--- title: "Tidal power generation and output: 3 km × 3 km" subject: "Power Plant Design" chapter: 1 key: "semester_8/power_plant_design:tidal-generation-3x3km" source: https://www.bctengineer.com/q/semester_8/power_plant_design/tidal-generation-3x3km site: BCT Engineering --- # Tidal power generation and output: 3 km × 3 km Power Plant Design · Chapter 1: Energy Sources and Electric Power Generation - Asked in: 2071 Bhadra, 4+4 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/power_plant_design/tidal-generation-3x3km - Whole chapter: https://www.bctengineer.com/md/semester_8/power_plant_design/chapter-1 ## Question How electric power is generated from a Tidal Power Project? Estimate the power output from a tidal project that has tidal range of approximately 10 m. The surface area of tidal harnessing plant is 3 km × 3 km. Consider that there are two high tides every day. Assume power conversion efficiency as 30%. Density of sea water is about 1025 kg/m³. ## Short answer Tides create a head between sea and basin; water flows through low-head bulbs turbines during ebb, driving generators. Energy per tide is 0.5 rho g A h^2. With area 9e6 m^2, range 10 m, density 1025 kg/m^3, two tides daily, and 30% efficiency, average power output is about 31.4 MW. ## Answer #### Generation of electric power from a tidal project Tides are the periodic rise and fall of sea level caused by the moon and sun's gravity; most coasts have two high and two low tides a day. A tidal power plant uses the head between the sea and a basin. ```text SEA BARRAGE BASIN high tide ~~~~~ +-----------+ | sluice | ~~~~~ stored low tide ~~~~ | turbine | water +-----------+ <--- flow through turbine on ebb (basin -> sea) ``` 1. A **barrage (dam)** is built across a bay or estuary, with sluice gates and low-head **bulb (Kaplan type) turbines**. 2. **Filling**: at rising tide the gates open and the basin fills. 3. **Holding**: at high tide the gates close and water is held. 4. **Generation (ebb)**: when the sea falls, a head forms; water flows from basin to sea through the turbines, driving generators. 5. In **double-effect** schemes, power is also generated on the flood tide (sea to basin). Examples: La Rance (France, 240 MW), Sihwa (South Korea, 254 MW). #### Power estimation Energy of water in the basin per tide (centre of gravity at $h/2$): $$ E = \frac{1}{2}\rho g A h^2 $$ Given: $A = 3000 \times 3000 = 9\times 10^6$ m², $h = 10$ m, $\rho = 1025$ kg/m³, $g = 9.81$ m/s², 2 tides per day, $\eta = 0.30$. $$ \begin{aligned} E &= 0.5 \times 1025 \times 9.81 \times 9\times 10^6 \times 10^2 \\ &= 4.525\times 10^{12}\ \text{J per tide} \\ &= 1256.9\ \text{MWh per tide} \\ E_{day} &= 2 \times 4.525\times 10^{12} = 9.050\times 10^{12}\ \text{J} \\ P_{avg} &= \frac{\eta E_{day}}{86400} = \frac{0.30 \times 9.050\times 10^{12}}{86400} \\ &= 3.142\times 10^{7}\ \text{W} \end{aligned} $$ **Answer:** Average power output $\approx 31.4$ MW (about 275 GWh per year). Assumption: one basin emptying per high tide, averaged over 24 hours. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In ebb generation, when does the tidal plant generate? A. While the basin fills B. When the sea falls and water flows from the basin to the sea through turbines C. Only at low tide with gates open and no head D. Only at night Answer: B. After holding at high tide, the head between basin and falling sea drives the turbines. (Key point: Generation on ebb) 2. What happens during the holding stage? A. Gates close at high tide and water is held B. Turbines run at full output C. Gates open fully D. Basin is emptied Answer: A. Gates close at high tide to hold water until a head develops. (Key point: Holding stage) 3. What is special about a double-effect scheme? A. Two barrages are used B. Power is also generated on the flood tide (sea to basin) C. Efficiency is 100% D. No turbines are needed Answer: B. Double-effect generates on both ebb and flood flows. (Key point: Double-effect scheme) 4. For 3 km x 3 km, h = 10 m, 30% efficiency and 2 tides per day, the average power is about A. 314 MW B. 3.14 MW C. 63 MW D. 31.4 MW Answer: D. 0.3 x 9.05 x 10^12 / 86400 = 31.4 MW. (Key point: Power estimate) ## Related in Power Plant Design - [Tidal power output: 3 km × 5.5 km barrage](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Atidal-barrage-3x5-5km) — Power Plant Design, chapter 1 - [Tidal versus wind power plant](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Atidal-vs-wind) — Power Plant Design, chapter 1 - [Design: 230 m head plant, 20 km line](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2070-230m-20km) — Power Plant Design, chapter 4, asked 14× - [Design: 230 m head plant, 55 km line](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2074-230m-55km) — Power Plant Design, chapter 4, asked 12× - [Design: 250 m head plant, 35 km line](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2074-250m-35km) — Power Plant Design, chapter 4, asked 12× - [Design: 230 m head plant, 45 km line](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2071-230m-45km) — Power Plant Design, chapter 4, asked 12× ## Related in other subjects - [Pondage surface area and weekly output](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Apondage-weekly-operation-40cumec) — Hydropower Engineering, chapter 3 - [Slope-area discharge, 10 km reach](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aslope-area-306-920) — Engineering Hydrology, chapter 4 - [Slope-area discharge, 10 km reach, 104.77 m](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aslope-area-104-77) — Engineering Hydrology, chapter 4 - [Every RE has NFA; ε-NFA for bb(a∪b)*ab](https://www.bctengineer.com/question.md?key=semester_3%2Ftheory_of_computation%3Are-to-nfa-bb-aub-ab) — Theory of Computation, chapter 2