An Attack Submarine in the Deep Sea

A 1:10 scale model of an attack submarine is being tested in a water tunnel. The drag force ratio the submarine in the deep sea and the submarine model in the tunnel need to be estimated. The submarine cruises at 4 m/s in seawater (viscosity, μ = 1.2×10^-3 N-s/m² and density, ρ = 1,030 kg/m³). The fresh water in the tunnel is maintained at a temperature of 40 ^oC.

What should the velocity of the model be in the tunnel? Determine the drag force ratio of the submarine prototype and model.

• Assume the submarine is far from the water surface.
• Assume the compressibility of water is negligible.