A soil has a field capacity of $28\%$ and permanent wilting point of $12\%$ on a dry weight basis. The apparent specific gravity of the soil is $1.40$ and root zone depth is $0.75\text{ m}$. If irrigation is applied when $50\%$ of available water is depleted, the net irrigation requirement is ________ $\text{mm}$ (in integer).
Answer Key:
84
Step-by-Step Solution & Explanation
Soil Moisture Calculations:
1. Total Available Water ($AWC$):
$AWC = \frac{FC - PWP}{100} \times \frac{\rho_b}{\rho_w} \times D_r = \frac{28 - 12}{100} \times 1.40 \times 0.75\text{ m} = 0.16 \times 1.40 \times 0.75 = 0.168\text{ m} = 168\text{ mm}$
2. Net Irrigation Requirement at $50\%$ depletion:
$NIR = 0.50 \times 168\text{ mm} = 84\text{ mm}$
Hence, the answer is **84** $\text{mm}$.