The power P required to drive a propeller is known to depend on the diameter of the propeller D, the density of fluid ρ, the speed of sound a, the angular velocity of the propeller ω, the freestream velocity V , and the viscosity of the fluid µ. (a) How many dimensionless groups characterize this problem? (b) If the effects of viscosity are neglected, and if the speed of sound is not an important variable, express the relationship between power and the other variables in nondimensional form. (c) A one-half scale model of a propeller is built, and it uses Pm horsepower when running at a speed ωm. If the full-scale propeller in the same fluid runs at ωm/2, what is its power consumption in terms of Pm if the functional dependence found in part (b) holds? What freestream velocity should be used for the model test?
The power P required to drive a propeller is known to depend on the diameter of the propeller D, the density of fluid ρ, the speed of sound a, the angular velocity of the propeller ω, the freestream velocity V , and the viscosity of the fluid µ.
(a) How many dimensionless groups characterize this problem?
(b) If the effects of viscosity are neglected, and if the speed of sound is not an important variable, express the relationship between power and the other variables in nondimensional form.
(c) A one-half scale model of a propeller is built, and it uses Pm horsepower when running at a speed ωm. If the full-scale propeller in the same fluid runs at ωm/2, what is its power consumption in terms of Pm if the functional dependence found in part (b) holds? What freestream velocity should be used for the model test?
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