- D = 40 cm = 0.4 m.
n = 1000 rpm = 1000 / 60 = 16.667 rps
CH = ΔH / [ (D2n2) / g ] = (3 × 9.81) / [(0.4) 2(16.6672] = 0.662
From Fig. 8-5 with CH = 0.662, find CQ = 0.65, and with CQ = 0.65, find CP = 0.54
CQ = Q / (nD3) = 0.65
Q = 0.65 nD3 = 0.65 × 16.667 × (0.4) 3 = 0.693 m3/s
CP = P / (ρ D5 n3)
ρ = 1 KN &sdot s2/m4
P = 0.54 ρ D5 n3 = 0.54 (1) (0.4)5 (16.667)3 [KN ⋅ m / s]
P = 25.6 KN ⋅ m / s = 25.6 KW
- D = 30 cm = 0.30 m
n = 1200 rpm / (60 s/m) = 20 rps
CQ = Q / (n D3) = 0.25 / [ 20 × (0.3)3 ] = 0.463
From Fig. 8-5, with CQ = 0.463, find CH = 1.24, and CP = 0.72
ΔH = CH D2 n2 / g = 1.24 (0.3)2 (20)2 / 9.81 = 4.55 m
ρ = 1 KN &sdot s2/m4
P = CP ρ D5 n3 = 0.72 (1) (0.3)5 (20)3 [KN ⋅ m / s]
P = 14 KN ⋅ m / s = 14 KW
- From Fig. 8-8, at maximum efficiency: ΔH = 95 m, and Q = 0.214 m3/s
( CH ) N = ( CH ) N = 2133.5
[ ΔH / (D2n2 / g) ] N = [ ΔH / (D2n2 / g) ] N = 2133.5
[ ΔH / (n2) ] N = [ ΔH / (n2) ] N = 2133.5
80 / N2 = 95 / (2133.5)2
N = 2133.5 (80/95)1/2 = 1958 RPM
(CQ) N = 1958 = (CQ) N = 2133.5
[Q / (nD3)] N = 1958 = [Q / (nD3)] N = 2133.5
QN = 1958 / QN = 2133.5 = 1958 / 2133.5 = 0.917
QN = 1958 = 0.917 QN = 2133.5 = 0.917 × 0.214 = 0.196 m3/s
n = 1958 / 60 = 32.63 rps
D = 0.371 m
CQ = Q / (nD3) = 0.196 / [ 32.63 × (0.371) 3 ] = 0.118
From Fig. 8-9: CP = 0.68
CP = P / (ρ D5 n3)
ρ = 1 KN &sdot s2/m4
P = 0.68 ρ D5 n3 = 0.68 × 1 × (0.371) 5 (32.63)3 [KN ⋅ m/ s]
P = 166 KN ⋅ m/ s = 166 KW
- hp = (z2 - z1) + [V2/(2g)] [f (L/D) + ∑ KL ]
hp = (z2 - z1) + [ Q2/(2gA2)] [ f (L/D) + Ke + Kb + KE ]
From Table 5-3 (in the text): Ke = 0.5; Kb = 0.19; KE = 1
hp = (500 - 450) + [ Q2/(2g ((π/4) D2)2) ] [ 0.016 (2000/0.5) + 0.5 + 0.19 + 1 ]
hp = 50 + [ Q2/(2 (9.81) (π/4)2 (0.5)4 ] (65.69)
hp = 50 + [ Q2/(0.7564) ] (65.69)
hp = 50 + 86.84 Q2
Pump performance curve: H = 70 - 700 Q 2
At H = hp: Q = 0.159 m3/s
hp = 50 + 86.84 (0.159) 2 = 52.195 m.