Pitch (or "Bitumen") is a material with a very high viscosity. It seems solid, when you walk on it, but on very long time scales it flows like a liquid. To demonstrate its flow, a spectacular experiment has been set up in the 1930's, which is still running (Fig. 1): The Bitumen was filled into a funnel, from which it is-due to its high viscosity-dripping at a very small rate. On the average, one drop falls every eight years. Determine the viscosity of the pitch by assuming the volume of the drop to be 1cm^3. Assume that the only resistance to flow occurs in the stem of the funnel (lower part), which has a diameter of 1cm and a length l = 3cm. Another possibility to determine the viscosity of the pitch is to let a ball sink through the material. Consider a steel ball (rho_steel = 7800 kg/m^3) with a diameter of 10 cm and determine the time that it needs to sink through 20 cm of the pitch. Could we observe this in our lifetime? Consider a homogeneous liquid with the same viscosity as that of pitch. The diffusion of molecules in such a liquid is also very slow. A molecular relaxation time can be defined as the time, in which a molecule in the material diffuses a distance equal to its own radius. Assume that diffusion happens in the same way as in a "normal" liquid. Determine the relaxation time of the material at room temperature assuming the molecule to be spherical and having a diameter d= 5 10^-10 m. How does this relaxation time compare to that of normal liquids of around 10 picoseconds (10 10^-12s) ?