Pipes often contain solid residue that adheres to the inner wall of the pipe. If these pipes are not properly cleaned before use, then the flow of water through the pipe will slowly dissolve the contaminant solid (solute A) into the water through a convective mass transfer process. Consider the system shown in the figure below. Pure liquid water flows into a 2.0 cm inner diameter tube of 25.0 m length (L) at a bulk velocity (v_∞) of 0.50 m/s at 1.2 atm and 20 C. The solid contaminant only coats the lower half of the inside surface of the pipe. The maximum solubility of solute A in water (c_AL*) is 10.0 mmole A/m³ (very dilute, but still toxic) and the diffusion coefficient of solute A in liquid water (B) is D_AB = 5.0 x 10^–5 cm²/s (5.0 10 9 m²/s).
You may assume that during the process, the solid does not completely dissolve away, and that the solid contaminant layer is thin relative to the inside diameter of the pipe
a. Identify the source and sink for the mass transfer process.
b. What is the mass flowrate of water into the tube?
c. What is the convective mass transfer coefficient for solute A in liquid water, k_L (m/s)?

d. What is the differential material balance model for describing the concentration of dissolved solute A down the length of the tube? State three primary assumptions of your model. The model must at least contain the following variables: c_AL*, c_AL, k_L, z, v_∞, D.

e. What is the dissolved solute concentration c_AL exiting the tube at z = L?
f. If the liquid velocity is doubled, with all other variables remaining constant, what happens to mass transfer coefficient k_c and c_AL at z = L?

Transcribed Image Text:

Water CALO0 gmole A/m³ V = 0.50 m/s 293 K D = 2.0 cm Z = L = 25 m CAL 0 Solid contaminant layer lining inside bottom half of tube CAL Tube cross section