A centrifugal pump with a 12- in diameter impeller requires a power input of 60 hp when the flowrate is 3200 gpm against a 60 ft head. The impeller is changed to one with a 10 in. diameter. Determine the expected flowrate, head, and input power if the pump speed remains the same

a) expected flow rate is 1852 gpm

b) head is 41.7 ft

c) input power is 21.1 hP

Explanation:

from flow coefficient equation C_Q = Q/(W×D³)

Q ∝ d³

Qd₁/Qd₂ = d₁³/d₂³

where Qd₁ and Qd₂ are different discharges with respect to different diameter, (Qd₁ = 3200 gpm) and d₁ is diameter one ( 12 in) while d₂ is diameter 2 ( 10 in),

now we substitute

Qd₂ = Qd₁(d₂³/d₁³)

Qd₂ = 3200( 10/12)³

Qd₂ = 1852 gpm

∴ expected flow rate is 1852 gpm

next we calculate the head

h ∝ d²

hd₁/hd₂ = d₁²/d₂²

where hd₁ and hd₂ are different heads with respect to different diameter, (hd₁ = 60 ft) and d₁ is diameter one ( 12 in) while d₂ is diameter 2 ( 10 in),

now we substitute

hd₂ = hd₁(d₂²/d₁²)

hd₂ = 60 ( 10/12 )²

hd₂ = 41.7 ft

∴ head is 41.7 ft

Now calculate the input power

W ∝ d⁵

Wd₁/Wd₂ = d₁⁵/d₂⁵

where Wd₁ and Wd₂ are different power with respect to different diameter, (Wd₁ = 60 hp) and d₁ is diameter one ( 12 in) while d₂ is diameter 2 ( 10 in),

now we substitute

Wd₂ = Wd₁(d₂⁵/d₁⁵)

Wd₂ = 60 ( 10/12 )⁵

Wd₂ = 21.1 hP

∴ input power is 21.1 hP

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