Irrigation, Drainage & Pumping Systems

Hydraulics of water impounding behind contour bunds:
On a sloping land with slope

\(S\) (fraction), the horizontal distance between bunds \(\text{HI} = \frac{\text{VI}}{S}\). The volume of excess rainfall (\(R\)) falling on a 1-meter wide strip between consecutive bunds is: \[V_{\text{rain}} = \text{HI} \times 1 \times R = \frac{\text{VI}}{S} \times R\]

The impounded water behind the bund forms a triangular wedge of depth

\(h\) at the bund face and spreading uphill to a length \(L = \frac{h}{S}\). The storage volume of this triangular wedge per 1-meter width is: \[V_{\text{stored}} = \frac{1}{2} \times h \times L \times 1 = \frac{1}{2} \frac{h^2}{S}\]

Equating stored volume to excess rainfall volume:

\[\frac{1}{2} \frac{h^2}{S} = \frac{\text{VI}}{S} \times R \implies h^2 = 2 \cdot \text{VI} \cdot R\] \[h = \sqrt{2 \cdot \text{VI} \cdot R}\]

Given

\(\text{VI} = 2\text{ m} = 200\text{ cm}\) and \(R = 1\text{ cm}\): \[h = \sqrt{2 \times 200\text{ cm} \times 1\text{ cm}} = \sqrt{400} = 20\text{ cm}\]

Components and design functions of straight drop spillways:
Statement (B) is correct: Transverse sills (end sills) placed across the stilling basin floor stabilize and force the formation of a hydraulic jump within the basin, effectively dissipating kinetic energy.
Statement (C) is correct: Longitudinal sills running parallel to the direction of flow prevent cross-currents and eddies, guiding and straightening discharge uniformly downstream.
Statement (A) is incorrect: Standard SCS criteria require straight reaches of typically 15 to 30 meters (not a rigid 50 m requirement).
Statement (D) is incorrect: Cutoff walls are designed to reduce (not increase!) seepage uplift pressure and eliminate piping failures beneath the structure.

Stream bank protection engineering:
Brushwood Edging: Specifically employed along small, meandering streams at sharp bends where water impinges directly on outer cut banks but channel bed scour is relatively shallow. Bundles of live branches/brushwood are staked and anchored longitudinally along the toe of the bank to cushion flow impact, entrap silt, and promote stabilizing vegetative growth.
Revetment: Riprap or masonry lining for high velocities and deep scour.