GATE AG 2019 • Q61 NAT • 2 Marks

Section 5: Irrigation and Drainage Engineering

Soil-Water-Plant Relationship

Subtopic: Water requirement of crops

Question Statement:

Soil-Water-Plant Relationship: Water requirement of crops; consumptive use and evapotranspiration; measurement of infiltration, soil moisture and irrigation water infiltration. An undisturbed soil sample is collected when soil moisture is at field capacity. Core sampler inside diameter = 7.5 cm, height = 15 cm. Weight of core cylinder with moist soil = 2.81 kg, with oven-dry soil = 2.61 kg. Weight of the empty core cylinder = 1.56 kg. Assuming π = 3.14, the water depth (cm) per meter depth of soil (rounded to 2 decimals) is ______.

Official Answer Key:

30.10 to 30.30

Step-by-Step Solution & Explanation

Mass of moist soil = 2.81 − 1.56 = 1.25 kg. Mass of oven-dry soil = 2.61 − 1.56 = 1.05 kg. Mass of water = 1.25 − 1.05 = 0.20 kg = 0.20 L (density of water = 1 kg/L) = 0.20 × 10⁻³ m³. Core sample cross-sectional area, A = (π/4)D² = (3.14/4)(0.075)² = 4.417×10⁻³ m². Depth of water (equivalent water column) in the 15 cm sample = Volume/Area = 0.20×10⁻³/4.417×10⁻³ = 0.04528 m = 4.528 cm. Expressed per metre depth of soil (scale up from the 15 cm sample height to 100 cm): Water depth per m soil = 4.528 × (100/15) = 30.18 cm/m. Answer: within 30.10–30.30.

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