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Engineering Formula Library

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Electrical Machines
Generator Efficiency
\eta_{gen}\% = (P_{electrical} / P_{mechanical}) \times 100
Electrical Machines
Turbine Efficiency
\eta_{turbine}\% = (P_{shaft} / P_{water}) \times 100
Electrical Machines
Turbine Specific Speed
N_s = N\sqrt{P} / H^{5/4}
Hydropower
Annual Energy Generation
AEG = P_{rated} \times CF \times 8760
Hydropower
Hydraulic (Water) Power Input
P_{water} = \rho \times g \times Q \times H
Hydropower
Hydropower Output Power
P = (\rho \times g \times Q \times H \times \eta) / 1000
Hydropower
Net Head
H_{net} = H_{gross} - H_{losses}
Hydropower
Overall Hydropower Plant Efficiency
\eta_{plant} = \eta_{turbine} \times \eta_{generator} \times \eta_{transformer}
Hydropower
Penstock Flow Velocity
V = Q / (\pi D^2 / 4)
Hydropower
Penstock Friction Head Loss (Darcy-Weisbach)
h_f = f \times (L/D) \times (V^2 / 2g)
Power System Utilization
Annual Load Factor
ALF\% = (Total\ Annual\ Energy / (Peak\ Demand \times 8760)) \times 100
Power System Utilization
Diversity Factor (Definition)
DvF = \Sigma(Individual\ Max\ Demands) / System\ Max\ Demand
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