Table 2. Open in new tab Comparison of...

Case	a_d	Q_g	ρ_d	Iv	Iv/Fu	\|$v_d^t$\|[m s^–1]	ω^t[s⁻¹]	ε_v	ε_ω
a03g1d2ob	10⁻⁴	10²⁶	1000.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0317	0.03	21.6	5.80
a03g2d1ob	10⁻⁴	10²⁷	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	14.0	0.3125	0.30	12.9	4.18
a03g2d2ob	10⁻⁴	10²⁷	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	5.0	0.1000	0.10	0.00	0.00
a03g3d1ob	10⁻⁴	10²⁸	100.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.9513	1.00	4.17	4.87
a03g3d2ob	10⁻⁴	10²⁸	1000.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.3125	0.10	5.41	213.0
a03g4d1ob	10⁻⁴	10²⁹	100.0	1.28· 10⁻²	3.315· 10⁴	158.114	140.0	2.6385	2.20	12.9	19.9
a03g4d2ob	10⁻⁴	10²⁹	1000.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.9513	1.00	4.17	4.87
b03g1d1ob	10⁻³	10²⁶	100.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0100	0.01	21.6	0.370
b03g2d1ob	10⁻³	10²⁷	100.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.8	0.0316	0.03	4.17	5.41
b03g2d2ob	10⁻³	10²⁷	1000.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0100	0.01	21.6	0.370
b03g3d1ob	10⁻³	10²⁸	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.0988	0.10	5.41	1.17
b03g3d2ob	10⁻³	10²⁸	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.8	0.0316	0.03	4.17	5.41
b03g4d1ob	10⁻³	10²⁹	100.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.3008	0.30	4.17	0.278
b03g4d2ob	10⁻³	10²⁹	1000.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.0988	0.10	5.41	1.17
c03g2d1ob	10⁻²	10²⁷	100.0	1.28· 10⁻⁶	3.315	1.581	1.2	0.0032	0.003	31.8	5.80
c03g3d1ob	10⁻²	10²⁸	100.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.6	0.0100	0.010	8.70	0.00
c03g3d2ob	10⁻²	10²⁸	1000.0	1.28· 10⁻⁶	3.315	1.581	1.2	0.0032	0.003	31.8	5.80
c03g4d1ob	10⁻²	10²⁹	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.5	0.0313	0.030	2.01	4.18
c03g4d2ob	10⁻²	10²⁹	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	5.0	0.0100	0.008	0.00	25.0

Case

a_d

Q_g

ρ_d

Iv/Fu

|$v_d^t$|[m s^–1]

ω^t[s⁻¹]

ε_v

ε_ω

[m]

[s⁻¹]

[kg m^–3]

Scaled

Computed

Scaled

Computed

per cent

a03g1d2ob

10⁻⁴

10²⁶

1000.0

1.28· 10⁻⁶

3.315

1.581

1.3

0.0317

0.03

21.6

5.80

a03g2d1ob

10⁻⁴

10²⁷

100.0

1.28· 10⁻⁴

3.315· 10²

15.811

14.0

0.3125

0.30

12.9

4.18

a03g2d2ob

10⁻⁴

10²⁷

1000.0

1.28· 10⁻⁵

3.315· 10¹

5.000

5.0

0.1000

0.10

0.00

a03g3d1ob

10⁻⁴

10²⁸

100.0

1.28· 10⁻³

3.315· 10³

50.000

48.0

0.9513

1.00

4.17

4.87

a03g3d2ob

10⁻⁴

10²⁸

1000.0

1.28· 10⁻⁴

3.315· 10²

15.811

15.0

0.3125

0.10

5.41

213.0

a03g4d1ob

10⁻⁴

10²⁹

100.0

1.28· 10⁻²

3.315· 10⁴

158.114

140.0

2.6385

2.20

12.9

19.9

a03g4d2ob

10⁻⁴

10²⁹

1000.0

1.28· 10⁻³

3.315· 10³

50.000

48.0

0.9513

1.00

4.17

4.87

b03g1d1ob

10⁻³

10²⁶

100.0

1.28· 10⁻⁶

3.315

1.581

1.3

0.0100

0.01

21.6

0.370

b03g2d1ob

10⁻³

10²⁷

100.0

1.28· 10⁻⁵

3.315· 10¹

5.000

4.8

0.0316

0.03

4.17

5.41

b03g2d2ob

10⁻³

10²⁷

1000.0

1.28· 10⁻⁶

3.315

1.581

1.3

0.0100

0.01

21.6

0.370

b03g3d1ob

10⁻³

10²⁸

100.0

1.28· 10⁻⁴

3.315· 10²

15.811

15.0

0.0988

0.10

5.41

1.17

b03g3d2ob

10⁻³

10²⁸

1000.0

1.28· 10⁻⁵

3.315· 10¹

5.000

4.8

0.0316

0.03

4.17

5.41

b03g4d1ob

10⁻³

10²⁹

100.0

1.28· 10⁻³

3.315· 10³

50.000

48.0

0.3008

0.30

4.17

0.278

b03g4d2ob

10⁻³

10²⁹

1000.0

1.28· 10⁻⁴

3.315· 10²

15.811

15.0

0.0988

0.10

5.41

1.17

c03g2d1ob

10⁻²

10²⁷

100.0

1.28· 10⁻⁶

3.315

1.581

1.2

0.0032

0.003

31.8

5.80

c03g3d1ob

10⁻²

10²⁸

100.0

1.28· 10⁻⁵

3.315· 10¹

5.000

4.6

0.0100

0.010

8.70

0.00

c03g3d2ob

10⁻²

10²⁸

1000.0

1.28· 10⁻⁶

3.315

1.581

1.2

0.0032

0.003

31.8

5.80

c03g4d1ob

10⁻²

10²⁹

100.0

1.28· 10⁻⁴

3.315· 10²

15.811

15.5

0.0313

0.030

2.01

4.18

c03g4d2ob

10⁻²

10²⁹

1000.0

1.28· 10⁻⁵

3.315· 10¹

5.000

5.0

0.0100

0.008

0.00

25.0

Case	a_d	Q_g	ρ_d	Iv	Iv/Fu	\|$v_d^t$\|[m s^–1]	ω^t[s⁻¹]	ε_v	ε_ω
a03g1d2ob	10⁻⁴	10²⁶	1000.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0317	0.03	21.6	5.80
a03g2d1ob	10⁻⁴	10²⁷	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	14.0	0.3125	0.30	12.9	4.18
a03g2d2ob	10⁻⁴	10²⁷	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	5.0	0.1000	0.10	0.00	0.00
a03g3d1ob	10⁻⁴	10²⁸	100.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.9513	1.00	4.17	4.87
a03g3d2ob	10⁻⁴	10²⁸	1000.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.3125	0.10	5.41	213.0
a03g4d1ob	10⁻⁴	10²⁹	100.0	1.28· 10⁻²	3.315· 10⁴	158.114	140.0	2.6385	2.20	12.9	19.9
a03g4d2ob	10⁻⁴	10²⁹	1000.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.9513	1.00	4.17	4.87
b03g1d1ob	10⁻³	10²⁶	100.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0100	0.01	21.6	0.370
b03g2d1ob	10⁻³	10²⁷	100.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.8	0.0316	0.03	4.17	5.41
b03g2d2ob	10⁻³	10²⁷	1000.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0100	0.01	21.6	0.370
b03g3d1ob	10⁻³	10²⁸	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.0988	0.10	5.41	1.17
b03g3d2ob	10⁻³	10²⁸	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.8	0.0316	0.03	4.17	5.41
b03g4d1ob	10⁻³	10²⁹	100.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.3008	0.30	4.17	0.278
b03g4d2ob	10⁻³	10²⁹	1000.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.0988	0.10	5.41	1.17
c03g2d1ob	10⁻²	10²⁷	100.0	1.28· 10⁻⁶	3.315	1.581	1.2	0.0032	0.003	31.8	5.80
c03g3d1ob	10⁻²	10²⁸	100.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.6	0.0100	0.010	8.70	0.00
c03g3d2ob	10⁻²	10²⁸	1000.0	1.28· 10⁻⁶	3.315	1.581	1.2	0.0032	0.003	31.8	5.80
c03g4d1ob	10⁻²	10²⁹	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.5	0.0313	0.030	2.01	4.18
c03g4d2ob	10⁻²	10²⁹	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	5.0	0.0100	0.008	0.00	25.0

Table 2.

Open in new tab

Comparison of scaled (via eqs. (17) and (20)) with numerically computed values from Ivanovski (2017). The referential case is a03g1d1ob (obolate spheroid) with a_d = 10⁻⁴ [m], Q_g = 10²⁶ [s⁻¹], ρ_d = 100 [kg m^–3], |$v_d^t$| = 5.0 [m s^–1], ω^t = 0.1 [s⁻¹]. The case’s labels correspond to the Tables B.8–B.10 in Ivanovski (2017).

Case	a_d	Q_g	ρ_d	Iv	Iv/Fu	\|$v_d^t$\|[m s^–1]		ω^t[s⁻¹]		ε_v	ε_ω
	[m]	[s⁻¹]	[kg m^–3]			Scaled	Computed	Scaled	Computed	per cent	per cent
a03g1d2ob	10⁻⁴	10²⁶	1000.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0317	0.03	21.6	5.80
a03g2d1ob	10⁻⁴	10²⁷	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	14.0	0.3125	0.30	12.9	4.18
a03g2d2ob	10⁻⁴	10²⁷	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	5.0	0.1000	0.10	0.00	0.00
a03g3d1ob	10⁻⁴	10²⁸	100.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.9513	1.00	4.17	4.87
a03g3d2ob	10⁻⁴	10²⁸	1000.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.3125	0.10	5.41	213.0
a03g4d1ob	10⁻⁴	10²⁹	100.0	1.28· 10⁻²	3.315· 10⁴	158.114	140.0	2.6385	2.20	12.9	19.9
a03g4d2ob	10⁻⁴	10²⁹	1000.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.9513	1.00	4.17	4.87
b03g1d1ob	10⁻³	10²⁶	100.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0100	0.01	21.6	0.370
b03g2d1ob	10⁻³	10²⁷	100.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.8	0.0316	0.03	4.17	5.41
b03g2d2ob	10⁻³	10²⁷	1000.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0100	0.01	21.6	0.370
b03g3d1ob	10⁻³	10²⁸	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.0988	0.10	5.41	1.17
b03g3d2ob	10⁻³	10²⁸	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.8	0.0316	0.03	4.17	5.41
b03g4d1ob	10⁻³	10²⁹	100.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.3008	0.30	4.17	0.278
b03g4d2ob	10⁻³	10²⁹	1000.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.0988	0.10	5.41	1.17
c03g2d1ob	10⁻²	10²⁷	100.0	1.28· 10⁻⁶	3.315	1.581	1.2	0.0032	0.003	31.8	5.80
c03g3d1ob	10⁻²	10²⁸	100.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.6	0.0100	0.010	8.70	0.00
c03g3d2ob	10⁻²	10²⁸	1000.0	1.28· 10⁻⁶	3.315	1.581	1.2	0.0032	0.003	31.8	5.80
c03g4d1ob	10⁻²	10²⁹	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.5	0.0313	0.030	2.01	4.18
c03g4d2ob	10⁻²	10²⁹	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	5.0	0.0100	0.008	0.00	25.0

Case	a_d	Q_g	ρ_d	Iv	Iv/Fu	\|$v_d^t$\|[m s^–1]		ω^t[s⁻¹]		ε_v	ε_ω
	[m]	[s⁻¹]	[kg m^–3]			Scaled	Computed	Scaled	Computed	per cent	per cent
a03g1d2ob	10⁻⁴	10²⁶	1000.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0317	0.03	21.6	5.80
a03g2d1ob	10⁻⁴	10²⁷	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	14.0	0.3125	0.30	12.9	4.18
a03g2d2ob	10⁻⁴	10²⁷	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	5.0	0.1000	0.10	0.00	0.00
a03g3d1ob	10⁻⁴	10²⁸	100.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.9513	1.00	4.17	4.87
a03g3d2ob	10⁻⁴	10²⁸	1000.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.3125	0.10	5.41	213.0
a03g4d1ob	10⁻⁴	10²⁹	100.0	1.28· 10⁻²	3.315· 10⁴	158.114	140.0	2.6385	2.20	12.9	19.9
a03g4d2ob	10⁻⁴	10²⁹	1000.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.9513	1.00	4.17	4.87
b03g1d1ob	10⁻³	10²⁶	100.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0100	0.01	21.6	0.370
b03g2d1ob	10⁻³	10²⁷	100.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.8	0.0316	0.03	4.17	5.41
b03g2d2ob	10⁻³	10²⁷	1000.0	1.28· 10⁻⁶	3.315	1.581	1.3	0.0100	0.01	21.6	0.370
b03g3d1ob	10⁻³	10²⁸	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.0988	0.10	5.41	1.17
b03g3d2ob	10⁻³	10²⁸	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.8	0.0316	0.03	4.17	5.41
b03g4d1ob	10⁻³	10²⁹	100.0	1.28· 10⁻³	3.315· 10³	50.000	48.0	0.3008	0.30	4.17	0.278
b03g4d2ob	10⁻³	10²⁹	1000.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.0	0.0988	0.10	5.41	1.17
c03g2d1ob	10⁻²	10²⁷	100.0	1.28· 10⁻⁶	3.315	1.581	1.2	0.0032	0.003	31.8	5.80
c03g3d1ob	10⁻²	10²⁸	100.0	1.28· 10⁻⁵	3.315· 10¹	5.000	4.6	0.0100	0.010	8.70	0.00
c03g3d2ob	10⁻²	10²⁸	1000.0	1.28· 10⁻⁶	3.315	1.581	1.2	0.0032	0.003	31.8	5.80
c03g4d1ob	10⁻²	10²⁹	100.0	1.28· 10⁻⁴	3.315· 10²	15.811	15.5	0.0313	0.030	2.01	4.18
c03g4d2ob	10⁻²	10²⁹	1000.0	1.28· 10⁻⁵	3.315· 10¹	5.000	5.0	0.0100	0.008	0.00	25.0

This Feature Is Available To Subscribers Only