Head-discharge relation in online pump-pipe system calculator, Victor Miguel Ponce, Thais H. Abissamra, Isabel Consoli, San Diego State University

online_pump_pipe_system: Operating discharge and head in a pump-pipe system

Definition sketch of a pump-pipe system

Conservation of energy:
E₁ + h_p = E₂ + [V²/(2g)] [K_e + ∑K_b + K_E + f(L/D)]
h_p = ΔE + [Q²/(2gA²)] [K_e + ∑K_b + K_E + f(L/D)]
h_p = ΔE + [Q²/(2g(πD²/4)²] [K_e + ∑K_b + K_E + f(L/D)]
h_p = ΔE + [16/(2gπ²D⁴)] [K_e + ∑K_b + K_E + f(L/D)] Q²
a = ΔE
b = [16/(2gπ²D⁴)] [K_e + ∑K_b + K_E + f(L/D)]
System head-discharge relation:
h_p = a + b Q²

Type 1 head-discharge relation
Pump head-discharge relation:
H = c - d Q²
System operating discharge:
Q_oper = [(c - a)/(b + d)]^1/2
System operating head:
H_oper = c - d [(c - a)/(b + d)]

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