A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V= 40 m/s and when rotating at 4800 rev/min. What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 10 m/s at 2000 m standard altitude? At 2000 m altitude, p = 1.0067 kg/m³. At sea level, p= 1.2255 kg/m³. The power developed is | KW.

S Algebraic equations such as Bernoulli's relation, Eq. (1) of Ex. 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the bound- ary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ди pu- du pv- ду + pgx + ax ду where 7 is the boundary-layer shear stress and g, is the component of gravity in the x direction. Is this equation dimensionally consistent? Can you draw a general con- cusion?

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