(a) A sedimentation tank is treating 5 million litres of sewage per day containing 250 ppm of suspended solids. The tank removes…

(a) Sludge from a sedimentation tank (20 marks)

Dry solids removed. The flow is 5 MLD = 5 × 10⁶ litres/day = 5000 m³/day, and 250 ppm = 250 mg/l = 0.25 kg/m³. The suspended solids entering are 5000 × 0.25 = 1250 kg/day, and the tank removes 60%:

dry solids = 0.60 × 1250 = 750 kg/day

Sludge at 97% moisture. The solids are 3% of the wet sludge by weight:

• weight of wet sludge = 750/0.03 = 25 000 kg/day = 25.0 t/day
• volume = weight/(specific gravity × 1000) = 25 000/(1.02 × 1000) = 24.51 m³/day

Sludge at 96% moisture. The solids are 4% of the wet sludge:

• weight of wet sludge = 750/0.04 = 18 750 kg/day = 18.75 t/day
• volume = 18 750/(1.02 × 1000) = 18.38 m³/day

Reduction caused by 1% less moisture.

Reduction in volume = (24.51 − 18.38)/24.51 = 6.13/24.51 = 25%

The same result follows from the ratio of the two weights, since the specific gravity is the same: (1/0.03 − 1/0.04)/(1/0.03) = 1 − 3/4 = 25%. A 1% drop in moisture cuts the volume of sludge to be handled by a quarter, which is why thickening and dewatering are worth doing.

(b) Diversion headwork: sketch and functions (15 marks)

A diversion headwork is a structure across a river that raises the water level and diverts a regulated supply into a canal. Its plan is shown, with the weir or barrage, the undersluices, the divide wall, the silt excluder, the canal head regulator, the fish ladder and the guide banks and marginal bunds.

Functions.

• (i) Silt excluder. It is a set of tunnels in the undersluice pocket in front of the head regulator, which carries the bottom layer of water, heavy with silt, through the undersluices to the river downstream. Only the clearer upper layer enters the canal. It acts before the silt gets into the canal, unlike a silt ejector, which removes it after it has entered.
• (ii) Cross regulator. It is a gated structure across the parent canal, just downstream of an offtake. It holds up the water level so that the required discharge enters the branch or distributary, regulates the flow in the parent canal, and can be closed for maintenance. It usually carries a road bridge as well.
• (iii) Canal fall. It is a drop in the canal bed where the ground slopes more steeply than the permitted canal gradient. It lets the water fall safely to the lower level and dissipates the excess energy, so that the bed and banks are not scoured, and the canal keeps its designed slope.
• (iv) Aqueduct. It is a cross-drainage work that carries the canal over a natural drainage or river in a trough, and the drainage flows below at a lower level, through the barrels.
• (v) Escape. It is a structure that lets surplus water from the canal out into a natural drain, and protects the canal from breaches when the inflow is too much, for example after heavy rain or when the downstream gates are closed. It also empties the canal for repairs.

(c)(i) Heights and hydrostatic force on a mass concrete dam (10 marks)

Definitions. The hydraulic height is the difference between the highest controlled water surface (here the spillway crest level) and the lowest point of the original river bed, which is the depth of water the dam holds back. The total (structural) height is the difference between the top of the dam and the lowest point of the foundation.

Assumptions. The reservoir is full to the spillway crest, RL 160.0 m, so the 10.0 m water depth in the river at the dam places the river bed at RL 160.0 − 10.0 = RL 150.0 m. The top of the dam is taken at the level of the spillway crest, RL 160.0 m, as no freeboard is given.

(I) Hydraulic height = 160.0 − 150.0 = 10.0 m.

(II) Total height = 160.0 − 100.0 = 60.0 m, so the foundation goes 50 m below the river bed.

(III) Total hydrostatic force on the upstream face. The face is loaded by the water only above the river bed, and the width of the river bed is 100 m:

F = ½ γ h² b = ½ × 9.81 × 10.0² × 100 = 49 050 kN ≈ 49.05 MN

It acts horizontally at h/3 = 3.33 m above the river bed.

(c)(ii) Classification of hydraulic structures (5 marks)

• Dams: storage works. They impound water in a reservoir, and regulate the supply over time, from the wet to the dry season.
• Weir and barrage: diversion (river) works. They raise the water level and divert a regulated supply into a canal, with little or no storage. A weir has a raised solid crest, and a barrage is mainly gated.
• Aqueduct and super passage: cross-drainage works. They carry a canal and a natural drainage across each other. An aqueduct carries the canal over the drainage, and a super passage carries the drainage over the canal.
• Falls: canal drop or energy-dissipation works. They lower the canal bed by a drop and dissipate the surplus energy, so that a gentle canal slope is kept on steep ground.