Table 3.
Scaling relationships for pond shapes and factors.
| Pond Attribute | Scales as | Cylinder | Cone | Spherical Cup |
|---|---|---|---|---|
| Contact with soil, rock | Non-planar area (soil) | (π/4) D2 (1 + 4α) | (π/4) D2 Q1 | π α D2 |
| Contact with atmosphere | Planar area (atmos.) | (π/4) D2 | (π/4) D2 | π α D2 (1 − α) |
| Number of Cells in Pond | Volume | (π/4) α D3 | (π/12) α D3 | (π/3) α2 D3 (1.5 − α) |
| Lifetime against evaporation | Volume/atmos. area | d = α D | d/3 = α D/3 | (αD/3) (1.5 − α)/(1 − α) |
| Lifetime against seepage | Volume/soil area | (αD)/(1 + 4α) | α D/(3 Q1) | (α D/3) (1.5 − α) |
| Foreshore (Shoreline area) | Δ non-planar area | π D Δd | (π/4) Q1 Q2 ·D ·Δd/α | ~π D Δd |
| Mineral concentration pond volume | Soil area/volume | (1 + 4α)/(α D) | 3 Q1/(α D) | 3/[(α D) (1.5 − α)] |
| Mineral conc × foreshore area | Mineral conc × Shore area | π D2 (α + 0.25) | ~(Δd/α2) (Q1)2 ·Q2 | Δd/[α (1.5 − α)] |
| Atmospheric input to concentration | Planar area/volume | 1/(α D) | 3/(α D) | [3/(α D)] (1 − α)/(1.5 − α) |
| Atmos input conc × foreshore area | Atmos. conc × Shore area | π Δd/α | ~(Δd/α3) Q1 Q2 | (Δd/α) (1 − α)/(1.5 − α) |
Q1 = [1 + 4α2]0.5 --> 1 + 2 * α2 for small α, and --> 1 for very small α; or, = 1.414 for d = D/2. Q2 = [1 + 0.5 (Δd/d)] --> 1 for small Δd/d, which typical (e.g., 1 cm rain into ≥10 cm deep pond).