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

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

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

 i Gnielinski’s correlation modified for mass transfer

 ii The Reynolds analog

 iii The Chilton–Coulburn analogy

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