Question

Problem 19.5 A centrifugal pump discharges 0.15 mº/s of water against a head of 12.5 m, the
speed of the impeller being 600 r.p.m. The outer and inner diameters of impeller are 500 mm and
250 mm respectively and the vanes are bent back at 35° to the tangent at exit. If the area of flow
remains 0.07 m² from inlet to outlet, calculate :
(i) Manometric efficiency of pump, (ii) Vane angle at inlet, and​

Answer 1

Answer:Given:

D2=0.5mD1=0.25m,B2=0.05mN=1200rpm,Hm=48m,Vf=Vf1=Vf2=3m/sϕ=40∘

Solution:

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u1=πD1N60=π×0.25×120060=15.7m/s

u2=πD2N60=π×0.5×120060=31.4m/s

Q=πD2B2Vf2=π×0.5×0.05×3=0.2355m3/s

Vane angle at inlet,

tanθ=Vf1u1=315.7=0.1911

θ=tan−1(0.1911)=10.81∘

Work done by impeller on water per sec,

W.D=Wg×Vw2.u2=ρgQg×Vw2.u2

=1000×9.81×0.23559.81×Vw2×31.4

tanϕ=Vf2u2−Vw2=331.4−Vw2

tan40=331.4−Vw2

Vw2=27.82m/s

WD=1000×9.81×0.23559.81×27.82×31.4

=205720.55Nm/s

Manometric efficiency: ηmano=gHmVw2.u2=9.81×4827.82×31.4=0.539≈53.9%

Explanation: