A 4 m horizontal-axis lift wind rotor runs a pump in 15 km/h wind, air density1.23 kg/m³. Far-wake velocity is one-third approach velocity. Find rotor thrust in N, to two decimals.
Actuator-disc velocity is the mean of upstream and far-wake velocities,$v_d=(v+v/3)/2=2v/3$. Mass flow=ρAv_d and thrust=mass flow×(v−v/3). Thus $T=(4/9)\rho A v^2=(4/9)(1.23)(\pi4^2/4)(15/3.6)^2=\mathbf{119.26}$ N. Using upstream velocity for mass flow would overestimate thrust.
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