Energy calculations
Turbine power
Tidal energy converters can have varying modes of operating and therefore varying power output. If the power coefficient of the device " C_P" is known, the equation below can be used to determine the power output of the hydrodynamic subsystem of the machine. This available power cannot exceed that imposed by the Betz limit on the power coefficient, although this can be circumvented to some degree by placing a turbine in a shroud or duct. This works, in essence, by forcing water which would not have flowed through the turbine through the rotor disk. In these situations it is the frontal area of the duct, rather than the turbine, which is used in calculating the power coefficient and therefore the Betz limit still applies to the device as a whole.
The energy available from these kinetic systems can be expressed as:
P = (( \rho A V^3 ) / 2 ) C_P
where:
C_P = the turbine power coefficient
P = the power generated (in watts)
\rho = the density of the water (seawater is 1027 kg/m³)
A = the sweep area of the turbine (in m²)
V = the velocity of the flow
Relative to an open turbine in free stream, ducted turbines are capable of as much as 3 to 4 times the power of the same turbine rotor in open flow.[47]