In lecture, we also considered pressure driven flow of an incompressible Newtonian fluid (INF) through the annular gap between two horizontal coaxial cylinders as shown in the figure below: PO>PL Z a. For question 1 on Assignment #1, you were tasked with determining what was the correct equation for Q, the volumetric flow rate of the INF in the annular gap. The correct equation was: [₁-(R.)² ¹-)* (R₁) In Using this piece of information, calculate Vavg (m/s) and then the Reynolds number for the following conditions: TRAP 8μ L v₂ (r) = [2R₁ 2RO Glycerin at 20 °C, a very viscous fluid (1.4 Pa*s), is the INF in the annular space R₁ = 10 mm R₁ = 2 mm AP/L = 30 kPa/m Based on your calculation of the Reynolds number, what can you conclude about the existence of laminar flow conditions? b. The axial velocity profile v₂(r) for the system described above is as follows: R² - R² R²-r²+ in (Ho/R.) 1 ΔΡ 4μ L r ·In. Equation 7.98 from Vlachopoulos' book Using Excel (or another suitable software), plot the axial velocity profile for the conditions given in part a). In order to match the physical nature of the system, plot the axial velocity (vz(r)) on the x-axis and the radial distance (r) on the y-axis. The range of y values should be from 0 to +R.-be VERY careful about what happens in the range of y values from 0 to +R₁.

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:QUESTION 2 In lecture, we also considered pressure driven flow of an incompressible Newtonian fluid (INF) through the annular gap between two horizontal coaxial cylinders as shown in the figure below: Po POPL a. For question 1 on Assignment #1, you were tasked with determining what was the correct equation for Q, the volumetric flow rate of the INF in the annular gap. The correct equation was: Q Z TRAP ---- 8μ L Ro = 12R, 2RO v₂ (r) = 4 Using this piece of information, calculate Vavg (m/s) and then the Reynolds number for the following conditions: In Glycerin at 20 °C, a very viscous fluid (1.4 Pa*s), is the INF in the annular space R₁ = 10 mm R₁ = 2 mm 1 ΔΡ 4μ L (Ro R₁ AP/L = 30 kPa/m Based on your calculation of the Reynolds number, what can you conclude about the existence of laminar flow conditions? In b. The axial velocity profile v₂(r) for the system described above is as follows: R² - R² r R²-r²+ ・In・ ₂ (Ro/R₁) Ro Equation 7.98 from Vlachopoulos' book Using Excel (or another suitable software), plot the axial velocity profile for the conditions given in part a). In order to match the physical nature of the system, plot the axial velocity (vz(r)) on the x-axis and the radial distance (r) on the y-axis. The range of y values should be from 0 to +R.-be VERY careful about what happens in the range of y values from 0 to +R₁.

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