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Select an appropriate observer and control volume. Then, derive the linear momentum balance equation governing the function v₂(r), proving that this reads: d(rTrz) dr r with P(z) = p(z) + pgz (1.1) Here, AP is the (positive) dynamic pressure change over a generic length L, g is the magnitude of the gravitational field and p is the fluid density. To answer this question, do not employ the general linear momentum balance equations.

Select an appropriate observer and control volume. Then, derive the linear momentum balance equation governing the function v₂(r), proving that this reads: d(rTrz) dr r with P(z) = p(z) + pgz (1.1) Here, AP is the (positive) dynamic pressure change over a generic length L, g is the magnitude of the gravitational field and p is the fluid density. To answer this question, do not employ the general linear momentum balance equations.

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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A falling-cylinder viscometer consists of a long vertical cylindrical tube (of radius R), capped at both ends, and a solid cylindrical slug (of radius KR). The system is sketched in Fig. 1. The slug is equipped with fins so that its axis coincides with that of the tube. One can observe the rate of descent of the slug in the cylindrical container when the latter is filled with fluid. The objective of this exercise is to find an equation that gives the viscosity of the fluid (assumed to be incompressible and Newtonian) in terms of the terminal velocity Vof the slug and of the various geometric quantities shown in Fig. 1. KR Cylindrical slug descends with speed V through the liquid Liquid fills the cylindrical cavity Figure 1: Sketch of the falling-cylinder viscometer. Assume that the flow is laminar and neglect the entrance and end effects that are present when the fluid enters and leaves the gap between the tube and the slug. Therefore, assume that the only nonzero component of the fluid velocity vector is v, and that in space this depends solely on r, where r denotes the radial coordinate of a cylindrical coordinate system. b) Select an appropriate observer and control volume. Then, derive the linear momentum balance equation governing the function v(r), proving that this reads: d(rTr2) AP with P(z) = p(z) + pgz (1.1) dr L Here, AP is the (positive) dynamic pressure change over a generic length L, g is the magnitude of the gravitational field and p is the fluid density. To answer this question, do not employ the general linear momentum balance equations.
Transcribed Image Text:A falling-cylinder viscometer consists of a long vertical cylindrical tube (of radius R), capped at both ends, and a solid cylindrical slug (of radius KR). The system is sketched in Fig. 1. The slug is equipped with fins so that its axis coincides with that of the tube. One can observe the rate of descent of the slug in the cylindrical container when the latter is filled with fluid. The objective of this exercise is to find an equation that gives the viscosity of the fluid (assumed to be incompressible and Newtonian) in terms of the terminal velocity Vof the slug and of the various geometric quantities shown in Fig. 1. KR Cylindrical slug descends with speed V through the liquid Liquid fills the cylindrical cavity Figure 1: Sketch of the falling-cylinder viscometer. Assume that the flow is laminar and neglect the entrance and end effects that are present when the fluid enters and leaves the gap between the tube and the slug. Therefore, assume that the only nonzero component of the fluid velocity vector is v, and that in space this depends solely on r, where r denotes the radial coordinate of a cylindrical coordinate system. b) Select an appropriate observer and control volume. Then, derive the linear momentum balance equation governing the function v(r), proving that this reads: d(rTr2) AP with P(z) = p(z) + pgz (1.1) dr L Here, AP is the (positive) dynamic pressure change over a generic length L, g is the magnitude of the gravitational field and p is the fluid density. To answer this question, do not employ the general linear momentum balance equations.
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