(a) An open drain is to be designed to prevent waterlogging for an area of 576 ha. Given that the drainage coefficient is 0·06…

(a) Open drain for 576 ha: capacity, section and slope

Capacity = area × drainage coefficient = 576 × 10⁴ m² × 0.06 m/d = 3.456 × 10⁵ m³/d = 4.0 m³/s.

Lacey's regime equations with f = 1:

• V = (Qf²/140)^(1/6) = (4/140)^(1/6) = 0.553 m/s
• A = Q/V = 4/0.553 = 7.23 m²
• P = 4.75√Q = 4.75 × 2 = 9.50 m
• R = A/P = 0.76 m (check: 5V²/2f = 0.76 m)

Trapezoidal section with side slopes 1:1, bed width b and depth y: A = by + y² and P = b + 2√2·y. Eliminating b gives 1.828y² − 9.50y + 7.23 = 0, so y = 0.927 m. The other root (4.27 m) gives a negative bed width and is rejected. Then b = 9.50 − 2.828 × 0.927 = 6.88 m.

Check: by + y² = 6.38 + 0.86 = 7.23 m².

Slope: S = f^(5/3)/(3340 Q^(1/6)) = 1/(3340 × 1.26) = 2.4 × 10⁻⁴.

Capacity 4.0 m³/s; bed width 6.88 m; depth 0.93 m; top width 8.73 m; slope about 1 in 4,200. A freeboard is added over this depth.

(b) Drawdown in the pumped well

For steady flow to a fully penetrating well in an unconfined aquifer (Dupuit–Thiem), Q = πK(h₂² − h₁²)/ln(r₂/r₁).

Q = 6 m³/min = 0.1 m³/s and H = 150 m. At r₁ = 10 m, h₁ = 150 − 10 = 140 m; at r₂ = 50 m, h₂ = 150 − 5 = 145 m.

h₂² − h₁² = 21,025 − 19,600 = 1,425 m².

K = 0.1 × ln 5/(π × 1,425) = 0.1609/4,477 = 3.6 × 10⁻⁵ m/s (about 3.1 m/d).

For the well radius r_w = 0.25 m and the nearer observation well:

h₁² − h_w² = (h₂² − h₁²) × ln(r₁/r_w)/ln(r₂/r₁) = 1,425 × ln 40/ln 5 = 1,425 × 3.689/1.609 = 3,266 m².

h_w² = 19,600 − 3,266 = 16,334, so h_w = 127.8 m.

Drawdown in the well = 150 − 127.8 ≈ 22.2 m. Assumptions: steady flow, homogeneous isotropic aquifer, no recharge, Dupuit flow.

(c) Grit and its control in grit chambers

Grit is the heavy inert mineral matter in sewage: sand, gravel, cinders, egg shells and bone chips, with specific gravity about 2.65 and size above about 0.2 mm.

It must be removed because it abrades pumps, valves and pipes, settles in channels and sumps, and accumulates in digesters and tanks, reducing capacity and increasing cleaning costs.

In an unaerated horizontal-flow chamber the horizontal velocity must stay near 0.3 m/s at all flows. If it is higher, grit is scoured and carried on; if lower, lighter organic solids also settle and the grit becomes putrescible and smelly. Sewage flow varies through the day, so a velocity control device keeps the velocity constant as the depth changes.

An aerated chamber needs no such device. Compressed air creates a spiral rolling motion in the tank, and its rate can be adjusted. The velocity at the bottom, which decides what settles, depends on the air supply and tank geometry and not on the flow, so grit settles while organics stay in suspension.

Velocity control devices: the proportional (Sutro) weir and the Parshall flume.