Power from tidal Current. (Note: The equation for tidal current power is include

Question

Power from tidal Current. (Note: The equation for tidal current power is included in the statement of this problem.) Tidal current energy is the kinetic energy of water in motion. Total tidal current energy flowing through an imaginary area Aduring the time t is: where is the water density; v is the current speed; Avt is the volume of water passing through A (which is considered perpendicular to the direction of the current); Avt is therefore the mass m passing per unit time. Power is energy per unit time, so the tidal current power incident on A (e.g. equal to the rotor area of a water turbine) is: As with wind power, the power in an open water stream is thus proportional to the third power of the water speed; the available power increases eightfold when the wind speed doubles. Use the above equation for the power P, to determine the power output of one turbine operating under the following conditions: Suppose the average tidal current velocity is 5.0 m/s and the turbine blades are 15 meters in length. (That means that the blades sweep out a circular area with a radius of 15 meters.) The density of seawater is approximately 1025 kg per cubic meter. Finally, suppose the coefficient of performance is 0.59, the maximum amount allowed byBetz’s law. (Betz’s theoretical result, studied when we considered wind power, states that the maximum energy that can be extracted by the turbine blades is approximately 59% of the available kinetic energy.) Use this information to calculate the power output of the turbine.

Explanation / Answer

mass per unit time = A(rho)vt
KE of this mass = 0.5(a(rho)vt)v^2 = 0.5A(rho)tv^3
Power = 0.5A(rho)v^3

Given, A = pi*(15)^2
rho = 1025
v = 5 m/s
P = 0.59*0.5*pi*(15)^2*1025*5^3 = 26.7034 MW

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