Extracts between parentheses - parentheses may be nested

Test data Wind energy is the kinetic energy of air in motion, also called wind. Total wind energy flowing through an imaginary surface with area A during the time t is: {\displaystyle E={\frac {1}{2}}mv^{2}={\frac {1}{2}}(Avt\rho )v^{2}={\frac {1}{2}}At\rho v^{3},} E={\frac {1}{2}}mv^{2}={\frac {1}{2}}(Avt\rho )v^{2}={\frac {1}{2}}At\rho v^{3},[248] where ρ is the density of air; v is the wind speed; Avt is the volume of air passing through A (which is considered perpendicular to the direction of the wind); Avtρ is therefore the mass m passing through "A". Note that ½ ρv2 is the kinetic energy of the moving air per unit volume. Power is energy per unit time, so the wind power incident on A (e.g. equal to the rotor area of a wind turbine) is: {\displaystyle P={\frac {E}{t}}={\frac {1}{2}}A\rho v^{3}.} P={\frac {E}{t}}={\frac {1}{2}}A\rho v^{3}.[248] Wind power in an open air stream is thus proportional to the third power of the wind speed; the available power increases eightfold when the wind speed doubles. Wind turbines for grid electric power therefore need to be especially efficient at greater wind speeds.