Page 87 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

Tidal Energy Chapter | 3 79

FIG. 3.31 Schematic of ebb generation in a tidal lagoon during 24 h.

Referring to Fig. 3.30, the total potential energy in a tidal lagoon can be
evaluated by summing the potential energy of each individual particle in the
reservoir with respect to a datum

–
–
E potential = (δm)gz = ρ(δ V )gz = ρzdV (3.49)
–
V
where z is the elevation above the datum and V is volume. First, consider a
–
tidal lagoon in which the surface area of the lagoon does not vary with water
elevation (which is not the case in Fig. 3.30); for this special case, dV = A L dz,
–
where A L is the surface area of the tidal lagoon. Therefore
h L h L
h L
2
E potential = ρzA L dz = ρA L zdz = ρA L (3.50)
0 0 2
where h L is the water surface elevation above a datum. Eq. (3.50) simply
indicates that the energy which can be stored in a tidal lagoon is proportional to
its surface area, and the square of water elevation.
Now we consider a more general case. Suppose that water surface elevations
inside and outside of a tidal lagoon are represented by h L and h O , respectively;
assuming no energy loss, the kinetic energy and the current velocity through the
tidal turbines can be evaluated using Bernoulli’s equation