Q = 50 m3/h or 0.01388888 m3/s
d = 5 cm or 0.05 m
V = Q / A = 0.01388888 / (π/4) 0.052 = 7.07355 m/s
By Haaland equation
1/sqrt(f) = - 1.8 log10 [{(e/d) / 3.7}1.11 + 6.9 / Re]
Re = ρ V d / μ = 1000 * 7.07355 * 0.05 / 1 * 10-3 = 3.53677 * 105
e/d = 0 (for smooth pipe)
1/sqrt(f) = - 1.8 log10 [ 0 + 6.9 / 3.53677 * 105 ]
sqrt(f) = 0.1179584
f = 0.34345
hf = f L V2 / 2 g d
hf = 0.34345 * 140 * 7.073552 / 2 * 9.81 * 0.05
hf = 2452.4344 m
Sharp entrance
h1 = k V2 / 2 g
h1 = 0.5 * 7.073552 / 2 * 9.81
h1 =1.2751 m
2 900 elbow
h2 = n k V2 / 2 g
h2 = 2 * 0.95 * 7.073552 / 2 * 9.81
h2 = 4.84539 m
HL = hf + h1 + h2
HL = 2452.4344 + 1.2751 + 4.84539
HL = 2458.55 m
By bernoulli equation
Pa + 0.5 ρ Va2/2g + ρ g za = Pb + 0.5 ρ Vb2/2g + ρ g zb + ρ g HL
Va = sqrt (2gh) = sqrt (2 * 9.81 * 10) = 14.00714 m/s
za = 0
Pb = 101325 N/m2
zb = 60 m
Pa + 0.5 * 1000 * 14.007142/ 2 * 9.81 + 0 = 101325 + 0.5 * 1000 * 7.073552 / 2 * 9.81 + 1000 * 9.81 * 60 + 1000 * 9.81 * 2458.55
Pa = 24804575.604 N/m2
P1 + Pw = Pa
Pw = ρ g h = 1000 * 9.81 * 10 = 98100 N/m2
P1 = 24804575.604 - 98100
P1 = 24706475.6 N/m2 atm
P1 = 24706475.6 - 101325
P1 = 24605150.6 N/m2 gauge
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