Hydroelectric Plant Model — Steady Flow & Power Analysis

Reservoir & Conduit

Gross head H220.0 m

5300600 m

Penstock diameter D3.20 m

0.54.258.0 m

Penstock length L640 m

5015253000 m

Wall roughness ε0.600 mm

drawnwelded steelcorroded

Minor loss coeff. ΣK1.10

0intake+bends5.0

ΣK covers intake, trashrack, bends, inlet valve and draft-tube exit. Applied to the penstock velocity head v²/2g.

Working Fluid

Water density ρ998.2 kg/m³

950fresh 9981200 silt

Dynamic viscosity μ1.002 mPa·s

80 °C20 °C0 °C

Kinematic viscosity ν = μ/ρ feeds the Reynolds number and therefore the friction factor.

Flow Control

Discharge setpoint Q45.0 m³/s

0125250 m³/s

Discharge is set by wicket-gate position. The delivered flow follows the setpoint through the rigid water-column time constant T_w = LQ / (gA·H_n).

Machine

Turbine efficiency η_t90.0 %

406896 %

Generator efficiency η_g97.2 %

859299 %

Grid frequency

Synchronous speed n = 120f / p. Pole count is selected as the fastest standard machine keeping specific speed within the Francis range.

View

Keys: space pause · g grade lines · p profile · r reset.

Power Output

Electrical power P_e

0.00MW

overall η = 0.0 %

Shaft power

0.00MW

η_t · P_h

Hydraulic power

0.00MW

ρgQH_n

Discharge

0.0m³/s

v = 0.00 m/s

Net head

0.0m

loss 0.0 m

Electrical Energy

Elapsed generation	0.000 MWh
At current output — hour	0.00 MWh
At current output — day	0.0 MWh
Annualised (8760 h)	0 GWh

Head Budget

Gross head H	—
Friction loss h_f	—
Minor losses h_m	—
Total head loss h_L	—
Loss fraction h_L/H	—
Impulse setting h_s	—
Net head H_n	—
Velocity head v²/2g	—
Conduit efficiency	—

Penstock Hydraulics

Flow area A	—
Mean velocity v	—
Reynolds number Re	—
Relative roughness ε/D	—
Friction factor f	—
Flow regime	—
Water column T_w	—
Mass flow ṁ	—
Conduit capacity Q_max	—
Horizontal run (plan)	—
Slope · level reach	—

Turbine Inlet Pressure

Piezometric head	—
Static pressure (gauge)	—
Static pressure (abs)	—
Required wall t_req	—

t_req = pD/2σ + c, with σ_allow = 120 MPa and c = 2 mm corrosion allowance. Static duty only — no surge allowance included.

Machine Selection

Specific speed N_s	—
Indicated type	—
Synchronous speed	—
Pole count	—
Shaft torque	—

Design Checks

Governing Equations

A = πD²/4 v = Q/A

Re = ρvD/μ

1/√f = −2 log₁₀(ε/3.7D + 2.51/Re√f)

h_f = f (L/D) v²/2g

h_m = ΣK · v²/2g

H_n = H − h_f − h_m

P_h = ρ g Q H_n

P_e = η_t η_g ρ g Q H_n

N_s = n √P_kW / H_n^1.25

DISCHARGE Q — m³/s

TOTAL HEAD LOSS — m

ELECTRICAL POWER — MW

CUMULATIVE ENERGY — MWh

HYDROELECTRIC PLANT MODEL / steady flow & power analysis