study of a pressure in masses of particles

8/12/2019 Study of a Pressure in Masses of Particles

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ChE 30

Chemical engineering laboratory - II

Experiment No. Group No. 03 (A2)

Name of the experiment:

STUDY OF APRESSUREIN MASSES OF PARTICLES

Submitted by:

Md. Hasib Al Mahbub

Student Id: 0902045

Level: 3; Term: 2

Section: A2

Date of performance:11/02/2014

Date of submission:25/02/2014

Partners Student Id.0902041

0902042

0902043

0902044

Department of Chemical Engineering.

Bangladesh University of engineering and technology, Dhaka.


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Experimental Setup

Figure 1. Schematic diagram of the experimental setup


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Observed data

Table 1: Observed data for weight and height.

Obs. no. Mass of sand added(Kg)

Mass of sand in

column(Kg)

Height of sand in

column(inch)

1 1 1 0.5

2 2 1.7 2

3 3 2.3 2.8

4 4 3.3 4.5

5 5 3.75 6

6 6 4.15 7.5

7 7 4.5 8.8

8 8 4.8 10.5

9 9 4.95 12

10 10 5.1 13

11 11 5.2 14.7

12 12 5.35 15.7

13 13 5.5 17.3

14 14 5.55 19

15 15 5.6 20.4

16 16 5.65 21.8

17 17 5.7 23.5


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Table 2: Data for calculation of mass flow rate.

Observation

No.

Mass of

particle,

Kg

Time of

collection,

sec

Mass flow

rate, m

Kg/sec

Average mass

flow rate, m

Kg/sec

1 0.4 10 0.04

0.0427

2 0.4 10 0.04

3 0.4 10 0.04

4 0.4 10 0.04

5 0.4 10 0.04

6 0.45 10 0.045

7 0.45 10 0.045

8 0.45 10 0.045

9 0.45 10 0.045

10 0.45 10 0.045

11 0.45 10 0.045


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Calculated data

Table 1.03 : Calculated data for ( PB) Th & ( PB) expt .

Obs

.no.

Volume

occupied bysand , V

ft 3

Bulk density,

blbm/ ft 3

angle of

internalfriction

of solids

m ( 0)

1 - Sin mK=

1 + Sin m

Theoretical

basepressure

( PB) Thlbf/ft2

Expt.

basepressure

( PB) expt.

lbf/ft2

1 0.00818571 269.3230031

23.020.43776

10.88944128 11.23076923

2 0.03274284 134.6615016 19.89112387 19.09230769

3 0.045839976 144.2801803 28.46173276 25.83076923

4 0.07367139 119.6991125 34.42197814 37.06153846

5 0.09822852 112.217918 39.59887257 42.11538462

6 0.12278565 107.7292013 43.85516383 46.60769231

7 0.144068496 107.1171035 47.83462617 50.53846154

8 0.17189991 102.5992393 50.21743195 53.90769231

9 0.19645704 100.9961262 52.5651913 55.59230769

10 0.21282846 103.5857704 55.74561057 57.27692308

11 0.240659874 100.76711 56.79499699 58.4

12 0.257031294 102.9259885 59.31429435 60.08461538

13 0.283225566 101.1907237 60.0596509 61.76923077

14 0.31105698 99.22426431 60.3745286 62.33076923

15 0.333976968 99.01580998 61.25190768 62.89230769

16 0.356896956 98.83412959 61.98203392 63.45384615

17 0.38472837 97.41470326 61.92427968 64.01538462


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Results and discussions

For one Kg mass of particle the experimental base pressure is 11.23 lbf/ft2, whereas using the

Janssen equation we got it 10.89 lbf/ft2. After a certain height 1.7 ft the pressure becomes

practically constant. And at this height the experimentally observed pressure is 64.01 lbf/ft2

and pressure using the Janssen equation is 61.9 lbf/ft2.

Graph 1 shows the behavior of both the experimental and theoretical base pressure with the

increment of the bed height. The two curves are very close. This indicates that the values of

experimental and theoretical pressures are almost same. The experimental values were little

higher than theoretical one. These discrepancies might be occurred due to improper addition of

sand particle. That means when sand was added into the column it was not possible to add thesand particle uniformly into the column.

Solid particle handling or storage is a regular requirement in our day-to-day life or in the

industries. It is a huge challenge for all sorts of people ranging from the plant engineer to the

food grain dealers or the sea-line operators. The challenge as clear from this experiment is the

pressure exerted by the masses of particles. This pressure has profound impact on the design

of bin, vessels, hoppers or silos as economics is always involved in building such storage tanks.

This experiment helps to determine the maximum pressure exerted by the solid particles.

Knowing this limit, the capacity or the size of the storage tank can be determined. Proper

materials of construction can be selected as well. It can save the storage tanks from being over

pressurized and being collapsed. Hence, this experiment is very important and gets a wide

range of application where design of storage tank is concerned.

Some of the fields of application of this experiment are as follows:

Food grain storage tank design. Design of vessels carrying various grains. Design of reactor handling solid particles. Design of silos in cement industries, etc.


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When granular solids are stored in a bin or hopper, the lateral pressure exerted on the walls at

any point is less than predicted from the head of material above that point. Furthermore there

usually is friction between the wall and the solid grains, and because of the interlocking of the

particles; the effect of this friction is felt throughout the mass. The frictional force at the wall

tends to offset the weight of the solid and reduces the pressure exerted by the mass on the floor

of the container. With many solids, when the height reaches about three times the diameter of

the bin, additional material has virtually no effect on the pressure at the base. The total mass of

bin plus material continues to increase, but the additional mass is carried by the wall and not

by the floor of the bin. In the extreme case this force causes the mass to arch, or bridge, so that

it does not fall, even when the material below is removed.

In solids the pressure is not the same in all directions. In general, a pressure applied in one

direction creates some pressure in other directions, but it is always smaller than the applied

pressure. It is a minimum in the direction at right angles to the applied pressure.

It has been observed that when the height reaches a certain limit, additional sand has virtually

no effect on the pressure at the base. The total mass of the column plus material continues to

increase, but the additional mass is carried by the wall and foundation, not by the floor of the

column.

From the readings, it is clear that after a certain height the pressure exerted by the solid grains

became constant. Nevertheless, the result could be improved by taking care to take the readings

of height. The top edge of the materials in the cylindrical glass tube was no at horizontal level

so that we had to take the average height reading. As a result the parallax error was introduced

in the experiment. Moreover, the weighing machines were not highly calibrated to take more

precisely weigh readings.

The experimental results revealed two concepts, which are, the lateral pressure that acts at

right angle with the applied pressure is always the minimum pressure; at a certain applied

pressure, base pressure of the column is constant.

This knowledge of pressure (exerted by the masses of particles) distribution characteristics will

help us to design the structure of bins, hoppers or silos to preserve the too valuable or too

soluble solids.


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Graphical comparison between experimental and theoretical base pressure

Graph 1: experimental base pressure vs. theoretical base pressure

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Base

Pressure

Height

Experimental

Theoretical

study of a pressure in masses of particles

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