Centrifugal Pumps
Example: (Cont.)
Step 3: Conservation of angular momentum (cont.) T = ρQ [ r2Vt2 ]
Vt2 = r2 ω ˗ Vr2 / tan β2 = (1/2)(200) ˗ 19 / tan (30) = 66.9 ft/sec
So T = (1.94) (10) (1/2)(66.9) = 650 ft lb (result)
Power = T ω = (650)(200) = 130,000 ft lb/sec = 235 hp (result)
Head = H = P / Q γ = 130,000 / [(10)(62.4)] = 208 ft (result)
Step 4: Conservation of energy:
∆P = P2 ˗ P1 = γ H + (1/2) ρ V12 ˗ (1/2) ρ V22 = pressure increase by pump
Note: V1 = Vr1 and V2 = Vr2 er + Vt2 et So V22 = (Vr2)2 + (Vt2)2
∆P = (62.4)(208) + (1.2)(1.94)(28.6)2 ˗ (1.2)(1.94)(19)2 ˗ (1/2)(1.94)(66.9)2
∆P = 9 kN/ft2 (result)
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