How the sizing chain works
Everything hangs off one number: the suction bell diameter D. Pick the bell velocity class from the pump head (low-head pumps are the most sensitive to poor intake flow — above ~6 ft/s at bell their efficiency can drop by up to 10 %), solve D from the flow, and every sump dimension follows as a fixed ratio of D. The table below is the full recommended set for a rectangular intake formed to the standard geometry.
1 · Bell diameter from flow
Bell diameter also needs to relate to the impeller eye: first estimates put the eye at 3–8 ft/s axial velocity, then D ≈ 1.5–2.0 × eye diameter.
2 · Minimum submergence — the Hecker relation
S is measured from the water surface to the bell inlet plane; V is the average velocity at the bell. The form is deliberate: one bell diameter of submergence is the base requirement, and the extra depth grows linearly with the bell Froude number — the dimensionless group that controls free-surface vortex formation. The 2.3 slope is an envelope of observed vortex onset across the classic model-test data, so meeting it keeps the surface quiet down to intermittent dip formation. Below the line you trade first surface dimples (Type 1–2), then intermittent air cores (Type 3–4), and finally a continuous air core to the pump (Type 5–6) — the last two are never acceptable.
3 · Recommended dimension set (rectangular intake)
| Variable | Meaning | Recommended value |
|---|---|---|
| D | Bell design OD | from flow & velocity class (above) |
| C | Bell-to-floor clearance | 0.3 D – 0.5 D (≈ 0.4 D used here) |
| S | Minimum bell submergence | D (1.0 + 2.3 FD) |
| H | Minimum liquid depth | H = S + C |
| B | Back wall → bell centerline | 0.75 D |
| W | Bay entrance width | 2 D min |
| w | Constricted bay width at the bell | 2 D |
| h | Min. height of constricted bay | max(H, 2.5 D) |
| X | Bay length | 5 D min (no significant cross-flow) |
| A | Bell centerline → intake entrance | 5 D min |
| a | Length of constricted bay | 2.5 D min |
| Y | Bell centerline → through-flow traveling screen | 4 D min (double-flow screens: model test) |
| Z1 | Bell centerline → diverging walls | 5 D min |
| Z2 | Bell centerline → sloping-floor start | 5 D min |
| α | Floor slope angle | −10° … +10° |
| β | Wall convergence angle | 0° … +10° (negative: model test with vanes) |
| φ | Convergence from constricted bay to walls | ≤ 10° |
Significant cross-flow is defined as an approach velocity ≥ 50 % of the bay entrance velocity — beyond that, add turning devices or justify with a model test.
4 · Flow-quality thresholds used by the checklist
| Check | Threshold | Meaning |
|---|---|---|
| Velocity non-uniformity at impeller inlet | < 5 % of mean | 🟢 below 5 % · 🔴 at or above — skewed approach flow loads the impeller asymmetrically and promotes trailing-vortex formation. |
| Swirl angle (vortimeter) | < 4° | 🟢 below 4° · 🔴 at or above — prerotation with the pump's rotation direction cuts head; against it, power rises. Vortimeter speed should stay under 1.7·Q/D₁³. |
| Approach-channel velocity (straight run) | ≤ 1.25 ft/s (0.4 m/s) | 🟢 compliant · 🟡 above — expect non-uniform approach flow; a model study is the standard remedy above this line. |
| Bay entrance velocity (computed from w×h) | ≤ 1.5 ft/s (0.46 m/s) | 🟢 quiet bay · 🟡 1.5–2 · 🔴 above 2 ft/s — also the limit for a closed duct discharging into the bay. |
| Floor clearance | 0.3–0.5 D (aim 0.33 D) | 🟢 inside band — too small digs a floor vortex, too large re-circulates under the bell and erodes NPSH margin. |
| Air entrainment | any continuous air-core vortex | 🔴 never acceptable — 3–5 % entrained air already costs efficiency; strong vortices can carry ~10 %. |
5 · When a model test is the answer
Trigger thresholds (single pump / station level):
$$Q_{pump} > 40{,}000\ \text{gpm}\ (2.5\ \text{m}^3/\text{s})\quad\text{or}\quad Q_{station} > 100{,}000\ \text{gpm}\ (6.3\ \text{m}^3/\text{s})$$…plus: circular intakes with ≥ 4 pumps or > 5,000 gpm each, asymmetric approach flow, shared multi-pump channels with many operating combinations, diffusing approach channels, clog-prone screens, obstacles near the bell, double-flow screens, or a negative wall-convergence angle β. If all the basic rules hold (straight approach, low velocities), the model test may be waived. Froude scaling governs: velocities scale with \(L_r^{1/2}\), flow with \(L_r^{2.5}\); keep model pipe Reynolds number above 7×10⁴, intake Re ≥ 3×10⁴, and Weber number above 120 so scale effects stay out of the vortex picture. Model vortex acceptance: surface types 1–3 maximum; anything entraining air is rejected.
Worked example (tool anchor)
Q = 10,000 gpm (0.6309 m³/s), mid class (V = 4 ft/s = 1.219 m/s):
| Quantity | Calculator | Ratio basis |
|---|---|---|
| Bell diameter D | 0.8117 m = 2.663 ft | D = √(4Q/πV) |
| Bell Froude number FD | 0.4322 | V/√(gD) |
| Minimum submergence Smin | 1.6186 m = 5.31 ft | S = D(1 + 2.3·FD) |
| Floor clearance C (0.4 D) | 0.3247 m | 0.3–0.5 D band |
| Back wall B (0.75 D) | 0.6088 m | Table ratio |
| Bay width W = w (2 D) | 1.6234 m | Table ratio |
| Liquid depth H = S + C | 1.9433 m | S + C |
| Constricted bay height h | 2.0293 m | max(H, 2.5 D) = 2.5 D governs |
| Bay length X (5 D) | 4.0586 m | Table ratio |
Submergence verdicts for this anchor: S = 1.62 m → 🟢 (meets 1.6186 m); S = 1.40 m → 🟡 (86.5 % of required, surface-vortex tendency); S = 1.20 m → 🔴 (74.1 %, air-core risk). The bay velocity implied by the recommended geometry is only 0.63 ft/s — comfortably quiet.