Interval and amount with 40% moisture limit

Given: FC = 35%, PWP = 12%, porosity $n = 0.42$, $D_r = 1.2$ m $= 1200$ mm, $ET_c = 12$ mm/day, $\eta_a = 60\%$. Moisture must stay at or above 40% of the maximum available moisture, so 60% of the available moisture may be used.

Interpretation: no dry density is given, only porosity, so the moisture contents are taken by volume. This is the only consistent reading: water held at FC (0.35 of the soil volume) is less than the pore volume (0.42). If FC were by weight, any realistic dry density (for example $(1-0.42)\times 2.65 = 1.54$) would give a volumetric FC of $0.35\times1.54 = 0.54 > 0.42$, which is impossible.

Step 1: Maximum available moisture

$$AM = \frac{35-12}{100}\times D_r = 0.23\times 1200 = 276\ \text{mm}$$

Step 2: Depth usable between irrigations (net depth)

$$d_{net} = 0.60\times 276 = 165.6\ \text{mm}$$

Step 3: Irrigation interval

$$I = \frac{165.6}{12} = 13.8\ \text{days}\approx 13\ \text{days}$$

Step 4: Gross irrigation water per irrigation

$$d_{gross} = \frac{d_{net}}{\eta_a} = \frac{165.6}{0.60} = 276\ \text{mm}$$

Answer: interval $\approx$ 13.8 days (irrigate every 13 days); net depth 165.6 mm; water to be supplied = 276 mm (2760 m$^3$/ha) per irrigation.