--- title: "Cross drainage: Q 25, uplift on roof of barrel" subject: "Irrigation and Drainage Engineering" chapter: 8 key: "semester_6/irrigation_and_drainage_engineering:cd-q25-uplift-roof-barrel-800" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/cd-q25-uplift-roof-barrel-800 site: BCT Engineering --- # Cross drainage: Q 25, uplift on roof of barrel Irrigation and Drainage Engineering · Chapter 8: Cross-Drainage structures - Asked in: 2081 Chaitra, 8 marks; 2080 Chaitra, 1+2+4+3 marks (asked 2 times) - Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/cd-q25-uplift-roof-barrel-800 - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-8 ## Question Design suitable cross-drainage structure based on the following data. Determine the drainage water way, canal water way, uplift pressure on roof barrel and impervious floor as well. Some relevant data is provided in figure and assume necessary data. Data: Full supply discharge of canal = 25 m³/sec; canal bed width = 30 m; canal bed level = 160.00 m; full supply level = 161.5 m; 100 years return period flood discharge = 800 m³/sec; high flood level = 160.5 m; river bed level = 158.0 m; general terrain level = 160 m. [Figure: siphon aqueduct section showing barrel with 0.4 m roof thickness, 0.4 m wall dimensions, 1 m and 1.4 m dimensions, 1:5 downstream slope and 4 m upstream cutoff/floor dimension] ## Short answer Siphon aqueduct with 32 barrels (4.0 m x 1.6 m), drainage waterway clear width 128 m. Canal waterway 30 m wide. Uplift on roof: head 0.9 m (8.8 kN/m2), empty canal FOS 1.09, adequate with canal water. Impervious floor total creep 59.9 m; required thickness 2.28 m, but designed with box action and weep holes. ## Answer The canal (25 m³/s, bed 160.00 m, FSL 161.50 m) crosses a drain of 800 m³/s with HFL 160.50 m, which is above the canal bed. The canal bed (160.00 m) is above the drain bed (158.00 m), so the structure is a **siphon aqueduct**: the drain flows through rectangular barrels under the canal trough, partly under pressure. #### 1. Drainage waterway (Lacey) $$ P = 4.75\sqrt{Q} = 4.75\sqrt{800} = 134.4\ \text{m} $$ Barrels of clear span 4.0 m with walls 0.4 m thick: 32 barrels give a clear width of 32×4.0 = 128 m (about the regime width, accepted as the obstruction is by walls only) and overall width 141.2 m. Barrel height: bed 158.00 m to the roof soffit $= 160.00 - 0.40 = 159.60$ m, so the clear height is 1.6 m (roof 0.4 m thick, whose top is the canal bed). Area $= 128\times1.6 = 205$ m²; velocity $V = 800/205 = 3.91$ m/s; $V^2/2g = 0.778$ m. Head loss (entry + exit $\approx 1.5V^2/2g$ plus Manning friction, $n = 0.015$, $R = 0.571$ m, length 34.5 m): $$ h_L = 1.5\times0.778 + \frac{n^2V^2L}{R^{4/3}} = 1.167 + 0.250 = 1.42\ \text{m} $$ (the afflux is absorbed by the flood bank and a flared u/s wing). #### 2. Canal waterway Canal width in the trough is kept equal to the bed width of 30 m, depth 1.5 m (FSL 161.50 m), so the canal waterway is 30 m; the trough is a rectangular concrete section, with transitions (not needed since full width is kept). Barrel length along the canal axis $= 30 + 2\times1.5\times1.5 = 34.5$ m (including the canal side slopes of 1.5:1). #### 3. Uplift pressure on the roof of the barrel Worst case: drain at HFL (160.50 m) and barrel full, canal empty. Pressure head at the roof soffit $= 160.50 - 159.60 = 0.90$ m. $$ \begin{aligned} \text{Uplift} &= 9.81\times0.90 = 8.83\ \text{kN/m}^2 \\ \text{Roof weight} &= 0.4\times24 = 9.6\ \text{kN/m}^2 \\ \text{FOS (canal empty)} &= 9.6/8.83 = 1.09 \end{aligned} $$ With the canal running at FSL, the water on the roof is $1.5\times9.81 = 14.7$ kN/m², so FOS $= (9.6+14.7)/8.83 = 2.75$ (safe). The roof is also checked against flow conditions: when the barrel runs full at Q = 800 m³/s the pressure at the soffit is negative (energy level 160.50 m is used in 1.17 m of entry loss and velocity head), so no uplift occurs; the still-water case governs. As FOS with empty canal is only 1.09, the roof should be reinforced and tied to the walls. #### 4. Impervious floor Maximum seepage head (drain at HFL u/s, d/s dry): $H_s = 160.50 - 158.00 = 2.50$ m. Scour: $q = 800/134.4 = 5.95$ m²/s, $R = 1.35(q^2/f)^{1/3} = 4.44$ m ($f = 1$), scour level $= 160.50 - 1.5R = 153.85$ m, so d/s cut-off $d_2 = 4.2$ m below the floor; u/s cut-off $d_1 = 2.5$ m. Creep path (Bligh): $2d_1 + 4 + 34.5 + 8 + 2d_2 = 59.9$ m. Uplift head at points on the floor (linear loss): | Point | Creep from u/s (m) | Residual head (m) | Uplift (kN/m²) | |---|---|---|---| | Start of barrel floor | 9.0 | 2.12 | 20.8 | | Middle of barrel | 26.2 | 1.40 | 13.8 | | End of barrel | 43.5 | 0.68 | 6.7 | With $G = 2.24$, the barrel floor slab of the box is designed together with the weight of the walls, roof and canal water. The required thickness at the start of the floor from uplift alone is $t = \dfrac{4}{3}\dfrac{h}{G-1} = 2.28$ m; the box action (walls, roof, canal water) and the u/s cut-off carry the uplift, so the floor slab is made 0.6 m with pressure relief by weep holes at the d/s end. **Answer:** drainage waterway 128 m clear (32 barrels of 4.0×1.6 m), canal waterway 30 m, uplift on the roof $= 8.8$ kN/m² (head 0.9 m, FOS 1.09 canal empty), and floor uplift heads 2.12 m (start) to 0.68 m (end). ```text canal FSL 161.5 ~~~~~~~~~~~~~~~~~~~~ canal bed 160.0 ==roof 0.4 m========== HFL 160.5 ~~~~ | 4 m | 4 m | barrels 1.6 m drain bed 158.0 |_____|_____|___________ u/s cut-off 2.5 m floor d/s cut-off 4.2 m ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is this crossing a siphon aqueduct? A. The drain HFL (160.50 m) is above the canal bed (160.00 m), so the barrels run under pressure beneath the trough B. The drain bed is above the canal FSL C. The drain HFL is below the canal bed D. The canal and drain are at the same level Answer: A. The canal is over the drain and HFL is higher than the canal bed, giving pressure flow in the barrels. (Key point: Type of structure) 2. How is the drainage waterway first estimated? A. Lacey's regime perimeter P = 4.75 sqrt(Q) B. P = Q / V C. P = 2 x canal width D. P = 1.5 x canal Q Answer: A. For a natural stream, P = 4.75 sqrt(800) = 134.4 m is the regime waterway. (Key point: Drainage waterway) 3. What is the worst case for uplift on the barrel roof? A. Canal full and drain dry B. Drain at HFL, barrel full, canal empty C. Both canal and drain empty D. Canal at FSL and drain at HFL Answer: B. Uplift is greatest with water pressure below the roof and no canal water on top: head 0.90 m gives 8.83 kN/m2 against roof weight 9.6 kN/m2, FOS 1.09. (Key point: Roof uplift) 4. Which formula gives the floor thickness needed to resist uplift head h? A. t = h x (G - 1) B. t = 4/3 x h/(G - 1) C. t = h / G^2 D. t = 4 x h x G Answer: B. Thickness of the floor weight must balance uplift with a safety allowance: t = 4/3 h/(G - 1). 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