A centrifugal pump with an impeller diameter of Di and speed n1 operating at its

Question

A centrifugal pump with an impeller diameter of Di and speed n1 operating at its best efficiency point develops a head of HÍ and a flow of Qi while requiring a power of W*si. This pump is scaled up to provide a flow of Q% and a head of H2. Determine the impeller diameter, speed, and brake power of the new pump Parameter List Speed, n1 1700 rpmm Brake power, W1-24 kW Flow rate, Q 14000 L/min Head, H1 34 m Diameter, D1 28 cm Flow rate, Q 2 10000 L/min Head, H 2-80 m Answer Table Value Description Speed, n? (rpm) Diameter, D2 (cm) Brake power, W2 (kW)

Explanation / Answer

the affinity law for discharge ensures that the scaled point has the same value of Q/nD3 as the test point i.e. Q2 = Q1 * (N2/N1) * (D2/D1)3

similarily, scaled speed N2 is obtained from the test point value N1 by means of

N2 = N1 * (H2/H1)3/4 * (Q1/Q2)1/2

and power can be given as

(power)2 = (power)1 * (N2/N1)3 * (D2/D1)5

these are the formulas which will be used to calculate speed, diameter and power

1. to calculate speed, we can use any of the mentioned formula according to our given data.

we have to use second formula as we have 2 known quantity out of 3.

N2 = N1 * (H2/H1)3/4 * (Q1/Q2)1/2

N2 = 1700 * (80/34)3/4 * (4000/10000)1/2

N2 = 2046.6 rpm

2. to calculate diameter we will use first formula, convert diameter unit from c.m. to meter

D1 = 28 cm= 0.28 meter

Q2 = Q1 * (N2/N1) * (D2/D1)3

10000 = 4000 * (2046.6/1700) * (D2/0.28)3

D2 = 0.357 meter = 35.7 cm.

3. to calculate power we will use third formula,

(power)2 = (power)1 * (N2/N1)3 * (D2/D1)5

(power)2 = 24 * (2046.6/1700)3 * (0.357/0.28)5

(power)2 = 147 .1 KW

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