SATHEE: Tidal Forcesenergy Conservation Topic

Tidal Forces- Energy Conservation (Detailed notes from Toppers)

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

$$W = - \Delta PE_{grav}$$

Derivation of the equation for tidal energy conservation
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 $$ -\frac{1}{2}mg(r_2-r_1)+ mg(r_2-r_1)=0 $$ $$\Delta K=\frac{1}{2}mg(r_2-r_1)$$
Energy balance in a tidal system -Tidal friction causes a deceleration in the Earth’s rotation.
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.
Dissipation of tidal energy due to friction and viscosity:
Some of the tidal energy is dissipated as heat because of water’s internal friction and bottom’s friction .
Loss of energy result in reduction in the amplitude of the tides and gradual slowing of the Earth’s rotation

Introduction to tidal power generation:
Tides can be harnessed to produce electrical energy through the process of “Tidal Power Generation "
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.
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.

Impact on marine life: -Alteration in the natural food chain . -Disruption in the reproductive cycle of marine species
Changes in coastline and sedimentation patterns:
- Construction of barrages can affect sediment transport, leading to coastal erosion or accretion.
Visual impact and noise pollution: -Visual intrusion of the tidal power plant and associated infrastructure. -Noise from turbines and other machinery.