6S.14 The falling film is widely used in chemical processing for the removal of gaseous species. It involves the flow of a liquid along a surface that may be inclined at some angle >> 0. Gas (A) -PA Liquid film (B) The flow is sustained by gravity, and the gas species A outside the film is absorbed at the liquid-gas interface. The film is in fully developed laminar flow over the entire plate, such that its velocity components in the y- and z-directions are zero. The mass density of A at y = 0 in the liquid is a constant PA, independent of z. (a) Write the appropriate form of the 2-momentum equation for the film. Solve this equation for the distribution of the z velocity component, u(y), in the film. Express your result in terms of 6, g, o, and the liquid properties and p. Write an expression for the maximum velocity max. (b) Obtain an appropriate form of the A species conservation equation for conditions within the film. If it is further assumed that the transport of species A across the gas-liquid interface does not penetrate very far into the film, the position y = 8 may, for all practical purposes, be viewed as y= ∞o. This condition implies that to a good approximation, u = Umax in the region of penetration. Subject to these assumptions, determine an expression for p (z,y) that applies in the film. Hint: This problem is analogous to conduction in a semi-infinite medium with a sudden change in surface temperature. (c) If a local mass transfer convection coefficient is defined as nAz PAP where n" is the local mass flux at the gas-liquid interface, develop a suitable correlation for Sh, as a function of Re, and Sc. (d) Develop an expression for the total gas absorption rate per unit width for a film of length L (kg/s-m). (e) A water film that is 1 mm thick runs down the inside surface of a vertical tube that is 2 m long and has an inside diameter of 50 mm. An airstream containing ammonia (NH3) moves through the tube, such that the mass density of NH3 at the gas-liquid interface (but in the liquid) is 25 kg/m³. A dilute solution of ammonia in water is formed, and the diffusion coefficient is 2 x 10 m²/s. What is the mass rate of NH3 removal by absorption? hm,z
6S.14 The falling film is widely used in chemical processing for the removal of gaseous species. It involves the flow of a liquid along a surface that may be inclined at some angle >> 0. Gas (A) -PA Liquid film (B) The flow is sustained by gravity, and the gas species A outside the film is absorbed at the liquid-gas interface. The film is in fully developed laminar flow over the entire plate, such that its velocity components in the y- and z-directions are zero. The mass density of A at y = 0 in the liquid is a constant PA, independent of z. (a) Write the appropriate form of the 2-momentum equation for the film. Solve this equation for the distribution of the z velocity component, u(y), in the film. Express your result in terms of 6, g, o, and the liquid properties and p. Write an expression for the maximum velocity max. (b) Obtain an appropriate form of the A species conservation equation for conditions within the film. If it is further assumed that the transport of species A across the gas-liquid interface does not penetrate very far into the film, the position y = 8 may, for all practical purposes, be viewed as y= ∞o. This condition implies that to a good approximation, u = Umax in the region of penetration. Subject to these assumptions, determine an expression for p (z,y) that applies in the film. Hint: This problem is analogous to conduction in a semi-infinite medium with a sudden change in surface temperature. (c) If a local mass transfer convection coefficient is defined as nAz PAP where n" is the local mass flux at the gas-liquid interface, develop a suitable correlation for Sh, as a function of Re, and Sc. (d) Develop an expression for the total gas absorption rate per unit width for a film of length L (kg/s-m). (e) A water film that is 1 mm thick runs down the inside surface of a vertical tube that is 2 m long and has an inside diameter of 50 mm. An airstream containing ammonia (NH3) moves through the tube, such that the mass density of NH3 at the gas-liquid interface (but in the liquid) is 25 kg/m³. A dilute solution of ammonia in water is formed, and the diffusion coefficient is 2 x 10 m²/s. What is the mass rate of NH3 removal by absorption? hm,z
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:6S.14 The falling film is widely used in chemical processing for the removal of gaseous species. It involves the flow of a liquid along a surface that may be inclined at some angle ø ≥ 0.
Gas (A)
-PA
111
Liquid film (B)
The flow is sustained by gravity, and the gas species A outside the film is absorbed at the liquid-gas interface. The film is in fully developed laminar flow over the entire plate, such that its velocity components in the
y- and z-directions are zero. The mass density of A at y = 0 in the liquid is a constant PA, independent of z.
(a) Write the appropriate form of the x-momentum equation for the film. Solve this equation for the distribution of the a velocity component, u(y), in the film. Express your result in terms of 6, g, o, and the liquid
properties and p. Write an expression for the maximum velocity umax.
(b) Obtain an appropriate form of the A species conservation equation for conditions within the film. If it is further assumed that the transport of species A across the gas-liquid interface does not penetrate very far
into the film, the position y = 8 may, for all practical purposes, be viewed as y = ∞o. This condition implies that to a good approximation, u = Umax in the region of penetration. Subject to these assumptions,
determine an expression for p(x, y) that applies in the film. Hint: This problem is analogous to conduction in a semi-infinite medium with a sudden change in surface temperature.
(c) If a local mass transfer convection coefficient is defined as
hm,x=
n
PA,0
where n" is the local mass flux at the gas-liquid interface, develop a suitable correlation for Sh, as a function of Re, and Sc.
(d) Develop an expression for the total gas absorption rate per unit width for a film of length L (kg/s - m).
(e) A water film that is 1 mm thick runs down the inside surface of a vertical tube that is 2 m long and has an inside diameter of 50 mm. An airstream containing ammonia (NH3) moves through the tube, such that
the mass density of NH3 at the gas-liquid interface (but in the liquid) is 25 kg/m³. A dilute solution of ammonia in water is formed, and the diffusion coefficient is 2 x 109 m²/s. What is the mass rate of NH3
removal by absorption?
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