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4.2 Flow through a bed of grain Flow of air through a bed of grain is analogous to fluid flow through a network of pipes. (a) Fig. 4.17(a) shows a cross-section of a solid block pierced by n paral- lel tubes, each of radius a. As a is small, the flow is laminar (why?), in which case it may be shown that according to Poiseuille's law, the volume of fluid flowing through each tube is: nat 8u (dx (4.28) where u is the dynamic viscosity (see Review 2) and dø/dx is the pressure gradient driving the flow. Use this to show that the bulk fluid flow speed through the solid block of cross-section A, is:

4.2 Flow through a bed of grain Flow of air through a bed of grain is analogous to fluid flow through a network of pipes. (a) Fig. 4.17(a) shows a cross-section of a solid block pierced by n paral- lel tubes, each of radius a. As a is small, the flow is laminar (why?), in which case it may be shown that according to Poiseuille's law, the volume of fluid flowing through each tube is: nat 8u (dx (4.28) where u is the dynamic viscosity (see Review 2) and dø/dx is the pressure gradient driving the flow. Use this to show that the bulk fluid flow speed through the solid block of cross-section A, is:

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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4.2 a, b

4.2 Flow through a bed of grain Flow of air through a bed of grain is analogous to fluid flow through a network of pipes. (a) Fig. 4.17(a) shows a cross-section of a solid block pierced by n paral- lel tubes, each of radius a. As a is small, the flow is laminar (why?), in which case it may be shown that according to Poiseuille's law, the volume of fluid flowing through each tube is: (4.28) 8u (ax where u is the dynamic viscosity (see Review 2) and dp/dx is the pressure gradient driving the flow. Use this to show that the bulk fluid flow speed through the solid block of cross-section A, is: Oal ea dp total A, 8 dx (a) (b) Area Ao A (c) Ax Fig. 4.17 For Problem 4.2: a block pierced by paralel tubes; b pores in a bed of grain; e volume of grain bed. where the porosity e is the fraction of the volume of the block which is occupied by fluid, and Qo is the total volume flow through the block. (b) The bed of grain in a solar drier has a total volume Vood = A,Ax (Fig. 4.17(c). The drier is to be designed to hold 1000 kg of grain of bulk volume V= 1.3 m2. The grain is to be dried in four days (= 30 hours of operation). Show that this requires an air flow of at least Q= 0.12 ms-1 (hint. refer to Worked example 4.1).
Transcribed Image Text:4.2 Flow through a bed of grain Flow of air through a bed of grain is analogous to fluid flow through a network of pipes. (a) Fig. 4.17(a) shows a cross-section of a solid block pierced by n paral- lel tubes, each of radius a. As a is small, the flow is laminar (why?), in which case it may be shown that according to Poiseuille's law, the volume of fluid flowing through each tube is: (4.28) 8u (ax where u is the dynamic viscosity (see Review 2) and dp/dx is the pressure gradient driving the flow. Use this to show that the bulk fluid flow speed through the solid block of cross-section A, is: Oal ea dp total A, 8 dx (a) (b) Area Ao A (c) Ax Fig. 4.17 For Problem 4.2: a block pierced by paralel tubes; b pores in a bed of grain; e volume of grain bed. where the porosity e is the fraction of the volume of the block which is occupied by fluid, and Qo is the total volume flow through the block. (b) The bed of grain in a solar drier has a total volume Vood = A,Ax (Fig. 4.17(c). The drier is to be designed to hold 1000 kg of grain of bulk volume V= 1.3 m2. The grain is to be dried in four days (= 30 hours of operation). Show that this requires an air flow of at least Q= 0.12 ms-1 (hint. refer to Worked example 4.1).
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