Civil, Structural & Geotechnical Engineering
Hooghoudt Subsurface Tile Drain Spacing Formula: Equivalent Depth d_e & Midpoint Mound m
Size parallel agricultural subsurface pipe/ditch drain spacing L (m) under steady-state rainfall or leaching recharge q using S. B. Hooghoudt’s (1940) equation L = SQRT((8 * K_b * d_e * m + 4 * K_a * m^2) / q).
Account for radial flow convergence near perforated tile pipes via Hooghoudt’s Equivalent Depth d_e!
Horizontal Dupuit-Forchheimer flow toward open ditches breaking all the way down to an impermeable barrier predicts L^2 = (8 * K_b * D * m + 4 * K_a * m^2) / q — where m (m) is midpoint water-table mound height above drain axis, q (m/day) is steady design drainage coefficient, and K_a, K_b (m/day) are hydraulic conductivities above and below drain elevation! However, small perforated tile pipes (radius r_0 ~= 0.05–0.10 m) perched D meters above bedrock force streamlines to converge radially near the pipe, creating extra head loss!
Dutch drainage pioneer Symen Barend Hooghoudt (1940) replaced physical thickness D with a smaller Equivalent Depth d_e <= D that incorporates radial convergence resistance analytically, giving the universal Hooghoudt Drain Spacing Formula: L = SQRT((8 * K_b * d_e * m + 4 * K_a * (m^2)) / q) (reducing to SQRT(4 * K * m * (2 * d_e + m) / q) in homogeneous soil K_a = K_b = K)!
| Drainage Scenario (m = 0.60 m, d_e = 1.40 m, q = 0.007 m/day = 7 mm/d) | Soil Conductivity (m/day) | Hooghoudt Drain Spacing L (m) |
|---|---|---|
| Silty Clay Loam (Homogeneous K_a = K_b = 0.45 m/day) | K = 0.45 m/day | L = 22.90 m |
| Sandy Loam (Homogeneous K_a = K_b = 1.20 m/day) | K = 1.20 m/day | L = 37.40 m |
| Layered Soil (K_a = 0.60 above, K_b = 1.50 below) | Higher permeable substratum | L = 39.54 m |
Hooghoudt Two-Layer Steady-State Tile Drain Spacing L (m)
Evaluates SQRT((8 * K_b * d_e * m + 4 * K_a * m^2) / q) across K_a above drain (B2 m/day), K_b below drain (B3 m/day), Hooghoudt equivalent depth d_e (B4 m), midpoint water-table height m (B5 m), and steady drainage rate q (B6 m/day, with q < K_a).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B6 >= B2), "Invalid Conductivity, Equivalent Depth, Mound Height, or Recharge q >= K_a", ROUND(SQRT((8 * B3 * B4 * B5 + 4 * B2 * (B5 ^ 2)) / B6), 2))Below-Drain Substratum Flow Share (%) of Total Drainage Discharge
Computes the percentage of total steady drain flow carried below drain level: 100 * (8 * K_b * d_e * m) / (8 * K_b * d_e * m + 4 * K_a * m^2).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Hooghoudt Inputs", ROUND(100 * (8 * B3 * B4 * B5) / (8 * B3 * B4 * B5 + 4 * B2 * (B5 ^ 2)), 2))Try the example
Use the original values or change them to test your understanding.