- Use P (KW) = 8 Q (m3/s) ht (m)
P = 8 × 1.5 × 17 = 204 KW.
- D = 6 in = 0.5 ft.
Calculate area: A = π (D2/4) = 3.1416 × 0.5 2 / 4 = 0.19635 ft2
Calculate velocity: V = Q / A = 0.7 / 0.19635 = 3.56 fps.
Calculate Reynolds number: R = V D/ ν = 3.56 × 0.5 / (1.0 × 10-3) = 1780.
Since R < 3000, the flow is laminar. The Hagen-Poiseuille equation applies.
hL = 128 ν L Q / (g π D4)
hL / L = 128 × 1.0 × 10 -3 × 0.7 / (32.2 × 3.1416 × 0.5 4 )
hL / L = 0.01417 ≅ 0.0142
- D = 0.3 m
Q = 60 L/s = 0.06 m3/s
V = Q / [(π/4) D2] = 0.06 / (0.7854 × 0.3 2 ) = 0.849 m/s
For T = 15o, ν = 1.14 × 10-6 m2/s
Reynolds number: R = VD / ν = 0.849 × 0.3 / (1.14 × 10-6) = 223,421
From Fig. 5-5: ks / D = 0.0009
From Fig. 5-4: f = 0.0195
hf = f (2000/D) V2/(2g) = 0.0195 × (2000/0.3) [(0.849) 2/(2 × 9.81)]
hf = 4.77 m.
- ν = 1.0 × 10-6 m2/s
D = 0.2 m.
From Fig. 5-5: ks / D = 0.00065
(D3/2/ν) (2ghf /L)1/2 = [0.23/2 /(1.0 × 10 -6 )]
[(2) (9.81) (0.01)]1/2 = 39,618
From Fig. 5-4: f = 0.019
V = [ (hf/L) 2g D / f ]1/2 = [(0.01) (2) (9.81) (0.2) / 0.0195 ]1/2 = 1.44 m/s
Q = VA = V (π/4) D2 = 1.44 (3.1416/4) (0.2)2 = 0.045 m3/s.
Q = 45 L/s.