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.