1. An infinitely long cylinder with a diameter of 10 cm is filled with a fluid. At x=0 and at t=0, a delta function mass input of 2.0 gm CO₂. Assume

25°C. Write governing equation, initial and boundary conditions and solution. Find the time to reach a concentration of 2 ppm at x=100 cm for (i) Molecular diffusion in air [2 pts]. Use D=0.164 cm²/s. [Be careful about converting mass/volume to mass/mass for air since 1 mg/l is not equal to 1 ppm in air! You will need the density of air: 1180 g/m³] (ii) Molecular diffusion in water [2 pts]. Use D=2E-5 cm²/s. (iii) Turbulent diffusion in water [2 pts]. As we will derive later, substitute a value of 1 cm²/s for D as a reflection of uniformly generated (isotropic and homogeneous) turbulence in water.