Hydropower converts the gravitational potential and kinetic energy of water into electricity. It is one of the most mature renewable technologies and can provide energy, operating reserves, frequency regulation, irrigation benefits, flood control, and, in some cases, navigation. Marine energy extends the same physical idea to seawater: tides, waves, ocean currents, salinity gradients, and ocean-temperature differences provide energy resources, although most commercial development currently focuses on tidal and wave systems.

Hydropower is not automatically sustainable. Dams can alter sediment transport, fish migration, river temperature, downstream flows, and communities. Marine devices can affect navigation, fisheries, marine mammals, benthic habitats, and coastal processes. Therefore, engineering design must combine fluid mechanics, electrical generation, economics, environmental assessment, safety, and regulatory compliance.

Learning objectives

1. Hydraulic energy fundamentals

1.1 Head and discharge

The potential energy available from water depends primarily on the difference in elevation between the upstream water surface and the turbine outlet. This elevation difference is the gross head, H_g. Not all of it reaches the turbine because of friction and local losses in intakes, tunnels, valves, and penstocks. The net head, H_n, is therefore:

where h_L is the total head loss, measured in metres of water. The equation assumes that pressure and velocity changes between the selected upstream and downstream reference sections have either been included in the head definition or are negligible. More generally, the steady-flow energy equation must be used when velocity and pressure terms are significant.

where Q is discharge in m³/s, A is flow area in m², and v is mean velocity in m/s. This relation assumes approximately one-dimensional mean flow through the selected section.

where P_h is hydraulic power in watts, ρ is water density in kg/m³, g is gravitational acceleration in m/s², Q is discharge in m³/s, and H_n is net head in m. For fresh water, ρ is commonly approximated as 1000 kg/m³; seawater is commonly about 1025 kg/m³, but site temperature and salinity should be considered for accurate work.

where η_o is overall efficiency, including hydraulic, mechanical, generator, and electrical losses. This equation is applicable to steady or representative operating conditions. For variable flow, annual energy requires integration or time-series simulation rather than multiplication by rated power.

Worked example: preliminary hydropower output

A run-of-river site has Q = 18 m³/s, gross head H_g = 42 m, and estimated losses of 3.5 m. If overall efficiency is 89%, estimate electrical power.

The estimated output is therefore approximately 6.1 MW. The value is a design-point estimate; seasonal discharge, environmental minimum flow, generator limits, and grid curtailment determine actual annual energy.

1.2 Energy, capacity factor, and flow duration

where E_year is annual energy, P_r is rated power, CF is capacity factor, and t_year is the number of hours in a year. A capacity factor is not an efficiency; it is the ratio of actual annual generation to generation at continuous rated output.

For hydropower, a flow-duration curve ranks daily or hourly discharges from highest to lowest. It helps engineers select turbine capacity. Oversizing increases capital cost and may leave equipment underused, while undersizing spills potentially valuable water during high-flow periods. Environmental release requirements must be included in the available-flow analysis.

2. Turbine principles and classification

2.1 Impulse turbines

In an impulse turbine, the available pressure head is converted almost entirely into jet velocity before water reaches the runner. The runner operates approximately at atmospheric pressure, and the water changes momentum as it passes through buckets or blades. The principal example is the Pelton turbine, which is suitable for high head and relatively low discharge. Turgo and cross-flow turbines are other impulse-type designs.

A Pelton unit uses one or more nozzles. A needle or spear regulates jet flow, while a deflector can divert the jet rapidly during load rejection. The runner speed is governed by the jet velocity and bucket geometry. Impulse turbines are attractive where steep terrain produces high head, because they tolerate large elevation differences without requiring a fully pressurized runner casing.

Cross-flow turbines pass water through a cylindrical runner twice. They are mechanically simple and can operate over a broad flow range, making them useful for small hydropower, although peak efficiency is generally lower than that of a well-designed Francis or Pelton turbine.

2.2 Reaction turbines

A reaction turbine develops power from both pressure change and velocity change through the runner. The runner is fully immersed, and a casing and draft tube guide the flow. Francis turbines are widely used for medium head and medium discharge. Kaplan and propeller turbines are suited to low head and high discharge; Kaplan blades and guide vanes can be adjustable, allowing good efficiency over varying flow.

A reaction turbine requires careful control of pressure distribution. If local pressure falls below the water vapour pressure, cavitation may occur. The draft tube recovers part of the exit kinetic energy by expanding the flow and converting velocity head into pressure head.

Feature	Impulse turbine	Reaction turbine
Main energy conversion	Head converted to jet velocity before runner	Pressure and velocity change in runner
Runner pressure	Approximately atmospheric	Below or above atmospheric locally
Typical examples	Pelton, Turgo, cross-flow	Francis, Kaplan, propeller
Typical site	High head, lower flow	Medium/low head, larger flow
Cavitation sensitivity	Generally lower	Often significant
Major equipment	Nozzle and free jet	Casing, runner, draft tube

2.3 Specific speed and selection

Specific speed is a dimensionless or convention-dependent index used to compare geometrically similar turbines. Its exact numerical form depends on the unit system and definition adopted, so manufacturers’ and standards-based definitions must not be mixed. Conceptually, increasing flow and reducing head tend to favour reaction turbines, while high head and lower flow tend to favour impulse turbines.

Preliminary selection must consider more than head and flow: sediment concentration, debris, load variation, grid requirements, maintenance capability, transport access, seasonal water availability, and environmental releases can dominate the final decision.

3. Penstocks, hydraulic losses, and water hammer

A penstock conveys pressurized water from the intake or forebay to the turbine. Its diameter is a compromise. A larger diameter reduces friction losses but increases material, excavation, and support cost. A smaller diameter is cheaper but causes greater energy loss and may create unacceptable transient pressures.

For steady full-pipe flow, friction loss can be estimated with the Darcy–Weisbach equation:

where h_f is friction head loss in m, f is the Darcy friction factor, L is pipe length in m, D is internal diameter in m, v is mean velocity in m/s, and g is gravitational acceleration. The equation applies to pressurized flow; f depends on Reynolds number and relative roughness. Local losses are commonly represented by:

where h_m is a minor-loss head and K is a dimensionless loss coefficient for a bend, entrance, valve, contraction, or other fitting. Total loss is the sum of distributed and local losses.

Rapid change in flow, such as sudden turbine closure, creates water hammer. The idealized pressure-wave relation is:

where ∆p is pressure change in Pa, a is pressure-wave speed in m/s, and ∆v is change in water velocity in m/s. Real systems require transient simulation because pipe elasticity, water compressibility, valve motion, surge tanks, air chambers, and wave reflections affect the result. Protection may include controlled wicket-gate closure, surge tanks, relief valves, and robust anchorage.

4. Cavitation and turbine performance

Cavitation begins when local absolute pressure approaches or falls below the vapour pressure of water. Vapour bubbles subsequently collapse in higher-pressure regions, causing noise, vibration, surface pitting, efficiency loss, and possible structural damage.

where σ is the cavitation coefficient, H_a is atmospheric pressure head at the site, H_v is vapour-pressure head, H_s is turbine setting head relative to the downstream reference (with sign convention defined by the design standard), and H_n is net head. Because sign conventions vary, the adopted turbine standard and datum must be stated. A turbine must operate above its critical cavitation coefficient with an appropriate safety margin.

Cavitation control includes correct turbine setting, adequate submergence, smooth blade surfaces, proper draft-tube design, avoidance of excessive local velocity, and regular inspection. Atmospheric pressure decreases at high altitude, making cavitation more likely.

5. Pumped-storage hydropower

Pumped storage is an energy-storage system rather than a primary energy source. During periods of surplus electricity, pumps move water from a lower reservoir to an upper reservoir. During high demand, the water flows back through turbines. Reversible pump-turbines are common, although separate pumps and turbines may be used.

where E_s is delivered electrical energy in J, V is stored water volume in m³, H is effective elevation difference in m, and η_rt is round-trip efficiency. The equation is an estimate and assumes that η_rt represents all pumping, hydraulic, turbine, generator, and electrical losses. Usable storage is reduced by dead storage, operating limits, evaporation, leakage, and environmental requirements.

Pumped storage provides fast response, peak shifting, frequency control, spinning reserve, and support for variable wind and solar generation. Its limitations include high capital cost, geographical constraints, ecological effects of reservoirs, and long permitting periods. Closed-loop systems may reduce river impacts but still require land, water, and geological suitability.

6. Small and micro hydropower

Definitions vary by jurisdiction, but small hydropower generally refers to projects below a specified capacity threshold, while mini-, micro-, and pico-hydropower denote progressively smaller systems. The classification is administrative rather than a universal physical law.

Small systems may be run-of-river, canal-based, or associated with existing dams and water-supply infrastructure. Their advantages include modular construction, local supply, reduced transmission distance, and potential rural electrification. Their risks include seasonal energy shortages, difficult access, inadequate maintenance, debris blockage, fish passage impacts, and high cost per installed kilowatt for remote civil works.

A sound feasibility study includes hydrology, topographic survey, geotechnical investigation, intake and sediment management, environmental flow, grid or isolated-load analysis, community consultation, lifecycle cost, and decommissioning provisions. Existing irrigation drops and water-treatment outfalls can offer lower-impact opportunities, but water rights and operational priorities remain decisive.

7. Marine energy technologies

7.1 Tidal-range systems

Tidal-range systems exploit the difference in water level between high and low tide. A barrage or lagoon stores water and passes it through turbines during ebb generation, flood generation, or both. The available ideal energy for a basin of area A and tidal range R is approximately proportional to:

This simplified expression assumes a suitable basin geometry and idealized single-cycle operation. Real output is lower because of turbine efficiency, hydraulic losses, ecological operating constraints, and the changing head during generation. Barrages can provide predictable generation but may alter sediment transport, tidal flats, fish habitat, and estuarine salinity.

7.2 Tidal-stream and ocean-current turbines

Tidal-stream devices extract kinetic energy from moving water, using horizontal-axis or vertical-axis rotors, ducted turbines, or oscillating hydrofoils. The extracted power is estimated by:

where P is electrical power in W, A is swept area in m², v is current velocity in m/s, C_p is the power coefficient, and η represents mechanical and electrical efficiency. The cubic dependence on velocity makes accurate resource measurement essential. As with wind turbines, C_p is limited by fluid-dynamic constraints and practical losses; it cannot be arbitrarily large.

The marine environment imposes special demands: corrosion, biofouling, fatigue, storm loading, subsea cables, retrieval logistics, and complex foundations. Tidal currents are highly predictable, but their direction reverses and peak velocity may occur for only part of each cycle.

7.3 Wave energy converters

Wave-energy devices convert oscillatory motion or pressure into electricity. Major families include point absorbers, attenuators, oscillating-water columns, overtopping devices, and oscillating surge converters. Wave power depends on wave height, period, spectrum, direction, and water depth. For an idealized regular deep-water wave, energy flux scales approximately with the square of wave height and increases with wave period; practical design requires spectral resource assessment rather than a single regular-wave formula.

Wave devices face severe survivability requirements. A device must capture energy during ordinary conditions but survive extreme storms, often by submergence, latching, shutdown, or load shedding. Reliability and maintenance access are central commercial challenges.

7.4 Ocean thermal and salinity-gradient energy

Ocean thermal energy conversion uses the temperature difference between warm surface water and cold deep water. It can provide continuous generation in suitable tropical regions, but the small temperature difference requires large water flows and heat exchangers. Salinity-gradient systems exploit the chemical-potential difference between fresh and seawater, generally through membranes. These technologies remain less mature than tidal and wave systems and face membrane fouling, pumping demand, cost, and ecological concerns.

Technology	Resource	Predictability	Main engineering challenge
Tidal range	Water-level difference	High	Estuarine and sediment impacts
Tidal stream	Current velocity	High	Subsea installation and fatigue
Wave energy	Surface-wave motion	Moderate	Storm survival and reliability
Ocean thermal	Temperature difference	High at suitable sites	Large seawater flow and heat exchange
Salinity gradient	Salt-concentration difference	High	Membrane cost and fouling

8. Site assessment and sustainability

A technically attractive site may be unsuitable after environmental or social assessment. Hydropower screening should examine catchment hydrology, extreme floods and droughts, sediment yield, geology, seismicity, access, transmission, land ownership, and competing water uses. Marine screening should examine bathymetry, seabed geology, wave and current statistics, shipping lanes, fishing activity, protected habitats, military zones, cable routes, and port access.

Environmental-flow design maintains a variable downstream flow regime rather than simply releasing a constant minimum. Fish ladders, bypass channels, fish-friendly turbines, sediment sluicing, selective withdrawal, and adaptive reservoir operation can reduce impacts, but none is universally effective. Cumulative effects from multiple dams or marine arrays must be assessed at basin or coastal-system scale.

Life-cycle assessment should include construction materials, excavation, transport, operation, maintenance, replacement, emissions, and end-of-life removal. Governance requires transparent consultation, legally valid water rights or seabed leases, navigation and safety plans, monitoring, benefit sharing where appropriate, and a credible decommissioning strategy.

9. Applied case: illustrative run-of-river project

Background

Consider an illustrative 25 MW run-of-river project in a mountainous catchment. The preliminary design head is 76 m, and the design discharge is 38 m³/s. A Francis turbine is initially proposed because the site lies in a medium-head, medium-flow range.

Problem

The developer must determine whether the project can meet its output target without excessive penstock losses, unacceptable cavitation, or unacceptable ecological effects.

Analysis

Suppose the gross head is 76 m, total hydraulic losses are estimated at 6 m, and overall efficiency is 91%. The net head is 70 m. Estimated electrical output is:

Thus, the proposed 25 MW rating would not be reached at the stated design point. The developer could increase discharge, reduce losses, select a larger unit, or accept a lower rating. Increasing discharge may reduce environmental compliance or require larger civil works.

This loss is much larger than the preliminary 6 m total-loss allowance. The assumed penstock is therefore hydraulically and economically problematic. A larger diameter, smoother lining, shorter alignment, or revised flow must be investigated. The calculation also demonstrates why penstock design cannot be separated from turbine selection.

Approach and solution

The project team should develop a flow-duration curve, reserve an environmental flow, model seasonal generation, and perform a diameter-cost optimization. A transient model should assess water hammer during load rejection. A cavitation check should use site atmospheric pressure, turbine setting, vapour pressure, and the manufacturer’s critical coefficient. Environmental studies should address sediment continuity, fish passage, downstream temperature, and community water use.

Outcome and learning points

The preliminary design does not justify final investment, but it identifies two important risks: insufficient rated output and excessive penstock loss. Iterative hydraulic, civil, environmental, and economic design is essential. A turbine selected only from a head-discharge chart may perform poorly when real pipe losses, seasonal flows, and environmental constraints are included.

10. Contemporary developments and professional practice

Digital hydraulic models, remote sensing, acoustic Doppler current profilers, digital twins, and condition-monitoring systems improve resource assessment and predictive maintenance. Machine-learning tools can identify abnormal vibration or forecast inflow, but their predictions must be validated against physical measurements and should not replace engineering safety margins.

Modern projects increasingly use modular equipment, fish-safe turbine geometries, recyclable composite materials, corrosion-resistant coatings, subsea inspection robots, and hybrid operation with batteries or solar power. The professional engineer must maintain traceable assumptions, uncertainty ranges, independent design review, cybersecurity controls for digital systems, and clear responsibility for automated decisions.

Chapter Summary

Hydropower output is governed by water density, gravity, discharge, net hydraulic head, and overall efficiency. Net head is gross head less hydraulic losses, and reliable design requires flow-duration analysis rather than reliance on a single design flow. Impulse turbines convert pressure head into a free jet before the runner and are commonly suited to high-head sites. Reaction turbines operate with pressure change through an immersed runner and are commonly suited to medium- and low-head applications, but they require careful cavitation and draft-tube design.

Penstocks impose friction and local losses and must be designed together with turbine capacity, economics, and transient-pressure protection. Pumped storage shifts energy in time and provides valuable grid flexibility, although it has geographical, environmental, and cost constraints. Small hydropower can support local energy services but requires rigorous hydrology, maintenance, environmental-flow, and community analysis.

Marine energy includes tidal range, tidal stream, wave, ocean thermal, and salinity-gradient systems. Tidal resources are highly predictable, while wave and other technologies face greater uncertainty or lower commercial maturity. Across all technologies, sustainable development requires life-cycle assessment, ecological monitoring, stakeholder participation, regulatory compliance, safety engineering, and responsible decommissioning.

Key Terms

Reaction turbine: Turbine in which pressure and velocity change through the runner.

Draft tube: Expanding passage that recovers exit velocity head from a reaction turbine.

Cavitation: Formation and collapse of vapour bubbles caused by low local pressure.

Flow-duration curve: Curve ranking flow rates by the percentage of time they are equalled or exceeded.

Pumped storage: Hydropower storage that pumps water uphill during low demand and generates during high demand.

Environmental flow: Water regime maintained to support downstream ecosystem functions.

Capacity factor: Actual annual generation divided by maximum possible generation at rated output.

Power coefficient: Fraction of kinetic-fluid power captured by a device before other losses.

Life-cycle assessment: Evaluation of environmental impacts over a technology’s complete life.

Review Questions

Short Answer Questions

Long Answer Questions

Analytical / Application Questions

Multiple Choice Questions with Answers

Question 1

Question 2

Which turbine is generally most suitable for a high-head, relatively low-discharge site?

Question 3

A hydropower site has Q = 10 m³/s, net head = 20 m, and overall efficiency = 0.90. Using ρ = 1000 kg/m³ and g = 9.81 m/s², the approximate electrical power is:

Question 4

Correct Answer: B. Local absolute pressure falling near or below vapour pressure

Question 5

Question 6

Correct Answer: B. To store electrical energy by moving water between reservoirs

Question 7

Which marine technology extracts energy primarily from the kinetic energy of moving seawater?

Question 8

If current velocity doubles in the idealized tidal-stream power relation, with all other variables unchanged, power changes by approximately:

Question 9

Which factor is especially important when sizing a hydropower turbine for annual generation?

Question 10

B. It considers energy, safety, ecology, communities, lifecycle impacts, and regulation

Correct Answer: B. It considers energy, safety, ecology, communities, lifecycle impacts, and regulation

Chapter 6 Hydropower and Marine Energy

Hydropower and Marine Energy

Introduction and context