⚡ Pelton / Francis / Kaplan Turbine Calculator
Select turbine type, compute specific speed, estimate runner diameter, efficiency, shaft power, and cavitation parameters using Euler turbine equation and empirical efficiency envelopes.
🔄 Turbine Schematic
📝 Configuration
Key Equations:
Phydro = ρgQH
Ns = N√PkW/H5/4
Nq = N√Q/H3/4
U = ϕ√(2gH); D = 2U/ω
Pshaft = η Phydro
Phydro = ρgQH
Ns = N√PkW/H5/4
Nq = N√Q/H3/4
U = ϕ√(2gH); D = 2U/ω
Pshaft = η Phydro
📊 Results
Configure inputs and click Design to view results.
📘 Methodology
Specific Speed
The metric specific speed Ns = N√P/H5/4 determines the optimal turbine type: Pelton for low Ns (<60), Francis for medium (60–300), Kaplan for high (>300). Nq uses flow instead of power.
Euler Equation
The peripheral speed U relates to runner diameter through U = ωD/2. A flow coefficient ϕ scales U relative to the spouting velocity √(2gH). Runner diameter follows from the chosen speed.
Assumptions
- Empirical Gaussian efficiency envelopes vs Ns.
- Simplified cavitation sigma from Nq correlation.
- Single-jet Pelton; no multi-jet correction.
- Constant head and flow (design point).