Slurry Critical Velocity in a Discharge Line
Durand's deposition velocity V_c = F_L sqrt(2 g D (S_s - 1)).
Example
You enter
- Pipe inside diameter (in) 24
- Solids specific gravity 2.65
- Durand coefficient F_L for the expected material 1
- Operating velocity (ft/s) 18
- Coefficient if a coarser layer is cut 1.2
- Coefficient for the coarsest layer expected 1.34
- Upsized pipe considered (in) 30
You get
- The square-root term 14.5781
- Critical velocity 14.6 ft/s -- the line runs, 23% of margin
- In a coarser layer 17.5 ft/s -- still runs, 3% of margin left
- In the coarsest layer 19.5346
- Margin (%) 23.4732
- Coarser margin (%) 2.89431
- Friction head against the threshold 1.52456
- In the upsized pipe 16.2988
Details, formula, and sources
With the margin at the operating velocity and the friction head that margin costs. The whole answer is F_L: the worked line runs fine sand with 23% of margin and will not carry coarse sand at all. A larger pipe raises the threshold, it does not lower it.
V_c = F_L x sqrt(2 g D (S_s - 1)), with D in feet and V_c in ft/s; relative friction head at the operating velocity = (V / V_c)^2.
Durand's deposition-velocity relation, with F_L read from Durand's curves by particle size and concentration, roughly 0.8 to 1.5.
The relation is public; the coefficient comes from published curves and the material's own gradation.
Estimate. AHJ and licensed professional govern.
Field names used by the API: pipe_diameter_in, solids_specific_gravity, durand_coefficient, operating_velocity_fps, coarser_coefficient, coarsest_coefficient, upsized_diameter_in, root_term_fps, critical_velocity_fps, coarser_critical_velocity_fps, coarsest_critical_velocity_fps, margin_pct, coarser_margin_pct, relative_friction_head, upsized_critical_velocity_fps
- F_L entered; it is where the answer lives and the material is what sets itDurand's curves / site gradation
- Operating point just above V_c, because friction head rises as the square of velocity while production rises linearlyspec-v1829 method