Standard recommended longitudinal land slopes for surface irrigation (border strip and furrow irrigation) according to soil texture:
Heavy (clay) soils: 0.05% to 0.20% (require flatter slopes due to low infiltration to prevent excessive runoff).
Medium (loamy) soils: 0.20% to 0.40% (safe limit providing optimum advance rate and uniform distribution without soil erosion).
Light (sandy) soils: 0.25% to 0.65% (steeper slope to ensure rapid advance before deep percolation losses occur).

Matching of agricultural engineering concepts:
(A) Irrigation matches with (II) Surge: Surge irrigation is an intermittent application of water in furrows or borders to reduce infiltration rate and advance time.
(B) Drainage matches with (IV) Land reclamation: Subsurface drainage removes excess water and leaches salts, reclaiming waterlogged and saline/alkali lands.
(C) Water Pumping matches with (III) Foot valve: A foot valve is a non-return valve installed at the bottom of the pump suction pipe to maintain priming.
(D) Soil Conservation matches with (I) Terrace: Terracing (bench terraces, broadbase terraces) is a mechanical soil conservation measure on sloping lands.
(E) Water Resources matches with (V) Dam: Dams are hydraulic structures built across rivers to store surface runoff and manage water resources.

Standard rules for sharp-crested weir installation for accurate discharge measurement:
Statement (C) is true: The head over the weir (\(H\)) must be measured at an upstream distance of at least \(4H\) to \(5H\) (typically 4 times maximum head) to avoid the drawdown (surface curve) effect immediately preceding the crest.
Statement (A) is false: The approach velocity must be kept low ($\lt 0.15\text{ m/s}$) or explicitly accounted for in discharge calculations.
Statement (B) is false: The height of the crest above the channel bottom must be at least \(2H\) to \(3H\) (NOT closer than \(2H\)) to prevent contraction suppression.
Statement (D) is false: Free flow with adequate nappe aeration underneath is mandatory to prevent suction and measurement errors.

Flow discharge equations for open channel weirs:
The universal theoretical equation for flow over any weir is given by the general power-law form: \(Q = C L H^m\) (Statement C is correct), where \(C\) is the weir coefficient, \(L\) is the crest length, \(H\) is the head over the crest, and \(m\) is an exponent dependent on the weir geometry (e.g., \(m = 1.5\) or \(3/2\) for rectangular/Cipolletti weirs, \(m = 2.5\) or \(5/2\) for V-notch weirs).
The Francis formula for a rectangular weir is \(Q = 0.0184 L H^{3/2}\) (when \(Q\) is in \(\text{L/s}\) and \(L, H\) in cm) or \(Q = 1.84 L H^{3/2}\) (in SI units with \(\text{m}^3/\text{s}\) and meters). Neither exponent \(2/3\) (Statement A) nor \(7/2\) (Statement B) is correct.