Fill characteristic: KaV/L on log-log axes, and what depth costs

KaV/L = C (L/G)^m on log-log axes, for one fill depth and for the same fill at twice the depth.

KaV/L = C (L/G)^m on log-log axes, for one fill depth and for the same fill at twice the depth — the negative exponent as a falling characteristic, and depth as an additive offset in decades rather than a doubling of cooling.

Reference conditions: L/G from 1.0 to 2.0 with C = 1.90 and m = −0.60 (illustrative, not a vendor’s data), giving KaV/L 1.703 at L/G 1.2 down to 1.490 at L/G 1.5 — a 12.5 % loss.

Formula: KaV/L = C (L/G)^m.

Fill characteristic chart on log-log axes: KaV/L = 1.9 (L/G)^−0.6, falling from 1.703 at L/G 1.2 to 1.490 at L/G 1.5, with the doubled-depth curve a constant 0.301 decades above it (illustrative)Illustrative film-fill characteristic on log-log axes. The lower straight line is KaV/L = C (L/G)^m with C = 1.90 and m = −0.60, evaluated from L/G 1.0 to 2.0: KaV/L is 1.900 at L/G 1.0, 1.703 at L/G 1.2, 1.490 at L/G 1.5 and 1.254 at L/G 2.0 — because the exponent is negative the characteristic falls as the water-to-air ratio rises, costing 12.5 % between L/G 1.2 and 1.5. The upper line is the same fill at twice the depth: 3.800 at L/G 1.0 and 2.979 at L/G 1.5, exactly twice the one-depth value, a constant offset of log10 2 = 0.301 decades — so doubling the depth is not a doubling of cooling. Values are computed from the formula, not measured; C and m are illustrative, not a vendor's data. (chart-fill-characteristic)Fill characteristic — Illustrative — not a measurementKaV/L = C (L/G)^m on log-log axes1.01.21.52.01.01.52.03.04.0Water-to-air ratio L/GKaV/L (log scale)1.7031.490depth 1×depth 2×Reference: film fill KaV/L = C (L/G)^m, C = 1.90, m = −0.60 (illustrative)Doubling the fill depth doubles the characteristic at the same loadings— a constant offset of log10 2 = +0.301 decadesC (illustrative)1.90m−0.60KaV/L at L/G 1.2 → 1.51.703 → 1.490cost of 1.2 → 1.5−12.5 %doubled depth (×2), log offset+0.301doubled depth: KaV/L at L/G 1.52.979Computed from the formula — not field data.
Illustrative, computed from the formula above — not a measurement. The lower line is one fill depth, the upper line the same fill at twice the depth: a constant offset of log10 2 = 0.301 decades.

Sources

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