Slurry Critical Deposition Velocity Calculator (Durand–Condolios) — Sample Report

1 · Design inputs

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.

2 · 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.

3 · Calculation

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%.

4 · Results PASS

5 · Verification statement

The result values above are locked as fixture slurry-velocity.json, case “sand-water NPS 12 (ID 12 in), FL=1.34, 5000 gpm — above deposition”, tolerance 0.001, in the calc-core continuous verification gate (see https://pipingtoolset.com/trust/validation.html). Allowable-stress and factor data are user-supplied inputs; 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.