(Solved): A student team is to design a human-powered submarine for a design competition. The overal length ...

A student team is to design a human-powered submarine for a design competition. The overal length of the prototype submarine is $4.85\mathrm{m}$, and its student designers hope that it can travel fully submerged through water at $0.3\mathrm{m}/\mathrm{s}$. The water is freshwater (a lake) at $T=15^{\circ }\mathrm{C}$. The design team builds a one-fifth scale model to test in their university's wind tunnel. 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 is at $25^{\circ }\mathrm{C}$ and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achieve similarity? At this air temperature, the speed of sound is around $346\mathrm{m}/\mathrm{s}$. Determine the Mach number of the flow. For water at $T=15^{\circ }\mathrm{C}$ and atmospheric pressure, $\rho =999.1\mathrm{kg}/{\mathrm{m}}^3$ and $\mu =1.138\times 10^{-3}\mathrm{kg}/\mathrm{m}\cdot \mathrm{s}$. For air at $T=25^{\circ }\mathrm{C}$ and atmospheric pressure, $\rho =1.184\mathrm{kg}/{\mathrm{m}}^3$ and $\mu =1.849\times 10^{-5}\mathrm{kg}/\mathrm{m}\cdot \mathrm{s}$. The wind tunnel velocity must be $\mathrm{m}/\mathrm{s}$. The Mach number of the flow is