DEVELOPMENT AND TESTING OF AN AIR PYCNOMETER.
U.A.Garba1, Z. Mustafa1, A. Ja’afaru2
Department of Agricultural Engineering, College of Engineering, Kaduna, Polytechnic,
Kaduna,2Department of Mechanical Engineering, College of Engineering, Kaduna Polytechnic,
Kaduna
1
ABSTRACT
Foods and crop processing machines design is dependent on the correct analysisand
determination and determination of their physical properties. An air pycnometer that can be used
to determine the volumes of solids that are powder,dried fruits and vegetables was developed.
The pycnometer was tested using fourdifferent samples each of 300g per replicate, namely
Cassava and Wheat flour, dried and grounded spinach leaves and dried grounded tomatoes. Five
setsfor each sample was used such that there are five replications for each sample. Results
obtained were used to compute volume of solid Vs and prosity Ps which were plotted against
number of replication in comparison to a “linear Vs” line on each plot. It was concluded that the
pynometer is functioning well especially for dried and grounded vegetable crops.
Key words: Pycnometer, porosity, replicates, valves, Chambers.
INTRODUCTION
The design of food and crop processing equipment depends on the correct analysis and
determination of their physical properties. Properties such as volume, porosity, specific
gravity, density etc. determine the design specifications of these machines to ensure
efficient processing. For example, Seed (or particle) density is one of the most important
physical properties of agricultural materials because it is needed in process design
calculations and it is used in the characterization of these materials (Fashina, 2010). Also,
the porous structure of dehydrated plant materials is a key parameter that affects the
transport properties and a number of quality characteristics of these materials; however
this porous structure may be determined by the bulk porosity, pore sizes and pore size
distribution parameters (Karanthanos et al, 1996). The volume and porosity of objects or
materials such as powders, soils, puffed cereals, pepped popcorn or dried fruits and
vegetables that are highly hygroscopic (readily take up and retain moisture) cannot be
measured by water displacement; however they can be determined using Air Pycnometer
method ( Ma et al, 1998). An air pycnometer is an equipment that uses air displacement
to determine volume and porosity of materials mentioned above. Different type of Air
Pycnometer exists. However, the application of Air Pycnometer varies in fields where the
need for specific weight calculation is desired. The need for the determination of
densities and porosity of substances such as soil, powder and food commodities cannot be
overemphasized. The determination of density, porosity, specific weight is required in
agricultural research, powder and granulates investigations for pharmaceutics industry,
road building, food industry etc. Also, Commercial Pycnometers are used for process and
manufacturing control in a wide range of applications (Geddis et al, 1996). Air
Pycnometer also referred to as Gas Pycnometer has been used for many years to measure
the volume of solid materials sealed in a gas tight system (Geddis et al, 1996). It provides
indirect Air space measurements by relating a system’s pressures and volumes using
Boyle’s Ideal Gas Law. (Agnew et al, 2003). This paper discuss the design and
fabrication of an Air pycnometer carried out at the department of Agricultural
Engineering, Kaduna Polytechnic Kaduna State of Nigeria.
MATERIALS AND METHOD
Pycnometry is often thought of as the liquid method described by Blake and Hartage
(ASTM, 1986). Air Pycnometer is a device that uses Air displacement to determine
volume. The system makes use of pressurized chambers: one empty and one containing
the material for which the volume is being determined. The volume of Air displaced by
the sample is determined from pressure-volume relationships based on Boyle’s Law.
Figure 1 below gives an illustration and description of how the pycnometer developed
operates.
Chamber #2
+ solid
Chamber #1
pressure
gauge
valve #1
valve #2
valve #3
air out
air in
Fig 1: Schematic diagram showing how the pycnometer operates.
The pycnometer was constructed using locally available materials. It comprises a wooden
frame made up of two 15mm thick plywood which are fitted at right angle to each other
to form a wall of 3.5m2 and base of 3m2in area respectively. Two air tight containers of
equal volume of 1809.79cm3 serving as chambers 1 and 2 were fitted 50cm apart on the
wall with an air inlet fitted at the top of each chamber. A 12kg gas cylinder was filled
with air and used to supply air via a hose of diameter 0.5cm and length 120cm to
chambers 1 and 2. The hose was fitted with 3 control valves with valve 1 fitted 60cm
from the cylinder outlet, valve 2, 30cm from valve 1, and valve 3, 30cm from valve 2.
Two other hoses of lengths 30cm were fitted in between valves 1 and 2, and valves 2 and
3 to supply air into chambers 1and 2. A SCOTT pressure gauge model no.PT 28
measuring up to 11kPa was fitted in between valves 1 and 2. Plate1 below shows The
diagram of the constructed pycnometer.
PLATE 1: Picture of the constructed pycnometer.
According to the well-known perfect gas law, pressure and volume are related by the
following relationship:
PV  nRT
Where P is the absolute pressure in the closed system, V is the volume, n is the number of
moles of Air in the closed system, R is the universal gas constant and T is the absolute
temperature of the system. For the pycnometer developed the pressure to volume
relationship in the two chambers at constant temperature is defined as;
P1  PV1  P2  PV2  VS   P3  PV1  V2  VS 
……………………………….. (1)
Where
P 1 = Pressure reading (gauge pressure) when valves 1 and 3 are open and valve 2 is
closed.
P 2 = Pressure of chamber 2 after it is filled with solids while valve 2 remains closed but
valve 3 is open.
P 3 = Pressure reading (gauge pressure) when valves 1 and 3 are closed and valve 2 is
open.
P = Atmospheric pressure (1.013x105pa, under sea level conditions)
V1 = Volume of chamber 1
V2 = Volume of chamber 2
VS = Total volume of specimens contained in chamber 2
Rearranging equation 1 and solving for VS the total volume of the specimen in chamber
2 is
 P  P3 
VS  V2  V1  1
 ………………………………………………………. (2)
 P3 
Porosity (Ps) is the part of a solid occupied by air or the fraction of volume not occupied
by solid. Based on this definition the porosity of granular materials can be calculated
from the same experimental data generated using the pycnometer by the following
equation;
Ps 
P1  P3
…………………………………………………………….. (3)
P3
TESTING AND RESULTS
The pycnometer was tested using four different samples of 300g each, namely Cassava
flour, Wheat flour, dried and grounded Spinach leaves, dried and grounded Tomatoes.
Five sets of 300g for each sample was used to test the equipment such that there are five
replications for each sample. This is done to monitor the consistency of readings of the
pressure gauge. Air was released from the cylinder via the hose to the entire system with
valves 1 and 2 open while valve 3 was closed for 30 minutes. This is to allow the entire
system to reach a stable condition and also to check for leakages using mixture of water
and detergent which was robbed all over the hose and chambers. Valve 2 was then closed
and valve 3 was opened and chamber 2 was filled with 300g of the first sample. After 15
minutes pressure P1 was recorded from the gauge. Valve 1 and 3 were then closed while
valve 2 was opened. After another 15 minutes pressure P3 after which valve 2 was closed.
Chamber 2 was emptied and second replicate was placed inside chamber 2 and valve
3was closed. The procedure was then repeated. Results obtained from five replicates for
each sample was used to calculate Volume of solid (Vs) and Porosity (Ps) for each
replication using equations (2) and (3) for each sample. The result obtained was
summarized as shown in the table 1 below. Also plots of Volume of solids (V s) and
porosity (Ps) against number of replications for each sample were presented below as
figures 2, 3, 4 and 5 so as to analyze the consistency of readings obtained during testing
of the pycnometer.
TABLE 1: Summary of results obtained.
CASSAVA
Vs.
Ps
REPLICATES
1
672.44
0.75
678.67
0.5
723.92
0.75
723.92
0.65
670.92
0.75
2
3
4
5
WHEAT
SPINACH
TOMATO
Vs.
Ps
Vs.
Ps
Vs.
Ps
0.7 376.2
452.44
5
2
0.88
0.7 381.6
440.81
3
3
0.83
0.7 387.8
433.44
9
1
0.79
0.7 389.0
467.82
4
5
0.82
382.4
458.9 0.8
4
0.83
500
452.44
450
467.82
440.81
458.9
433.44
400
VOLUME (cm3)
350
300
Vs
250
Ps
200
Linear (Vs)
150
100
50
0.75
0.73
0.79
0.74
0.8
1
2
3
4
5
REPLICATES
0
0
6
FIG 2: Variation in volume and porosity forCassava flour
VOLUME (cm3)
500
450
400
350
300
250
200
150
100
50
0
452.44
440.81
467.82
458.9
433.44
Vs
Ps
Linear (Vs)
0
0.75
0.73
0.79
0.74
0.8
1
2
3
4
5
REPLICATES
6
FIG 3: Variation in volume and porosity for Wheat flour
700
598.87
603.26
603.26
600.99
599.89
VOLUME (cm3)
600
500
400
Vs
300
Ps
Linear (Vs)
200
100
0.69
0.72
0.71
0.69
0.68
1
2
3
4
5
0
0
FIG 4: Variation in volume and porosity forSpinach
6
REPLICATES
700
598.87
603.26
603.26
600.99
599.89
600
VOLUME (cm3)
500
400
Vs
300
Ps
Linear (Vs)
200
100
0.69
0.72
0.71
0.69
0.68
1
2
3
4
5
REPLICATES
0
0
6
FIG 5: Variation in volume and porosity for Tomato
DISCUSSION OF RESULTS
As shown in figures 2, 3, 4, and 5 a line referred to as “linear Vs” is indicated on each plot.
Values of computed volume of solid (Vs ) for each replicate were also shown. The linear line of
Vs means all the values of Vs per replicate are equal and therefore the pycnometer is functioning
very well. From the plots presented it can be seen that deviation from the linear line of Vs for the
replicates is more in cassava and wheat flour compared to dried and grounded spinach and
tomato. However variation in computed porosities of all samples is negligible. But computation
of porosity is dependent only on pressure gauge reading while that of the volume of solid is
influenced by volumes of chambers 1 and 2. Also it can be observed that Cassava (a tuber crop)
and wheat (a seed grain crop) flour have prominent variation compared to spinach and tomato
which are vegetable crops.
CONCLUSION
Based on the result presented and discussed above it was concluded that even though there are
variations of values the pycnometer constructed is functioning very well because the variations
are not significantly high especially for spinach and tomato. Also the equipment may be
considered more functional for dried grounded vegetables than grounded tuber and seed grain
crops.
REFERENCES
Blake P. and Hartage .W (1986) American Society of Tractor and Machineries”
Handbook U.S.A.
Fashina O. (2010) “Technical Note: Measuring Grains and Legume seed
density using pycnometer and envelop density analyser”
Unpublished.
Geddis. A.M, Guzman A.G, Basset R.L. (1996) “Rapid estimate of solid volume
in large Tuff cores using a gas pycnometer” University of Arizona
U.S.A.
Karanthanos V.T., Kanallopoullos N.K, Belessiotis V.G. (1996) “Development of
Porous structure during air drying of Agricultural plant products”
University of Greece, Greece.
Li M, Denny C.D, Leonard G.O, Gustavo V.B.C (1998) “Engineering Properties of
Foods and other Biological materials” Washington American Society of
Agricultural Engineers and Washington University U.S.A.