(E) जलधारा विसर्जन बनाम प्रतिशत समय जब प्रवाह बराबर या अधिक हो... | Agrigyan

Calculation of average depth of irrigation:
1. Discharge rate

\(Q = 230\text{ litres/min}\). \(Q = 230 \times 60\text{ litres/hr} = 13,800\text{ litres/hr} = 13.8\text{ m}^3/\text{hr}\). 2. Total operating time \(t = 50\text{ hours}\). Total volume of water pumped \(V = Q \times t = 13.8\text{ m}^3/\text{hr} \times 50\text{ hr} = 690\text{ m}^3\). 3. Irrigated Area \(A = 1\text{ ha} = 10,000\text{ m}^2\). 4. Average depth of irrigation \(d = \frac{V}{A}\): \[d = \frac{690\text{ m}^3}{10,000\text{ m}^2} = 0.069\text{ m} = 6.9\text{ cm}\]

Hooghoudt's equation is a steady-state drainage equation used to design the spacing of agricultural subsurface relief drains:

\[S^2 = \frac{4 K_1 m^2 + 8 K_2 d_e m}{q}\]

Key assumptions of Hooghoudt's equation include:
Statement (A) is correct: It directly computes the drain spacing (\(S\)) as a function of steady recharge rate (\(q\)), soil hydraulic conductivity, and the hydraulic head/water table elevation midway between drains (\(m\)).
Statement (B) is correct: Flow through the porous soil medium is laminar and strictly follows Darcy's law.
Statement (C) is incorrect: The equation assumes the soil is homogeneous and isotropic within distinct profile layers (or two uniform layers above and below the drain line). It explicitly does NOT assume arbitrary heterogeneity.

Matching of soil, water, and groundwater engineering terms:
(A) Erosivity matches with (III) Rainfall: Rainfall erosivity (the \(R\) factor in USLE) is the potential kinetic energy ability of rain to cause soil detachment and erosion.
(B) Erodibility matches with (IV) Soil: Soil erodibility (the \(K\) factor in USLE) is the inherent susceptibility or vulnerability of a soil type to detach and transport by erosive agents.
(C) Application efficiency matches with (V) Irrigation: Water application efficiency (\(E_a\)) is an irrigation metric measuring the ratio of water stored in the crop root zone to the water delivered to the field.
(D) Radial flow matches with (I) Tubewell: Groundwater pumping from a tubewell creates radial converging flow patterns from all directions toward the well bore.
(E) Cone of depression matches with (II) Tubewell spacing: The cone of depression formed around a pumping tubewell governs the radius of influence, which directly determines the minimum spacing between adjacent tubewells to avoid hydraulic interference.

Calculation of fertilizer application per sprinkler setting:

• Area covered by each sprinkler \(A_s = S_l \times S_m\), where: - Sprinkler spacing on the lateral \(S_l = 14\text{ m}\) - Lateral spacing on the main line \(S_m = 20\text{ m}\) \[A_s = 14\text{ m} \times 20\text{ m} = 280\text{ m}^2\]
• Number of sprinklers on the lateral \(N = 12\). Total area covered per setting \(A_{\text{setting}} = 12 \times 280\text{ m}^2 = 3360\text{ m}^2\). 3. Convert area into hectares: \[A_{\text{setting}} = \frac{3360}{10,000}\text{ ha} = 0.336\text{ ha}\]
• Fertilizer dose recommended = \(80\text{ kg/ha}\). Amount of fertilizer per setting = \(\text{Dose} \times A_{\text{setting}} = 80\text{ kg/ha} \times 0.336\text{ ha} = 26.88\text{ kg} \approx 27\text{ kg}\).