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Example 11.1. Figure 11.3 shows a water softener in which water trickles by gravity through a bed of spherical ion-exchange resin particles, each 0.03 in (0.76 mm) in diameter. The bed has a porosity of 0.33. Calculate the volumetric flow rate of water. Applying B.E. from the top surface of the fluid to the outlet of the packed bed and ignoring the kinetic-energy term and the pressure drop through the support screen, which are both small, we find

Example 11.1. Figure 11.3 shows a water softener in which water trickles by gravity through a bed of spherical ion-exchange resin particles, each 0.03 in (0.76 mm) in diameter. The bed has a porosity of 0.33. Calculate the volumetric flow rate of water. Applying B.E. from the top surface of the fluid to the outlet of the packed bed and ignoring the kinetic-energy term and the pressure drop through the support screen, which are both small, we find

Introduction to Chemical Engineering Thermodynamics
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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**11.5.** Calculate the permeability of the bed of ion-exchange particles in Example 11.1.
Transcribed Image Text:**11.5.** Calculate the permeability of the bed of ion-exchange particles in Example 11.1.
**Example 11.1.** Figure 11.3 shows a water softener in which water trickles by gravity through a bed of spherical ion-exchange resin particles, each 0.03 in (0.76 mm) in diameter. The bed has a porosity of 0.33. Calculate the volumetric flow rate of water. Applying B.E. from the top surface of the fluid to the outlet of the packed bed and ignoring the kinetic-energy term and the pressure drop through the support screen, which are both small, we find \[ g (\Delta z) = -\mathcal{F} \] \[ (11.C \] --- **FIGURE 11.3** *Description*: The diagram illustrates the gravity drainage of fluid through a porous medium. It depicts a vertical column through which water passes over a bed composed of ion-exchange resin. - The column height is marked as 1 ft. - The top section contains "Large" text indicating the water inlet, leading into a narrower passage. - The passage is 2 inches in width. - The ion-exchange resin bed is located below, with particles described as having a diameter (\( D_p = 0.03 \) in or 0.76 mm). - A wire mesh support screen is located at the column's bottom, supporting the resin bed while allowing water to pass through. This setup demonstrates the basic principle of water softening through ion-exchange resins, where water flows by gravity.
Transcribed Image Text:**Example 11.1.** Figure 11.3 shows a water softener in which water trickles by gravity through a bed of spherical ion-exchange resin particles, each 0.03 in (0.76 mm) in diameter. The bed has a porosity of 0.33. Calculate the volumetric flow rate of water. Applying B.E. from the top surface of the fluid to the outlet of the packed bed and ignoring the kinetic-energy term and the pressure drop through the support screen, which are both small, we find \[ g (\Delta z) = -\mathcal{F} \] \[ (11.C \] --- **FIGURE 11.3** *Description*: The diagram illustrates the gravity drainage of fluid through a porous medium. It depicts a vertical column through which water passes over a bed composed of ion-exchange resin. - The column height is marked as 1 ft. - The top section contains "Large" text indicating the water inlet, leading into a narrower passage. - The passage is 2 inches in width. - The ion-exchange resin bed is located below, with particles described as having a diameter (\( D_p = 0.03 \) in or 0.76 mm). - A wire mesh support screen is located at the column's bottom, supporting the resin bed while allowing water to pass through. This setup demonstrates the basic principle of water softening through ion-exchange resins, where water flows by gravity.
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