4.2 a, b 4.2 Flow through a bed of grainFlow of air through a bed of grain is analogous to fluid flow through anetwork 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, thevolume of fluid flowing through each tube is:(4.28)8u (axwhere u is the dynamic viscosity (see Review 2) and dp/dx is thepressure gradient driving the flow. Use this to show that the bulkfluid flow speed through the solid block of cross-section A, is:Oal ea dptotalA,8 dx(a)(b)AreaAoA(c)AxFig. 4.17For 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 whichis occupied by fluid, and Qo is the total volume flow throughthe 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 ofbulk volume V= 1.3 m2. The grain is to be dried in four days (= 30hours of operation). Show that this requires an air flow of at leastQ= 0.12 ms-1 (hint. refer to Worked example 4.1).

The solid work is pierced with n parallel tubes. Radius of tube is a, which is small. a) To derive:-…

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

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Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Free Body Diagram

The system of forces acting on a body tends to either rotate it or make the body undergo motion. In general, when an external agent exerts a force on a body, the body undergoes translational motion and rotational motion. The body has six degrees of freedom under the influence of that force. Here, three degrees of freedom are from the translational motion while the other three are from the rotation motion. However, sometimes the bodies are not allowed to undergo any motion and are fixed, under such conditions the body is said to be constrained.

Question

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).

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