A One-Dimensional Flow Analysis for the Prediction of Centrifugal Pump Performance Characteristics

Table 3

Pump variable-parameters.

Order	Variable parameter equation	Eq. no.
	𝑉𝜓≡^𝑟22𝑔𝐻=0.002 to 0.12 step=0.001
Initial	𝜎=𝜎0, 𝑥=1, 𝜂vol=1
	Start of iteration
1	1𝜑=−2𝜓cot𝛽𝑏2+12𝜓^2cot^2𝛽𝑏2+2𝑥𝜎	(69)
2	𝑦=𝐶𝐻∞≡𝐻∞𝑢^22𝜓/𝑔=1+𝜑cot𝛽𝑏2	(21),; (65b)
3	𝜎=1−(1−𝜎0)𝑦	(20)
4	𝐶ℎ𝑙slp  ≡ ℎ𝑙slp𝑢^22=()𝐶/𝑔1−𝜎𝐻∞	(65d)
5	𝐶𝐻0≡𝐻0𝑢^22𝜓/𝑔=𝜎1+𝜑cot𝛽𝑏2	(65c)
6	𝐶𝑉5≡𝑉5=2𝑔𝐻4𝜖2𝜂vol𝑏2/𝐷2𝐷𝑡ℎ/𝐷3^2𝐷3/𝐷2^2⋅𝜓	(37)
7	𝐶𝑉4≡𝑉4=𝜖2𝑔𝐻^2𝜂vol𝐷3/𝐷2𝑏3/𝑏2tan𝛼𝑉⋅𝜓	(33)
8	𝐶𝑉eye≡𝑉eye=2𝑔𝐻4𝜖2𝑏2/𝐷2𝐷𝑡ℎ/𝐷3^2𝐷3/𝐷2^2⋅𝜓	(39)
9	𝐶𝑉3𝑝=𝐶𝑉4cos𝛼𝑉	(54a)
10	𝐶𝑉3𝑑=𝜎𝜑+𝜓cot𝛽𝑏2−𝐶𝑉4	(54b)
11	𝐶𝑉3𝑟≡𝑉3𝑟=𝜖2𝑔𝐻^2𝜂vol𝐷3/𝐷2𝑏3/𝑏2⋅𝜓	(54c)
12	𝜂vol𝑦=1−^𝑐𝐷eye𝐷eye𝐷1^2𝐷1𝐷2^21𝑏2/𝐷2√2𝐶dL𝜖2𝜑𝜓∗ 𝐶𝐻0−𝐶^2𝑉4−𝐶^2𝑉5+𝐶eye⋅𝐶^2𝑉eye2𝜑^2−18𝐷1−^1𝐷2^2𝐷eye𝐷1^2	(99)
13	Re𝑉=𝑉3𝑝⋅𝐷ℎ𝑉𝜈𝐶=2^𝑉3𝑝𝜑𝐷ℎ𝑉𝐷2⋅Re2	(52)
14	𝑓𝑉=0.3086log6.9/Re𝑉+𝜅/𝐷ℎ𝑉/3.7^1.112	(50)
15	𝐶𝑓𝑉=𝑓𝑉𝐿𝑉𝐷ℎ𝑉=𝑓𝑉𝐿𝑉𝐷21𝐷ℎ𝑉/𝐷2	(46)
16	ℎ𝑙𝑉𝐻=𝐶𝑓𝑉𝐶^2𝑉3𝑝+𝐶𝑑𝑉𝐶^2𝑉3𝑑+𝐶^2𝑉3𝑟+𝐶𝑓𝑡ℎ𝐶^2𝑉4	(45)
17	ℎ𝑙eye𝐻=𝐶eye⋅𝐶^2𝑉eye	(57)
18	1𝑥ℎ=1+^𝑙𝑉𝐻+ℎ𝑙eye𝐻	(61)
	End of iteration
19	𝐶ℎ𝑙𝑉+eye≡ℎ𝑙𝑉+ℎ𝑙eye𝑢^22=()/𝑔1−𝑥𝜎𝐶𝐻∞	(65e)
20	𝐶𝐻≡𝐻𝑢^22𝜓/𝑔=𝑥𝜎1+𝜑cot𝛽𝑏2	(65a)
21	𝐶𝑄≡𝑄(𝑁/60)𝐷^32=𝜂vol𝜖2𝜋^2𝑏2𝐷2⋅𝜓𝜑	(6)
22	𝑊av𝑢2=𝜖2(𝜋/𝑍)𝑏2/𝐷2⋅𝜓/𝜑1/2𝑑1/𝐷2𝑏1/𝑏2𝑏2/𝐷2+𝑑2/𝐷2𝑏2/𝐷2	(81)
23	𝑊Re=^av⋅𝐷hyd𝜈𝑊=2^av𝑢2𝐷hyd𝐷2⋅Re2	(86)
24	𝑓𝑖=0.3086log(6.9/Re)+𝜅/𝐷hyd/3.7^1.112	(84)
25	4𝐶𝑑𝑖=(𝑓𝑖𝑏+0.006)1.1+4^2𝐷2	(83)
26	𝐶ℎ𝑙𝑓  ≡ ℎ𝑙𝑓𝑢^22/𝑔=4𝐶𝑑𝑖(𝐿𝑏/𝐷2)(𝐷hyd/𝐷2)12𝑊av𝑢2^2	(78)
27	𝐶ℎ𝑙𝐷  ≡ ℎ𝑙𝐷𝑢^22/𝑔=𝐾𝐷⋅1𝜂vol𝜑𝜓	(91)
28	𝐶ℎ𝑙cirin  ≡ ℎ𝑙cirin𝑢^22=/𝑔1−𝜖1𝜋𝑍sin𝛽𝑏1𝐷1𝐷2^2−cot(180−𝛽𝑏1)𝑏1/𝑏2𝜖1/𝜖2⋅𝜓𝜑	(101)
29	𝐶ℎ𝑙vol  ≡ ℎ𝑙vol𝑢^22=1/𝑔𝜂vol−1⋅𝐶𝐻0+𝐶ℎ𝑙𝑓+𝐶ℎ𝑙cirin	(93)
30	𝐶𝐻sh≡𝐻sh𝑢^22/𝑔=𝐶𝐻0+𝐶ℎ𝑙𝑓+𝐶ℎ𝑙cirin+𝐶ℎ𝑙vol+𝐶ℎ𝑙𝐷	(73)
31	𝑃𝜂≡^𝑤𝑃sh=𝐶𝐻𝐶𝐻sh	(74)
32	𝐶𝑃sh≡𝑃sh𝜌(𝑁/60)^3𝐷^52=𝜋^2𝐶𝑄𝐶𝐻sh	(75)
33	𝐶𝑃𝑤≡𝑃𝑤𝜌(𝑁/60)^3𝐷^52=𝜋^2𝐶𝑄𝐶𝐻	(76)
34	𝐶NPSH𝑅1=0.02+2sin^2𝛽𝑏1𝜓/𝜑^2𝐷1/𝐷2^2𝑏1/𝑏2^2𝜖1/𝜖2^2	(107)
35	𝑛𝑠=9977√𝜖2𝑏2𝐷2⋅√𝜂vol⋅𝜑√𝜓	(110)