 1,634/144 = 11.347 ft/s.
3. Ratio = 11.347/13.807 ≈ 0.82 — the line is running at about 82% of the velocity needed to keep the sand suspended.
4. Verdict: FAIL. A 20% cut in throughput moved this line from a passing design to one that will build a bed.

This is the whole argument for checking minimum flow rather than design flow. Velocity is linear in throughput, so a 20% turndown is a 20% velocity cut — there is no hydraulic cushion absorbing it. A line designed at ratio 1.03 has, in practice, no turndown at all. The fixes are structural rather than clever: a smaller bore raises velocity at every flow (and lowers V_D at the same time, since V_D scales with √D, so it helps twice), a recirculation or flush loop holds velocity up when production drops, or the line runs in batches at full rate instead of continuously at part rate.

Fixture case “below deposition velocity fails” (tolerance 0.001) — locked in the same release gate as the example above.

Sources & citations

• R. Durand and E. Condolios, experimental work on the transport of solids in pipes (1952) — origin of the limiting-velocity correlation and the F_L chart against particle size and concentration.
• ASME B31.11, Slurry Transportation Piping Systems — the historical slurry code; requires operation above the deposition velocity without prescribing a determination method.
• ASME B31.4, Pipeline Transportation Systems for Liquids and Slurries — recent editions absorb slurry service; confirm which document your project is contracted to.
• Constants: g = 32.174 ft/s²; 0.4085 converts gpm and inches of bore to ft/s. Both are unit/physical constants, not code values.

Per the source & citation policy, allowable-stress and factor table values are user-supplied. Where a page does reproduce specific ASME data (the B16.5 ratings, the quick-reference tables), it does so under ASME authorization and states the source table and conditions inline.

FAQ

Where do I get the FL coefficient?

From the published Durand limiting-velocity chart, read against the particle d₅₀ and the delivered volumetric concentration — it is not reproduced here, and this tool does not select it for you. Practical values for typical settling slurries fall broadly in the 0.8–1.5 region, but treat that as orientation rather than a design input: the whole empirical content of the method sits in this one number, and the right value depends on your material. If your particle size distribution is wide or bimodal, read the chart for the coarse fraction as well and take the more demanding result — a single d₅₀ read can badly understate the velocity a coarse tail needs.

Is the deposition velocity the velocity I should design to?

No — it is the floor, not the target. Designing at V_D means designing at the exact point where solids start dropping out, with no allowance for turndown, coarser batches, or the uncertainty in F_L itself. Common practice sits somewhere in the 1.1–1.5 ratio band, chosen against the minimum expected flow rather than the design flow. Going far above that band trades a deposition problem for an erosion problem: wear rate on slurry lines rises very steeply with velocity, so the economic design is a genuine compromise between two failure modes, not a maximisation of margin against one.

Why does a bigger pipe need a higher velocity, not a lower one?

Because V_D scales with √D. It is counter-intuitive if you are used to clean-liquid hydraulics, where bigger pipe means lower velocity for the same flow and everyone is happier. For a settling slurry the turbulence that keeps particles suspended has to work across a larger bore, and the velocity required to generate it rises. This is why oversizing a slurry line is actively dangerous rather than merely wasteful: the larger bore simultaneously lowers the actual velocity (for the same flow) and raises the velocity required. Both effects push the same way, and a generously sized slurry line is a classic way to build a plugged one.

What if my carrier is not water?

Enter its actual specific gravity — the correlation uses the ratio s = SG_solids/SG_carrier, so a denser carrier genuinely reduces the required velocity, which is exactly the principle dense-medium transport exploits. Two cautions. First, the Durand form was developed for water-like carriers, so a carrier that differs substantially in viscosity is outside the data the correlation was fitted to, and the result becomes indicative rather than reliable. Second, the engine will reject SG_solids ≤ SG_carrier: at or below neutral buoyancy there is no settling slurry to describe, and the equation would return a meaningless number rather than fail honestly.

Does clearing the deposition velocity mean the line will not plug?

It means the steady-state hydraulics will keep the solids moving at the flow you checked. It says nothing about the transients that actually plug slurry lines: startup into a line that settled overnight, an unplanned shutdown that leaves solids in a horizontal run, a valve closure that stalls flow in one leg, or a slug of coarse material outside the design distribution. Those are addressed by operating procedure and layout — flush and recirculation provisions, avoiding low-point traps, restart procedures that clear a settled bed rather than pumping into it — not by the design velocity. Deposition velocity is a necessary condition, not a sufficient one.

Which code applies — B31.11 or B31.4?

Check the contract, not the habit. ASME B31.11 was the dedicated slurry transportation piping code; more recent editions of ASME B31.4 have absorbed slurry service into their scope, and many projects that would once have cited B31.11 now cite B31.4. It matters less for this calculation than you might expect, because neither code prescribes a deposition-velocity method — both require that the line operate above it and leave the hydraulics to the designer. Where the code choice does bite is in wall thickness and the design factors that go with it; take that to the pipeline wall thickness calculator with the correct code selected.

Related calculators

• ASME B31.4 / B31.8 / B31.11 Pipeline Wall Thickness Calculator — Wall thickness for the slurry line, B31.4 / B31.11 form
• Pipeline MAOP Calculator — Maximum Allowable Operating Pressure (ASME B31.8 / B31.4) — Pressure ceiling for the same slurry line
• Water Hammer Calculator — Joukowsky Surge Pressure and Wave Speed — Valve closure on a dense slurry surges harder than on water
• API RP 14E Erosional Velocity Calculator (Line Sizing) — The ceiling at the other end of the same window — solids that stay up also erode