Tidal Forcesenergy Conservation Topic
Tidal Forces- Energy Conservation (Detailed notes from Toppers)
Conservation of Energy in Tidal Forces
- Gravitational potential energy and relation to tidal forces
- Gravitational potential energy (PE): Gravitational PE of a water particle of mass m located at a height h above a reference level due to Earth and Moon’s gravitational force is given by:
$$PE_{grav} = mg(R+h)$$ Where, R = Radius of the Earth g = Acceleration due to gravity
- Tidal work done by tidal forces on a unit mass of water:
- Work done by the tidal force is given by the equation:
$$W = - \Delta PE_{grav}$$
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Derivation of the equation for tidal energy conservation
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Using conservation of Energy $$K_i+PE_i=K_f+PE_f$$ $$\Delta K+\Delta PE_{grav}=0$$ Here, we make use of the shallow water approximation, the water particle will move in a circular motion with radius “r” and tangential speed “v”. $$v=\sqrt{rg}$$ $$K=\frac{1}{2}mv^2=\frac{1}{2}mrg$$ $$\Delta K=\frac{1}{2}mr_1g-\frac{1}{2}mr_2g$$ Now the change in gravitational potential energy of a water particle of mass m from r_1 to r_2 is given by: $$\Delta PE_{grav} = mg(R+r_2) - mg(R+r_1)$$ Substituting these values in the equation $$\Delta K+\Delta PE_{grav}=0$$ We get $$ -\frac{1}{2}mg(r_2-r_1)+ mg(r_2-r_1)=0 $$ $$\Delta K=\frac{1}{2}mg(r_2-r_1)$$
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Energy balance in a tidal system -Tidal friction causes a deceleration in the Earth’s rotation.
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The rotational energy lost by the Earth is transferred to the Moon in the form of orbital energy. This increases the Moon’s orbital angular momentum.
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Dissipation of tidal energy due to friction and viscosity:
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Some of the tidal energy is dissipated as heat because of water’s internal friction and bottom’s friction .
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Loss of energy result in reduction in the amplitude of the tides and gradual slowing of the Earth’s rotation
Tidal Power Generation
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Introduction to tidal power generation:
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Tides can be harnessed to produce electrical energy through the process of “Tidal Power Generation "
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Types of tidal power plants:
- Single basin :
- Uses a barrage (wall like structure) to separate a part of the coast from the sea during high tide.
- As water levels rise during the next high tide, potential energy is built up behind the barrage.
- Double Basin:
- Contains two basins , an upper and a lower one, separated by a dike with sluice gates.
- The process of filling and emptying of basins produce the potential energy.
- Run of the River:
- Does not require any barrage.
- Utilizes the natural flow of water through the turbines during high/low tides.
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Advantages and Disadvantages of tidal power generation: Advantages: -Renewable and sustainable source of energy. -Predictable and reliable. -Does not produce greenhouse gas emissions. Disadvantages: -High initial investment costs. -Impacts on marine life and ecosystems. -Limited to areas with significant tidal ranges.
Environmental Impact of Tidal Power Generation:
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Impact on marine life: -Alteration in the natural food chain . -Disruption in the reproductive cycle of marine species
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Changes in coastline and sedimentation patterns:
- Construction of barrages can affect sediment transport, leading to coastal erosion or accretion.
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Visual impact and noise pollution: -Visual intrusion of the tidal power plant and associated infrastructure. -Noise from turbines and other machinery.