Water flows in a tube that has an inner diameter of 2.54 cm and a length of 2.5 m. The tube wall is covered with a layer of a sparingly soluble substance (the transferred species), whose properties...

Water flows in a tube that has an inner diameter of 2.54 cm and a length of 2.5 m. The tube wall is covered with a layer of a sparingly soluble substance (the transferred species), whose properties are similar to those of benzene. The mass fraction of the transferred species at the wall surface is equal to 0.15. The temperature of the water and the pipe is 25 ◦C. The water is pure at the inlet to the tube. The water mean velocity at inlet is 4.6 m/s.

1. Calculate the average mass fraction of the transferred species in water at tube exit, assuming that the surface is smooth, using

(a) Gnielinski’s correlation modified for mass transfer,

(b) the Reynolds analogy,

(c) the Chilton–Coulburn analogy.

2. Repeat the calculations of part 1, assuming that the tube has an average surface roughness value of approximately 4.6 × 10⁻²
mm.