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2C4 Falling-cylinder viscometer (see Fig. 2C.4). A falling-cylinder viscometer consists of a long vertical cylindrical container (radius R), capped at both ends, with a solid cylindrical slug (ra- dius KR). The slug is equipped with fins so that its axis is coincident with that of the tube. One can observe the rate of descent of the slug in the cylindrical container when the lat- ter is filled with fluid. Find an equation that gives the viscosity of the fluid in terms of the ter- minal velocity of the slug and the various geometric quantities shown in the figure. Cylindrical slug descends with speed 0¹¹0 filled with fluid Cylindrical container Fig. 2C.4 A falling-cylinder viscom- eter with a tightly fitting solid cylin- der moving vertically. The cylinder is usually equipped with fins to maintain centering within the tube. The fluid completely fills the tube, and the top and bottom are closed. (a) Show that the velocity distribution in the annular slit is given by (1)-(1+²) In (1/8) (1-¹)-(1+²) In (1/K) in which = 1/R is a dimensionless radial coordinate. (b) Make a force balance on the cylindrical slug and obtain (Pop)g(xR)² | 60 - Pig(x R³² ( (In 2) - (+ = =)] 20% (Po -pigR¹e 60% in which p and p, are the densities of the fluid and the slug, respectively. (c) Show that, for small slit widths, the result in (b) may be expanded in powers of a = 1- K to give -(1--²+) (2C.4-1) See $C.2 for information on expansions in Taylor series. (2C.4-2) (2C.4-3)

2C4 Falling-cylinder viscometer (see Fig. 2C.4). A falling-cylinder viscometer consists of a long vertical cylindrical container (radius R), capped at both ends, with a solid cylindrical slug (ra- dius KR). The slug is equipped with fins so that its axis is coincident with that of the tube. One can observe the rate of descent of the slug in the cylindrical container when the lat- ter is filled with fluid. Find an equation that gives the viscosity of the fluid in terms of the ter- minal velocity of the slug and the various geometric quantities shown in the figure. Cylindrical slug descends with speed 0¹¹0 filled with fluid Cylindrical container Fig. 2C.4 A falling-cylinder viscom- eter with a tightly fitting solid cylin- der moving vertically. The cylinder is usually equipped with fins to maintain centering within the tube. The fluid completely fills the tube, and the top and bottom are closed. (a) Show that the velocity distribution in the annular slit is given by (1)-(1+²) In (1/8) (1-¹)-(1+²) In (1/K) in which = 1/R is a dimensionless radial coordinate. (b) Make a force balance on the cylindrical slug and obtain (Pop)g(xR)² | 60 - Pig(x R³² ( (In 2) - (+ = =)] 20% (Po -pigR¹e 60% in which p and p, are the densities of the fluid and the slug, respectively. (c) Show that, for small slit widths, the result in (b) may be expanded in powers of a = 1- K to give -(1--²+) (2C.4-1) See $C.2 for information on expansions in Taylor series. (2C.4-2) (2C.4-3)

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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2C.4 Falling-cylinder viscometer (see Fig. 2C.4). A falling-cylinder viscometer consists of a long vertical cylindrical container (radius R), capped at both ends, with a solid cylindrical slug (ra- dius KR). The slug is equipped with fins so that its axis is coincident with that of the tube. One can observe the rate of descent of the slug in the cylindrical container when the lat- ter is filled with fluid. Find an equation that gives the viscosity of the fluid in terms of the ter- minal velocity of the slug and the various geometric quantities shown in the figure. Cylindrical slug descends- with speed t -XR- Cylindrical container filled with fluid Fig. 2C.4 A falling-cylinder viscom- eter with a tightly fitting solid cylin- der moving vertically. The cylinder is usually equipped with fins to maintain centering within the tube. The fluid completely fills the tube, and the top and bottom are closed. (a) Show that the velocity distribution in the annular slit is given by (1-)-(1+¹) In (1/8) (1-¹)-(1+¹) In (1/K) in which = r/R is a dimensionless radial coordinate. (b) Make a force balance on the cylindrical slug and obtain (P₁- pligte R³² [ (in 2) - (¹)] 20% (Po-pigR's 60% See $C.2 for information on expansions in Taylor series. (2C4-1) in which p and p, are the densities of the fluid and the slug, respectively. (c) Show that, for small slit widths, the result in (b) may be expanded in powers of s = 1 - k to give -(1-²) (2C.4-2) (2C.4-3)
Transcribed Image Text:2C.4 Falling-cylinder viscometer (see Fig. 2C.4). A falling-cylinder viscometer consists of a long vertical cylindrical container (radius R), capped at both ends, with a solid cylindrical slug (ra- dius KR). The slug is equipped with fins so that its axis is coincident with that of the tube. One can observe the rate of descent of the slug in the cylindrical container when the lat- ter is filled with fluid. Find an equation that gives the viscosity of the fluid in terms of the ter- minal velocity of the slug and the various geometric quantities shown in the figure. Cylindrical slug descends- with speed t -XR- Cylindrical container filled with fluid Fig. 2C.4 A falling-cylinder viscom- eter with a tightly fitting solid cylin- der moving vertically. The cylinder is usually equipped with fins to maintain centering within the tube. The fluid completely fills the tube, and the top and bottom are closed. (a) Show that the velocity distribution in the annular slit is given by (1-)-(1+¹) In (1/8) (1-¹)-(1+¹) In (1/K) in which = r/R is a dimensionless radial coordinate. (b) Make a force balance on the cylindrical slug and obtain (P₁- pligte R³² [ (in 2) - (¹)] 20% (Po-pigR's 60% See $C.2 for information on expansions in Taylor series. (2C4-1) in which p and p, are the densities of the fluid and the slug, respectively. (c) Show that, for small slit widths, the result in (b) may be expanded in powers of s = 1 - k to give -(1-²) (2C.4-2) (2C.4-3)
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