Vertical Airflow Resistance of Chickpea (C. Arietinum) Cultivars as Affected by Bulk Density and Moisture Content

Figures & data

Figure 1 Schematic diagram of apparatus for measuring the airflow resistance of seeds.

Table 1 Physical attributes of three chickpea cultivars measured at initial moisture content

	Moisture content (% w.b.)	Dimensions ^† (mm)			Particle density ^‡ (kg/m^3)	Bulk density ^‡ (kg/m^3)
Type		Major	Intermediate	Minor			Porosity ^‡ (%)
Large kabuli	8.91	10.42 (0.04)∗	8.35 (0.03)	8.25 (0.03)	1473 (9.5)	808 (1.92)	43.79 (0.35)
Small kabuli (chico)	9.32	8.53 (0.05)	7.06 (0.03)	6.81 (0.03)	1422.8 (6.6)	823.31 (2.37)	42.13 (0.11)
Desi	9.21	8.08 (0.05)	6.46 (0.04)	5.89 (0.11)	1394.9 (3.3)	780.74 (3.38)	44.03 (0.33)
∗Standard deviation; ^†N = 150; and ^‡N = 3.

Table 2 Experimental data of airflow resistance (Pa/m) of three chickpea cultivars as affected by moisture content, bulk density and airflow rate. ^∗

	Airflow rate(m^3s^−1m^−2)	Moisture content ^†
		M1			M2			M3
Cultivar		Bulk density (ρb) (kg/m^3)
		ρb1 = 770	ρb2 = 827.3	ρb3 = 837.9	ρb1 = 764.3	ρb2 = 821	ρb3 = 831.6	ρb1 = 738.9	ρb2 = 778.5	ρb3 = 809.6
Large kabuli	0.02	4.5	4.8	4.9	4.0	4.2	6.1	3.4	4.01	6.0
	0.04	11.1	11.2	11.3	7.0	10.2	11.2	6.1	9.0	10.9
	0.08	21.9	31.1	32.3	19.6	28.8	30.8	14.3	20.6	28.0
	0.1	37.4	41.4	44.1	27.1	32.6	42.8	22.2	30.4	40.2
	0.2	125.0	129.1	140.6	84.4	118.5	135.9	84.2	101.9	113.2
	0.3	226.9	262.5	275.2	162.3	233.3	250.6	161.5	194.8	244.6
	0.4	369.7	410.6	491.6	273.3	327.5	381.3	244.8	299.5	373.6
		ρb1 = 806.8	ρb2 = 841.5	ρb3 = 863.4	ρb1 = 785.6	ρb2 = 819.5	ρb3 = 840.8	ρb1 = 753	ρb2 = 788.4	ρb3 = 815.3
Small abuli(chico)	0.02	8.1	8.6	9.3	5.3	6.1	7.4	3.5	5.8	6.6
	0.04	17.1	17.2	18.7	10.8	13.3	15.6	7.6	12.1	14.5
	0.08	40.3	42.8	45.9	23.0	23.2	31.6	18.8	20.9	30.0
	0.1	51.9	52.8	59.7	37.2	47.8	49.7	29.0	43.5	48.1
	0.2	161.8	163.0	176.5	117.9	141.1	161.7	106.4	137.8	149.8
	0.3	306.4	309.0	312.7	210.1	249.9	267.5	181.3	210.1	250.1
	0.4	515.6	430.0	473.4	351.0	401.6	438.1	306.0	370.4	402.2
		ρb1 = 754.4	ρb2 = 792.6	ρb3 = 809.6	ρb1 = 720.5	ρb2 = 756.6	ρb3 = 772.9	ρb1 = 693.6	ρb2 = 741.7	ρb3 = 760.8
Desi	0.02	8.9	9.0	10.3	5.5	6.3	6.8	3.9	5.8	6.2
	0.04	15.5	16.4	16.8	10.5	16.1	16.1	8.7	14.9	15.7
	0.08	31.9	38.5	53.3	25.0	38.2	47.0	24.0	37.3	43.3
	0.1	48.8	62.6	67.0	39.3	49.3	61.1	35.4	48.8	56.7
	0.2	162.2	174.0	179.4	112.5	124.3	156.6	109.5	114.4	137.8
	0.3	325.9	342.0	362.3	269.9	279.5	334.0	199.7	261.5	325.4
	0.4	467.3	487.1	550.7	317.4	390.9	496.8	351.0	370.0	447.9
∗Each value represents an average of three replicates. ^†M1: 9.32, 9.82, 9.56 (% w.b.) for large kabuli, small kabuli and desi, respectively. M2: 12.72, 15.1, 13.83 (% w.b.) for large kabuli, small kabuli and desi, respectively M3: 16.1, 18.2, 17.15 (% w.b.) for large kabuli, small kabuli and desi, respectively. ρb1, ρb2, ρb3: low, medium and high bulk density, respectively.

Figure 2 Effect of bed depth on airflow resistance of large kabuli chickpea at moisture content of 9.32% (wet basis), bulk density of 770 kg/m³ and four airflow rates: (Δ) 0.3; (×) 0.2; (s) 0.1; and (u) 0.08 m³s⁻¹m⁻².

Table 3 Estimated parameters of three airflow resistance models at different combinations of moisture content and bulk density for large kabuli chickpea

		Moisture content∗ (% w.b.)
		M1 9.32			M2 12.72			M3 16.10
Model	Constants				Bulk density (ρb) (kg/m^3)
		ρb1 = 770	ρb2 = 827.3	ρb3 = 837.9	ρb1 = 764.3	ρb2 = 821	ρb3 = 831.6	ρb1 = 738.9	ρb2 = 778.5	ρb3 = 809.6
Shedd
	A	1639.8	1754.2	1588.4	1287.6	13.94.3	1264.9	1063.7	1277.4	1491.4
	B	1.63	1.62	1.52	1.70	1.69	1.62	1.59	1.58	1.51
	R^2 ^†	0.9989	0.9914	0.9996	0.9992	0.9968	0.9960	0.9981	0.9991	0.9989
	MSE ^‡	18.98	17.19	7.40	7.30	36.47	41.85	14.70	10.07	13.25
Hukill & Ives
	C	6928.2	7329.4	5603.2	6069.1	6231.4	5395.8	4324.7	4937.9	5049.3
	D	47.49	44.79	21.61	86.72	69.52	48.01	37.78	31.47	18.82
	R^2	0.9987	0.9990	0.9988	0.9995	0.9973	0.9953	0.9971	0.9986	09983
	MSE	21.59	19.94	24.06	4.55	30.09	48.21	22.22	16.26	19.73
Ergun
	E	227.3	261.29	340.59	142.53	166.18	184.13	174.82	225.99	340.63
	F	1379.2	1848.3	1626.5	1348.1	1446.6	1340.5	1123.1	1333.3	1509.9
	R^2	0.9980	0.9985	09979	09997	09978	09942	09958	0.9971	09976
	MSE	23.69	29.62	41.09	2.72	24.15	59.08	32.10	25.68	27.48
∗Value represents an average of three replicates of the moisture contents of samples, which were selected before and after each experiment. ^†Coefficient of multiple determination for relationship between predicted and measured values. ^‡Mean square error (MSE) of predicted values with respect to the measured values.

Table 4 Estimated parameters of three airflow resistance models at different combinations of moisture content and bulk density for small kabuli (chico) chickpea

		Moisture content∗ (% wet basis)
		M1 9.82			M2 15.10			M3 18.20
Model	Constants				Bulk density (ρb) (kg/m^3)
		ρb1 = 806.8	ρb2 = 841.5	ρb3 = 863.4	ρb1 = 785.6	ρb2 = 819.5	ρb3 = 840.8	ρb1 = 753	ρb2 = 788.4	ρb3 = 815.3
Shedd
	A	2372.5	1608.3	1779.6	1554.5	1047.3	982.4	1312.4	1411.6	1951.6
	B	1.68	1.43	1.44	1.63	1.40	1.38	1.58	1.43	1.56
	R^2 ^†	0.9989	0.9986	0.9998	0.9989	0.9979	0.9951	0.9983	0.9944	0.9942
	MSE ^‡	34.82	32.63	6.58	17.72	21.90	47.65	20.01	101.52	163.05
Hukill & Ives
	C	10528.9	4676.9	5306.9	6491.2	2868.6	2572.5	5197.2	4200.5	7266.1
	D	64.71	11.28	12.34	46.45	9.45	8.35	33.80	11.94	26.19
	R^2	0.9994	0.9971	0.9993	0.9990	09959	0.9920	09973	09919	09928
	MSE	20.88	67.57	19.07	14.96	42.93	75.98	31.96	145.73	202.07
Ergun
	E	294.00	484.00	504.08	224.77	346.53	348.97	227.33	418.15	384.12
	F	2476.8	1533.4	1726.0	1628.7	967.9	879.6	1379.2	1350.3	2023.7
	R^2	0.9996	0.9960	0.9988	0.9989	0.9948	0.9906	0.9961	0.9903	0.9913
	MSE	11.40	90.10	33.08	16.45	53.54	88.29	46.72	172.00	242.64
∗Value represents an average of three replicates of the moisture contents of samples, which were selected before and after each experiment. ^†Coefficient of multiple determination for relationship between predicted and measured values. ^‡Mean square error (MSE) of predicted values with respect to the measured values.

Table 5 Estimated parameters of three airflow resistance models at different combinations of moisture content and bulk density for desi chickpea

		Moisture content∗ (% wet basis)
		MC1 9.56			MC2 13.83			MC3 17.15
Model	Constants	Bulk density (ρb) (kg/m^3)
		ρb1 = 754.4	ρb2 = 792.6	ρb3 = 809.6	ρb1 = 720.5	ρb2 = 756.6	ρb3 = 772.9	ρb1 = 693.6	ρb2 = 741.7	ρb3 = 760.8
Shedd
	A	1921.5	1589.0	2256.2	1392.6	1165.3	1984.4	1689.4	1746.8	1879.0
	B	1.52	1.46	1.54	1.62	1.55	1.78	1.73	1.52	1.45
	R^2 ^†	0.9962	0.9990	0.990	09971	0.9876	0.9886	0.9979	0.9985	0.9973
	MSE ^‡	108.98	21.72	38.52	36.43	124.97	218.88	32.03	36.02	84.43
Hukill & Ives
	C	6830.3	4841.2	7899.2	5693.6	3841.9	9943.2	8443.9	6027.4	5785.7
	D	21.95	13.34	21.89	42.34	19.52	152.4	120.83	20.26	13.41
	R^2	0.9948	0.9991	0.9990	0.9973	0.9899	0.9889	0.9982	0.9979	0.9957
	MSE	147.66	20.42	36.52	33.40	99.91	202.37	26.72	48.73	133.51
Ergun
	E	412.88	428.52	470.01	209.64	241.68	177.50	165.54	383.56	518.71
	F	1968.8	1557.9	2304.1	1455.7	1171.4	1974.0	1760.3	1777.0	1833.0
	R^2	0.9934	0.9988	0.9987	0.9972	0.9914	0.9911	0.9987	0.9972	0.9944
	MSE	186.05	26.28	48.7	34.34	84.76	166.42	20.36	66.07	168.74
∗Value represents an average of three replicates of the moisture contents of samples, which were selected before and after each experiment. ^†Coefficient for multiple determination for relationship between predicted and measured values. ^‡Mean square error (MSE) of predicted values with respect to the measured values.

Figure 3 Percentage error in the prediction of pressure drop as a function of airflow rate of large kabuli at moisture content of 9.32% wet basis, bulk density of 770 kg/m³. (Δ) Shedd model, (♦) Hukill and Ives model, and (□) Ergun model.

Table 6 Estimated model coefficients and standard error obtained by stepwise regression procedure

Model coefficient	Large kabuli	Small kabuli (chico)	Desi
a	1656.75	1654.75	1672.72
b	−22.81	−23.24	−16.08
c	0.62	0.87	0.82
R^2	0.97	0.96	0.95
MSE	839.37	1386.54	2302.10