Summary

The aim of this experiment was to observe how pressure changed with increase in mass at the

bottom of a container when solid particles were stored, and to verify the Jansen equation. When

granular solids are placed in a bin or silo, the vertical pressure on the vessel floor is much

smaller than that exerted by a column of liquid of same density and height. The actual pressure

from solid depends on value of coefficient of friction between solids and vessel wall. In this

experiment a long column was taken in which sand was added in certain noted quantities and

weight exerted in the column was noted along with height of column. After a while it was seen

the weight exerted stopped increasing. Then flow out of a bin was measured experimentally from

which angle of internal friction was calculated. Using this value coefficient of friction, ratio of

normal pressure to applied pressure was obtained. From this theoretical and experimental values

of base pressure were obtained. The values range from 54.82 kg/m2 and 317.96 kg/m

2 for

experimental base pressure and between 53.16kg/m2 and 95.36 kg/m

2 for theoretical base

pressure. A graph was plotted using experimental and theoretical base pressure values against

height of sand column.

Experimental Set-up

Figure 1: Experimental Setup for study of pressure in masses of particles

Observed Data

Particle diameter, Dp , size range= -50+60 mesh

Diameter of long bin, D = 6 inch

Diameter of opening of short bin, D0 = 0.5 inch

Table 1: Table of observed data for measuring flow rate

No. of

Obs

Weight of sand

(kg)

Time

(Sec)

Rate of discharge

(kg/min)

01. 2.268 60 2.268

Table 2: Table of observed data for the weight and height of the sand bed

No. of

Observation

Mass of sand

(kg)

Weight of sand in column

(kg)

Height of sand in column,Z

(inch)

01. 1 1 0.5

02. 2 2 1.75

03. 3 2.6 3

04. 4 3.3 5

05. 5 3.8 6.8

06. 6 4.15 7.6

07. 7 4.45 9

08. 8 4.7 10.7

09. 9 4.9 12

10. 10 5.05 13.6

11. 11 5.2 15.1

12. 12 5.35 16.6

13. 13 5.45 18.2

14. 14 5.55 19.7

15. 15 5.6 21

16. 16 5.7 22.8

17. 17 5.75 24.2

18. 18 5.8 25.8

Calculated Data

Particle Diameter, Dp = 0.0099 inch 1

Particle Density, p = 165.75 lb/ft3

= 2655 kg/m3

Table 3: Calculated data for bulk density, experimental and theoretical base pressure

Number of

Observation

Cumulative

sand weight

taken,

M (kg)

Cumulative Sand

weight in the

column,

W (kg)

Height of

sand,

Z (m)

Bulk

density,

b

(kg/m3)

Experimental

base

pressure,

PBE (kg/m2)

Theoretical

base

pressure,

PBT(kg/m2)

1 1 1 0.0127 4316.547 54.82 53.16

2 2 2 0.04445 2466.598 109.64 98.56

3 3 2.6 0.0762 1870.504 142.53 119.03

4 4 3.3 0.127 1424.460 180.91 134.84

5 5 3.8 0.17272 1206.094 208.32 140.76

6 6 4.15 0.19304 1178.531 227.50 147.36

7 7 4.45 0.2286 1067.146 243.95 147.01

1 Foust et al, Principles of unit operation, 2nd edition, page 701

8 8 4.7 0.27178 948.0267 257.65 142.69

9 9 4.9 0.3048 881.295 268.62 139.79

10 10 5.05 0.34544 801.418 276.84 133.79

11 11 5.2 0.38354 743.246 285.06 128.87

12 12 5.35 0.42164 695.588 293.29 124.33

13 13 5.45 0.46228 646.296 298.77 118.56

14 14 5.55 0.50038 608.0415 304.25 113.76

15 15 5.6 0.5334 575.539 306.99 109.20

16 16 5.7 0.57912 539.568 312.47 104.02

17 17 5.75 0.61468 512.813 315.22 99.85

18 18 5.8 0.65532 485.193 317.96 95.36

Sample Calculation

Particle Diameter, Dp = 0.0099 inch

Particle Density, p = 165.75 lb/ft3

= 2655 kg/m3

Diameter of bin, D = 6 inch = 0.1524 m

Diameter of the discharge opening, D0 = 0.5 inch = 0.0127 m

Area of large bin, A = ( D2)/4

= (3.1416 0.15242)/4

= 0.01824 m2

n=3

Calculation of angle of internal friction

The solid discharge rate; = 2.268 kg/min=5lb/min

Now, the empirical discharge rate equation,

=pDo

n

6.288tanm+23.16 Dp+1.889 -44.90

or,5=165.750.53

6.288tanm+23.16 0.0099+1.889 -44.90

or, tan m = 0.4242

Angle of internal friction, m = 22.987

Ratio of pressures, k = 1- sin m

1+ sin m =0.4383

Co-efficient of friction, = tan m = 0.4242

For third set of observed Data,

Experimental base pressure,

PBE =

= 2.6

0.01824

= 142.5323 kg/m2

Bulk density of particle, b =

= 2.6

0.01824 0.0762

= 1870.504 kg/m3

Theoretical base pressure using Janssen Equation

PBT =

r

zk

cb ek

ggr''2

1''2

/

=

0254.06

0762.04383.04242.02

14383.04242.02

1504.1870)0254.06(e

= 119.033 kg/m2

Graphical Representation

Base pressure vs. Height of column of solids for experimental and theoretical values

Graph 1: Graphical representation of theoretical and experimental values of Base Pressure against

Height of column of solids.

Results

Angle of internal friction, m = 22.987

Co-efficient of friction, ' = 0.4242

Ratio of normal pressure to applied pressure, k' = 0.4383

Table 4: Comparison of experimental and theoretical base pressure with height of sand

Height of sand,

z

(m)

Experimental base

pressure,

PBE

(kg/m2)

Theoretical base

pressure,

PBT

(kg/m2)

0.0127 54.82 53.16

0.04445 109.64 98.56

0.0762 142.53 119.03

0.127 180.91 134.84

0.17272 208.32 140.76

0.19304 227.50 147.36

0.2286 243.95 147.01

0.27178 257.65 142.69

0.3048 268.62 139.79

0.34544 276.84 133.79

0.38354 285.06 128.87

0.42164 293.29 124.33

0.46228 298.77 118.56

0.50038 304.25 113.76

0.5334 306.99 109.20

0.57912 312.47 104.02

0.61468 315.22 99.85

0.65532 317.96 95.36

Discussions

The graph obtained contained two curves, the first one being the experimental base pressure

against height of column of solids and the second one being the theoretical base pressure against

the same heights of column of solids. The experimental values showed that after reaching a

certain height of solid in the bin, even with addition of more solid, increase in height was

observed but it did not affect the base pressure. Rather the base pressure became almost constant.

This similarity with theoretical plot justifies the Jansen equation.

The plot contained three main regions. The first region started from zero and showed a linear

relationship similar to liquid (upto 0.03 m bed height). At this low pressure particles had not

interlocked with each other and wall friction was negligible. The second region showed

exponential form (upto bed height about 0.62 m). In that part interlocking and wall friction both

Figure 2: Three regions observed in the graph

became important with the increase of sand height. And the third or last region was almost

horizontal and showed constant pressure as the additional mass was carried by the support of the

vessel.

Using the values obtained experimentally and known factors, theoretical base pressures were

calculated and it was seen that after a certain height the base pressures started decreasing instead

of remaining constant.

From the results obtained it was found that the experimental values were between 54.82 kg/m2

and 317.96 kg/m2. The theoretical values were found to be between 53.16kg/m

2 and 95.36 kg/m

2

where the pressure had risen and then fell again. The mass flow rate was found to be 2.268

kg/min. The mass flow rate depends on gravity, diameter of the opening and the nature of the

granular solids. The reason which caused the theoretical base pressure to fall was mainly friction

between the wall and the solid particles, and the interlocking of solid particles. The frictional

force caused the weight of the solid to spread and reduced the pressure exerted by the mass on

the base of the container. Thus it can be said interlocking of particle causes distribution of

pressure on wall side reducing the base pressure.

In general, when the height of solids column is greater than about 3 times the diameter of

container, additional solids have no effect on pressure at the base. Although total mass increases,

additional mass is carried by the walls and foundations. The diameter of the base of cylinder was

6 inches and after reaching 18.2 inches, it was observed that weight exerted increased very

slightly with each addition.

High pressure usually causes a liquid material to flow, but in case of granular solids it packs the

grains even more closely and makes flow difficult. In extreme cases this might cause solids to

arch or bridge.

The reasons that caused the variation in theoretical and experimental base pressure are discussed

below:

One of the main assumption of Jansen Equation is that the particles are spherical, which

might not occur in practical.

The angle of internal friction is an experimental parameter and its value might change for

non homogeneity of particles.

The weighing machine readings were taken with utmost care but some instrumental error

might be present.

As the sand bed was filled manually it was not possible to evenly distribute the sand over

the entire surface so readings taken might have deviated from actual values slightly.

The experiment was performed with utmost care and effort. However the results can be

improved greatly if more readings were taken. The experiment performed provided knowledge

of pressure distribution characteristics for solid and also gave idea about basic structure of silos,

bins and hoppers for solid storage.