--- title: "Uplift pressure diagram with drainage gallery" subject: "Hydropower Engineering" chapter: 4 key: "semester_7/hydropower_engineering:uplift-pressure-diagram-gravity-dam" source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/uplift-pressure-diagram-gravity-dam site: BCT Engineering --- # Uplift pressure diagram with drainage gallery Hydropower Engineering · Chapter 4: Headworks of Storage Plants - Asked in: 2069 Chaitra, 3+2 marks - Video: [Uplift pressure diagram with Numerical](https://www.youtube.com/watch?v=juVB4KNRLHc) — Civil Engineering Studies - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/uplift-pressure-diagram-gravity-dam - Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-4 ## Question Draw the uplift pressure diagram (i) for a dam holding 50 m water depth at the upstream vertical face with top and bottom widths 10 m and 30 m respectively. Uplift may be considered to be acting on 60% of the area of the section. Tail water depth is 5 m. (ii) For the same dam there is a drainage gallery at 6 m from the face. ## Short answer (i) Uplift acts on 60% area; heel ordinate 294 kN/m², toe 29 kN/m², total uplift ≈ 4856 kN/m. (ii) Gallery at 6 m reduces gallery pressure to 196 kN/m²; total uplift ≈ 3002 kN/m, 38% reduction. ## Answer #### Data Water depth $h=50$ m, tail water $h_t=5$ m, base width $B=30$ m (top width 10 m), $\gamma_w=9.81$ kN/m³. Uplift acts on 60% of the base area, so the intensity is reduced to 60% of the full hydrostatic value (reduction factor 0.6). Full hydrostatic pressures: heel $p_h=\gamma_wh=490.5$ kN/m²; toe $p_t=\gamma_wh_t=49.05$ kN/m². #### (i) Without a drainage gallery The uplift varies linearly from the heel to the toe, giving a trapezoidal diagram below the base. ```text Heel Toe +--------------------------------+ <- base of dam (30 m) | | | uplift (trapezoid) ____| | _________/ 29.43 kN/m2 | _________/ |_______/ 294.3 kN/m2 (full values: 490.5 at the heel, 49.05 at the toe) ``` Effective ordinates (60%): heel $=0.6\times490.5=294.3$ kN/m², toe $=0.6\times49.05=29.43$ kN/m². $$ U_1=0.6\times\tfrac12(p_h+p_t)B=0.6\times\tfrac12(490.5+49.05)\times30=4,856\ \text{kN/m} $$ (Full value without the 60% factor: 8,093 kN/m.) #### (ii) With a drainage gallery 6 m from the u/s face The gallery reduces the pressure at its position to the tail water pressure plus one-third of the difference: $$ p_g=p_t+\tfrac13(p_h-p_t)=49.05+\tfrac13(490.5-49.05)=196.2\ \text{kN/m}^2 $$ The diagram is then a two-segment line: heel $\to$ gallery $\to$ toe. Effective ordinates (60%): heel 294.3, gallery 117.7, toe 29.43 kN/m². ```text Heel G (6 m) Toe 490.5 --. `-. 196.2 (gallery) `-.______ 49.05 0 6 30 m ``` Areas: - Heel to gallery: $\tfrac12(490.5+196.2)\times6=2,060.1$ kN/m - Gallery to toe: $\tfrac12(196.2+49.05)\times24=2,943.0$ kN/m - Total (full) $=5,003$ kN/m; with the 60% factor $U_2=0.6\times5,003=3,002$ kN/m **Answer: (i) total uplift ≈ 4,856 kN/m (heel ordinate 294 kN/m², toe 29 kN/m²). (ii) With the gallery the uplift falls to ≈ 3,002 kN/m, a reduction of 38%.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Without a drainage gallery, how does the uplift pressure vary from heel to toe? A. Linearly, from the full head at the heel to the tail water head at the toe B. It is constant across the base C. Parabolically, with a maximum at the middle D. It is zero at the heel and maximum at the toe Answer: A. Uplift is a straight line (trapezoid) from heel hydrostatic pressure to toe tail water pressure. (Key point: Shape of uplift without gallery) 2. What does 'uplift acting on 60% of the area' mean for the calculation? A. Only 60% of the base width is considered B. The uplift intensity is reduced to 0.6 times the full hydrostatic value C. The tail water is reduced by 60% D. The uplift is increased by 60% Answer: B. A reduction factor of 0.6 is applied to the ordinates: heel 294.3 and toe 29.43 kN/m^2. (Key point: The 60% factor) 3. With a drainage gallery, the pressure at the gallery is taken as A. The heel pressure B. The toe pressure only C. Zero D. Tail water pressure plus one-third of the difference between heel and tail water pressures Answer: D. p_g = p_t + (1/3)(p_h - p_t) = 196.2 kN/m^2. (Key point: Gallery pressure) 4. What is the effect of the drainage gallery on total uplift? A. It reduces it, from about 4,856 to about 3,002 kN/m B. It increases it C. It leaves it unchanged D. It makes it zero Answer: A. The diagram falls sharply at the gallery, reducing total uplift by about 38%. 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