Determining the Potential Energy in the Tidal Wave A dam-type tidal energy system consists of a lagoon on one side and an open ocean on the other side. The base of the lagoon is approximately semicircle with a radius of 1 km. At a high tide, the head on the high water side of the dam is 25 m

Question

Determining the Potential Energy in the Tidal Wave

A dam-type tidal energy system consists of a lagoon on one side and an open ocean on the other side. The base of the lagoon is approximately semicircle with a radius of 1 km. At a high tide, the head on the high water side of the dam is 25 m and the head on the low side is 15 m. Calculate (a) the potential energy in the tidal water, and (b) the electrical energy generated by the tidal system. Assume the power coefficient of the blades is 35%, the efficiency of the turbine is 90%, and the efficiency of the generator is 95%.

Accepted Answer

[latex]H_{high} = 25 m, H_{low} = 15 m, g = 9.807 m/s^2, R = 1000 km, ρ= 1000 kg/m^3 C_p = 0.35, η_t = 0.9, n_g = 0.95[/latex]

a. Equation (16.56) gives

[latex]\Delta H=\frac{H_{high} - H_{low}}{2}=\frac{25-15}{2}=5 m[/latex]

The total volume of water

[latex]vol= \frac{1}{2}\pi R^2\Delta H = 0.5 imes \pi imes 1000^2 imes 5 = 7.854 imes 10^6 m^2[/latex]

Equation (16.57)

[latex]PE = mg ΔH[/latex] (16.57)

gives the potential energy

[latex]PE = vol imes ho imes g imes \Delta H = 7.854 imes 10^6 imes 9.807 imes 5 = 3.851 imes 10^{11} J[/latex]

b. The electrical energy of the tidal system

[latex]E_{out} = PE imes C_p\eta _t\eta _g = 3.851 imes 10^{11} imes 0.35 imes 0.9 imes 0.95 = 1.152 imes 10^{11} J[/latex]

Question 16.7: Determining the Potential Energy in the Tidal Wave A dam-typ...

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