Answer Happy

(a) The power required to drive a propeller, P, is measured to be a function of the freestream velocity U, fluid density e, speed of sound a, angular speed of the propeller w fin a unit of rad/s), the less groups diameter D and the viscosity of the Huid (in a unit of Pa s). Find how many independent d should be used to describe such a relation. Also, find the independent dimensionless-groups. To get the full credits, the dimensionless groups should include Mach, Strouhal and Reynolds numbers (U/a, wD/U and pUD/, respectively). (b) You decide to perform an experiment on a model propeller where air is the working fluid that has density of 1.225 kg/m and dynamic viscosity of μ-18 10-5Pa-s, flowing at a freestream velocity of 5 m/s- Find the diameter of this model propeller if the full-scale propeller with 1 m in diameter is working under water as fluid with density of 1000 kg/m³ and dynamic viscosity of 1.0 x 10 Pas, flowing at a velocity of 1 m/s. In both model and full-scale experiments, the Mach numbers are negligibly small, and it is only necessary to match the Reynolds number and the Strouhal number to achieve dynamic similarity. (c) Find the power required to drive the full-scale propeller if the model propeller requires power of 20 kW. You can use all the necessary information from parts (a) and (b).