A stirrer is used to mix chemicals in a large tank. The shaft power W supplied to the stirrer blades is a function of stirrer diameter D, liquid density ρ, liquid viscosity μ, and the angular velocity ω of the spinning blades. Use the method of repeating variables to generate a dimensionless relationship between these parameters. Modify your ∏ groups as necessary.

(Table 7-5: Some common established nondimensional parameters or ∏'s encountered in fluid mechanics and heat transfer, in the textbook may be consulted for this question)

A student team is to design a human-powered submarine for a design competition. The overall length of the prototype submarine is 5.46 m, and its student designers hope that it can travel fully submerged through water at 0.456 m/s. The water is freshwater (a lake) with a density of 999.1 kg/m³ and dynamic viscosity of 1.138 x 10^-3 kg/ms. The design team builds a 0.24 scale model to test in their university’s wind tunnel, as shown in the figure below. A shield surrounds the drag balance strut so that the aerodynamic drag of the strut itself does not influence the measured drag. The air in the wind tunnel has a density of 1.184 kg/m³ and dynamic viscosity of 1.849 x 10^-5 kg/ms, and is at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achieve similarity?