Merkel number and the entering-air convention that shifts it

Two entering-air conventions, one enthalpy curve, and the offset they carry into the fill calculation.

The same enthalpy curve with the two entering-air conventions as two operating lines — hin taken as saturated air at the entering wet bulb, and hin taken as the real moist-air state at the stated dry bulb — and what the offset between them costs in fill.

Reference conditions: cold water 32 °C, hot water 42 °C, entering air 33 °C dry bulb / 27 °C wet bulb, L/G 1.50, cp,w 4.18 kJ/kg·K; the two conventions differ by 0.29 kJ/kg and 1.07 % of KaV/L.

Formula: the same KaV/L = ∫ cp,w dTw / (hs(Tw) − ha(Tw)), with hin evaluated from each convention in turn.

Merkel number: the saturation-enthalpy curve with two entering-air conventions — saturated at the 27 °C wet bulb and the real moist-air state at 33 °C dry bulb — showing an offset of 0.29 kJ/kg (illustrative)Illustrative Merkel demand chart showing the two entering-air enthalpy conventions. The rising curve is the saturation enthalpy of air at the local water temperature, hs(Tw). The two straight lines are the operating line ha(Tw) = hin + (L/G) cp,w (Tw − Tc) with hin taken as saturated air at the entering wet bulb (85.05 kJ/kg) and as the real moist-air state at 33 °C dry bulb / 27 °C wet bulb (84.76 kJ/kg) — an offset of 0.29 kJ/kg. Reference condition: cold water 32 °C, hot water 42 °C, L/G 1.50, cp,w 4.18 kJ/kg·K. Over the same range the saturated-at-wet-bulb convention needs KaV/L 1.52 against 1.50 for the real moist-air convention, 1.06 % more — the post's "about 1.1 % higher", computed here. Values are computed from the formulas, not measured. (chart-merkel-conventions)Air conventions — Illustrative — not a measurementTwo entering-air enthalpy conventions32343638404280100120140160180Water temperature Tw (°C)Air enthalpy (kJ/kg dry air)85.0584.76saturated at the wet bulbreal moist airReference: water 32–42 °C · entering air 33 °C db / 27 °C wb · L/G 1.50Saturated-at-wet-bulb vs real moist-air entering enthalpyhin saturated at 27 °C wb (kJ/kg)85.05hin real moist air 33/27 (kJ/kg)84.76offset Δhin (kJ/kg)0.29KaV/L: saturated ÷ real air1.52 ÷ 1.50Computed from the formula — not field data.
Illustrative, computed from the properties — not a measurement. Two operating lines, one entering-air convention each; the gap between them is the enthalpy offset that a convention change carries into the fill calculation.

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