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Micro-Hydro Penstock Sizing — Head Loss, Power, and Velocity

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Inputs

Flow rate, Q		X
Gross head, H_gross		X
Penstock diameter, D		X
Penstock length, L		X
Pipe roughness, e (See notes)		X
Junction (or “minor”) loss coefficient, k_m (See notes)		X
Kinematic viscosity, ν, in m²/s (1E-6 for water near 20°C)		X
Plant efficiency, η (0–1)		X

Results

Head Loss: Total penstock loss h_L = h_f + h_m, where h_f = f(L/D)(v²/2g) is Darcy-Weisbach friction loss and h_m = k_m·v²/2g covers entrance, bends, and valves. Net head H_net = H_gross − h_L.
Velocity: Target 1–3 m/s. Below 1 m/s over-sizes the pipe for the flow; above 3 m/s increases friction losses and water hammer risk.
Head Loss Target: Penstock losses below 10% of gross head are generally economic. The optimal trade-off between pipe cost and lost power often falls around 4–6% for high-value electricity sites.
Junction (Point) Losses k_m: These losses occur at pipe junctions, entrances, bends, and valves — the term “minor” is conventional but misleading; in a short penstock they can equal or exceed friction losses. Typical k values: sharp intake entrance 0.5, each 45° bend 0.2–0.3, gate valve (fully open) 0.1, butterfly valve 0.2. Sum all fittings for the total k_m. Default 1.5 assumes one entrance and two bends.
Pipe Roughness e: Typical absolute roughness: steel (new) 0.046 mm, steel (used) 0.15 mm, HDPE 0.003 mm, PVC/uPVC 0.0015 mm, concrete 0.3–3 mm. HDPE is common for small micro-hydro penstocks.