has been suggested that tidal turbines could be used to generate power
from ocean currents. The Gulf Stream, for example, has a constant velocity of about 1.5 m/s. Discuss the advantages or disadvantages of this approach compared to the use of turbines in a tidal current that varies from $$- 3.0 \mathrm {~m} / \mathrm { s }$$ (in one direction) to +3.0 m/s (in the other direction).

Question

Quizplus · Accepted Answer

The Answer is For the Gulf Stream, the velocity is constant so the power output will be constant. This is advantageous compared to the tidal stream current which varies between 0 and a maximum velocity. On the other hand, the total energy produced by the tidal stream generator is greater than that produced by the Gulf Stream generator. This is because the power is proportional to the cube of the velocity and the mean value of v3 for (e.g.) a linearly varying velocity is greater than half the maximum value. This can be shown quantitatively as follows:

For a constant velocity of

v _ { 0 } / 2

, the total power over half a tidal cycle (time

\left. = T / 2 ight)

will be proportional to

E \sim \left( v _ { 0 } / 2 ight) ^ { 3 } imes ( T / 2 ) = v _ { 0 } T / 16

For a velocity that varies linearly between 0 and

v _ { 0 }

over half a tidal cycle then the velocity may be written as

v ( t ) = 2 v _ { 0 } t / T

So the energy will be proportional to

E \sim \frac { 8 v _ { 0 } ^ { 3 } } { T ^ { 3 } } \int _ { 0 } ^ { T / 2 } t ^ { 3 } d t = \left[ \frac { 8 v _ { 0 } { } ^ { 3 } } { T ^ { 3 } } \frac { t ^ { 4 } } { 4 } ight] _ { 0 } ^ { T / 2 } = \frac { v _ { 0 } { } ^ { 3 } T } { 8 }

Or twice the energy for the constant velocity case.

Has Been Suggested That Tidal Turbines Could Be Used to Generate