Some Physical and Mechanical Properties of Black-Plum

Some physical and mechanical properties of vitex doniana fruits were studied. The average fruit length, width and thickness were 26.79mm, 24.08mm and 20.16mm respectively. The average fruit mass was 11.12g. The average sphericity and aspect ratio of the fruit were 87.79% and 88.35% respectively. The average true density and bulk density of the fruit bed were 92.87kg/m 3 and 47.82kg/m 3 respectively. The average porosity of the bed of the fruit was 46.95%. The angle of repose for the fruit on plywood, galvanized sheet and mild steel sheet were 6.0 0 , 7.0 0 and 6.0 0 respectively. Forces at peak for both longitudinal and transverse position were 1450.5N and 1382.2N respectively. Also, the energies at peak for both longitudinal and transverse position were 3.2Nm and 2.7Nm respectively. The stresses at break for both longitudinal and transverse positions were 2.88N/m 2 and 2.37N/m 2 respectively. The design of any extraction device for this fruit can utilize these physical and mechanical properties.


INTRODUCTION
Black plum (vitex doniana) is a member of verbenaceae family and has been described as woody or herbaceous often with quadrangles or branch-lets.Vitex is a large genus and distributed throughout the tropics and sub-tropics.It has rare exceptional leaves which are composite and digitately.In Nigeria this combinations distinguishes it from other genera (Hutchinson et al., 1963).Black plum of the family verbanaceae is a tree crop that grows in open woodland and savannah region of tropical Africa, it is the commonest of the vitex species in West Africa, Dalziel et al. (1964).
The physical property of vitex doniana fruits, like those other fruits are essential for the design of equipment for processing the fruit into juice for human consumption.The properties are affected by numerous factors such as the size, shape, mass, bulk density, density ratio, porosity, angle repose, coefficient of static friction and fracture resistance.Moreover, the knowledge of fracture resistance of the fruit is imperative to design the machine for processing juice for vitex doniana.Limited research has been conducted on the physico-chemical properties and sensory evaluation of jam.Ajenifujah-Solebo and Aina (2011).

Physical Properties
Fresh samples of vitex doniana were collected within the metropolis of Saki, Southwest of Nigeria approximately 50 kg fruits.The fruits was divided into smaller samples and analyzed immediately.
Fruit size: In order to determine the size, shape indices and fruit mass, 20 fruits sample each were collected and measurement of each was taken.This measurement was taken five times independently.The parameters determined include length (major diameter) (a), width (minor diameter) (b) and thickness (intermediate) (c) using Vernier caliper.The accuracy of the instrument is 0.01 mm.Shape: Vitex doniana fruit shape was expressed in terms of its sphericity index and aspect ratio.For the sphericity index, Sp, the dimensions obtained for the 100 vitex doniana fruits selected at random were used to compute the index using standard method (Mohsenin, 1978)  For the aspect ratio, 100 vitex doniana fruits samples were also selected at random for conducting the experiment.Thus measurement of shape indices was replicated one hundred times.The aspect ratio (R a ) was calculated as recommended by Maduako and Faborode (1990).Ra = b/a ×100 ……………………………………2 Average Mass: The mass of randomly selected individual fruits were determined using a Mettler Toledo PB 153 electronic balance to an accuracy of 0.001g measurements were determined ten times independently.
True Density: The true density (ߩ t ) of the fruit was determined by water displacement method.Fifty randomly selected vitex doniana fruits were weighed and lowered into a graduated measuring cylinder containing 1000 ml of water.It was ensured that the fruit was submerged during immersion in water.The increase in volume was noted.
The ratio of the mass (kg) of the fruit to the volume (m 3 ) of water displaced due to the immersed fruit gave the density of the fruit (Amin et al., 2004).

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Bulk Density:A cylindrical container of known mass and volume was filled with vitex doniana and weighed.The mass of the vitex doniana was calculated by the difference between the weight of the empty cylinder and the mass after it was filled with the vitex doniana.The ratio of the mass of the vitex doniana to the volume of the cylindrical container gives the bulk density (ߩ b ).The process was repeated 10 times Amin et al. (2004).

Density Ratio and Porosity:
The porosity (P) was determined as a function of the bulk density and true density of the fruit.The volume fraction occupied by the fruit is given by the ratio of the bulk density ߩ b to the true density ߩ t of the fruit.(D t = ߩ b / ߩ t ).The porosity (void fraction) expressed in percent was calculated from average values of bulk and particle densities using equation 4 (Joshi et al., 1993;Deshpande et al., 1993;Suthar and Das, 1996;Jha, 1999;Nelson, 2002).
The density ratio (D t ) is expressed as a percentage is given by Owolarafe et al. ( 2007)

Determination of mechanical properties
The mechanical properties determined in the study include angle of repose, sliding coefficient of friction and fracture resistance.

Determination of angle of repose:
A regular cylindrical container opened at both ends and placed on a galvanized steel surface was filled with the vitex doniana fruit to the brim.Afterwards the container was lifted gradually and finally emptied to form a conical heap with the fruits.The tangent of the angle of inclination to the horizontal (tan Ø) was calculated from the height (h) and base radius (r) of the formed heap as Amin et al. (2004);.
Where, Ø is the angle of repose This was repeated 5 times for each replicate.

Determination of the coefficient of static friction:
Coefficient of static friction is the tangent of the angle of inclination at which a material begins to slide on the surface.Using the method described by Solomon and Zewdu (2009), five vitex doniana fruits were placed on an inclined plane apparatus with mild steel.The plane portion of the apparatus was raised.The angle of inclination to the horizontal, as soon as the fruits began to slide, was measured from a protractor attached to the inclined plane.The tangent of the angle of inclination measured gives the coefficient of static friction.This was repeated 10 times.
Determination of fracture resistance: Compression tests were conducted using Universal Compressive Testing Machine (UCTM) controlled by a microcomputer.The fruit was placed between two parallel plates on the machine and compressed till failure occurred Aviara et al. (2007).. Two loading orientations were used (transverse and longitudinal) and twenty-four randomly selected fruits from ripe and unripe were compressed laterally and longitudinally by the UCTM at a compression rate of 5 mm/min.Test results, statistics and graph were automatically generated.The compressive load, compressive stress, compressive strain, stress energy and modulus of elasticity were obtained.

RESULT AND DISCUSSION
The average length, width and thickness for ripe fruit were 26.79, 24.08 and 20.17 mm respectively (Table 1).These measurements are of great value because the dimensions are important in determining aperture size in materials separation (Mohsenin, 1978); Omobuwajo et  (1999) For this type of fruit, these parameters may be useful in determining the size of the components of machine for extracting the fruit juice.
The average sphericity and aspect ratio of the fruit were 87.79% and 88.35% respectively.The high sphericity is an indication of the fruit tending to the shape of a sphere.The other implication of the high sphericity and aspect ratio can also be measured of the ability of the fruit to roll rather than slide on a flat surface.This is very important in design of hoppers for machines.Omobuwajo et al. (2000).The average fruit mass, average true density and bulk density were 11.12 kg, 92.87 kg/m 3 and respectively.Interestingly, this result is a reflection of the smaller volume (based on the dimensions) expected from the fruit of vitex doniana The average porosity of a bed of the fruits was 47.0%.The low porosity value observed could explained in term of the high sphericity that is an indication of compact arrangement as reported for spondias mombin by Owolarafe et al. (2006);.Both the true and bulk density characteristics are useful in the estimation of load and hence in the design of load shafts for processing machine.The angle of repose for the fruit on plywood, galvanized sheet and mild sheet were 6.0, 7.0 and 6.0 o respectively.An explanation for the close value of angle of repose obtained can be given as the smooth surface of the fruit.This is in agreement with results obtained for some other fruits previously studied.
The result of fracture resistance analyses showed on Table 2a and 2b.that the average force at peak for both transverse and longitudinal position were 1382.1 and 1450.5 N respectively.This implies that more forces will be required to extract the juice at the longitudinal position than the transverse position.From the same Table, it also shows that average stress at break at transverse and longitudinal positions were 2.37 and 2.88 N/mm 2 respectively.

CONCLUSION AND RECOMMENDATION
The following conclusions are drawn from this investigation into physical properties of vitex doniana fruit: (i) Physical properties of vitex doniana fruit studied in this work change linearly with an increase in seed moisture content with high correlation.
(ii) The dimensions of the vitex doniana fruit increased: the major axis by 3.44%, medium axis by 2.35% and minor axis by 6.17%.
(iii) The sphericity and thousand seed mass varied from 82.1 to 96.9% and 7.39 to 14.41 g, respectively.
(iv) The bulk and true densities decreased from 59.10 to 40.10 kg/m 3 and 117.10 to 51.50 kg/m 3 , respectively.(v) The aspect ratio and porosity increased linearly from 74.8 to 100% and 20.1 to 59.1% respectively.
(vi) The forces at peak at longitudinal and transverse positions were 1450.5 and 1382.1 N respectively.
(vii) The energies to peak at longitudinal and transverse positions were 3.30 and 2.05 Nm respectively.(viii) The forces at break at longitudinal and transverse positions were 1450.50 and 1382.10N respectively.(ix) The stresses at break at longitudinal and transverse positions were 2.89 and 2.37 N/mm 2 respectively.(x) The energies at break at longitudinal and transverse positions were 3.30 and 2.05 Nm respectively.
(xi) The Young modules at longitudinal and transverse positions were 17.34 and 14.06 N/mm 2 respectively.(xii) The deformations at peak at longitudinal and transverse positions were 15.04 and 12.36 mm respectively.(xiii) The deformations at break at longitudinal and transverse positions were 15.04 and 12.36 mm respectively.