Tidal Power Energy Calculation

The potential energy (PE) stored in the trapped water of a tidal power station is determined by the volume of water, its density, the height it's trapped at, and gravity. The formula often used for the total potential energy available in the basin is:

$ PE = \frac{1}{2} \rho g A h^2 $

This formula accounts for the energy generated as the water level drops from height $h$ to the low tide level, considering the average effective head.

Given Information:

• Basin Area ($A$) = $10,000 \, m^2$
• Trapped Water Height ($h$) = $2.0 \, m$
• Density of Seawater ($\rho$) = $1025 \, kg/m^3$
• Acceleration due to Gravity ($g$) $\approx 9.81 \, m/s^2$

Energy Calculation Steps:

1. Substitute values into the formula:

   $ PE = \frac{1}{2} \times (1025 \, kg/m^3) \times (9.81 \, m/s^2) \times (10,000 \, m^2) \times (2.0 \, m)^2 $

2. Calculate the term $(2.0 \, m)^2$:

   $ (2.0 \, m)^2 = 4.0 \, m^2 $

3. Multiply the terms:

   $ PE = 0.5 \times 1025 \times 9.81 \times 10,000 \times 4.0 \, J $

   $ PE = 1025 \times 9.81 \times 20,000 \, J $

   $ PE \approx 201,105,000 \, J $

4. Convert Joules (J) to Megajoules (MJ):

   Using the conversion $1 \, MJ = 10^6 \, J$,

   $ PE \approx \frac{201,105,000}{1,000,000} \, MJ $

   $ PE \approx 201.1 \, MJ $

Therefore, the potential energy available for every tidal period is approximately 201 MJ.