A small autonomous underwater vehicle (AUV) has the following design requirements: Speed, Vo = 10 m/s, vehicle radius, r = 0.5 m. The shape of the AUV has a drag coefficient, CD = D V∞ (2r) 1x104, where D is the drag on the = : 0.15, at design Reynolds number, Rep = PV²Axs vehicle, Axs = πr² is the frontal area of the vehicle, and here we take water properties: v= 1x10-³ m²/s, p = 1,000 kg/m³. We wish to test propeller designs using a scale model in a water tunnel, where design-to-model geometry scale, Ldesign/Lscale = 2. We need to match design Reynolds number in the test. The propeller, which can be viewed as an axial compressor rotor (axial pump) must meet the thrust requirement, T = D. The scale propeller must match Voo the full-scale propeller advance ratio, JD = where No is the full-scale rotation rate in NDdpp rotations per second (rps), and dp is the full-scale propeller diameter. The scale propeller must also match the thrust coefficient, KT = We wish to use a family of propellers that have optimum efficiencies at J = 1.25, K = 0.19. Determine the following: a) the delivered thrust of model propeller, b) the rotation rate ratio, Ndesign/Nscale, c) the diameter of the model propeller. T pN²d* V =

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