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Water turbine

A water turbine is a rotary engine that takes energy from moving water.

Water turbines were developed in the nineteenth century and were widely used for industrial power prior to electrical grids. Now they are mostly used for electric power generation. They harness a clean and renewable energy source.




Water wheels have been used for thousands of years for industrial power. Their main shortcoming is size, which limits the flow rate and head that can be harnessed. They also tend to rotate slower than the machines they power.

The migration from water wheels to modern turbines took about one hundred years. Development occurred during the Industrial revolution, using scientific principals and methods. They also made extensive use of new materials and manufacturing methods developed at the time.

The word turbine was coined by the French engineer Claude Bourdin in the early 19th century and is derived from the Latin word for "whirling" or a "vortex". The main difference between early water turbines and water wheels is a swirl component of the water which passes energy to a spinning rotor. This additional component of motion allowed the turbine to be smaller than a water wheel of the same power. They could process more water by spinning faster and could harness much greater heads. (Later, impulse turbines were developed which didn't use swirl).

Time line

Ján Andrej Segner developed a reactive water turbine in the mid 1700's. It had a horizontal axis and was a precursor to modern water turbines. It is a very simple machine that is still produced today for use in small hydro sites. Segner worked with Euler on some of the early mathematical theories of turbine design.

A Francis turbine runner being installed at the Grand Coulee Dam
A Francis turbine runner being installed at the Grand Coulee Dam

In 1820, Jean V. Poncelet developed an inward-flow turbine.

In 1826 Bénoit Fourneyron developed an outward-flow turbine. This was an efficient machine (~80%) that sent water through a runner with blades curved in one dimension. The stationary outlet also had curved guides.

In 1844 Uriah A. Boyden developed an outward flow turbine that improved on the performance of the Fourneyron turbine. Its runner shape was similar to that of a Francis turbine.

In 1849, James B. Francis improved the inward flow reaction turbine to over 90% efficiency. He also conducted sophisticated tests and developed engineering methods for water turbine design. The Francis turbine, named for him, is the first modern water turbine. It is still the most widely used water turbine in the world today.

Inward flow water turbines have a better mechanical arrangement and all modern reaction water turbines are of this design. Also, as the swirling mass of water spins into a tighter rotation, it tries to speed up to conserve energy. This property acts on the runner, in addition to the water's falling weight and swirling motion. Water pressure decreases to zero as it passes through the turbine blades and gives up its energy.

Around 1913, Victor Kaplan created the Kaplan turbine, a propeller-type machine. It was an evolution of the Francis turbine but revolutionized the ability to develop low-head hydro sites.

A New concept

All common water machines until the late 19th century (including water wheels) were reaction machines; water's pressure head acted on the machine and produced work. A reaction turbine needs to fully contain the water during energy transfer.

In 1866, California millwright Samuel Knight invented a machine that worked off a completely different concept1,2. Inspired by the high pressure jet systems used in hydraulic mining in the gold fields, Knight developed a bucketed wheel which captured the energy of a free jet, which had converted a typically high head (hundreds of vertical feet in a pipe or "penstock")of water to kinetic energy. This is called an impulse or tangential turbine. The water's velocity is roughly twice the velocity of the bucket, does a u-turn in the bucket and drops out at 0 velocity.

In 1879, Lester Pelton, experimenting with a Knight Wheel, developed a double bucket design, which exhausted the water to the side, eliminating some energy loss of the Knight wheel which exhausted some water back against the center of the wheel. In about 1895, William Doble improved on Pelton's half-cylindrical bucket form with an eliptical bucket with a cut in it to allow the jet to more cleanly enter the bucket. This is the modern form of the impulse turbine which today achieves up to 92% efficiency. Pelton had been quite an effective promotor of his design and although Doble took over the Pelton company he did not change the name to Doble because it had brandname recognition. The impulse turbine is thus, usually inaccurately, called the "Pelton Wheel."

Turgo turbine and Crossflow turbines were later impulse designs.

Theory of operation

Flowing water is directed on to the blades of a turbine runner, creating a force on the blades. Since the runner is spinning, the force acts through a distance (force acting through a distance is the definition of work). In this way, energy is transferred from the water flow to the turbine.

Water turbines are divided into two groups; reaction turbines and impulse turbines.

The precise shape of water turbine, whatever its design, is driven by the supply pressure of water.

Reaction turbines

Reaction turbines are acted on by water, which changes pressure as it moves through the turbine and gives up its energy. They must be encased to contain the water pressure (or suction), or they must be fully submerged in the water flow.

Newton's third law describes the transfer of energy for reaction turbines.

Most water turbines in use are reaction turbines. They are used in low and medium head applications.

Impulse turbines

Impulse turbines change the velocity of a water jet. The jet impinges on the turbine's curved blades which reverse the flow. The resulting change in momentum (impulse) causes a force on the turbine blades. Since the turbine is spinning, the force acts through a distance (work) and the diverted water flow is left with diminished energy.

Prior to hitting the turbine blades, the water's pressure (potential energy) is converted to kinetic energy by a nozzle and focused on the turbine. No pressure change occurs at the turbine blades, and the turbine doesn't require a housing for operation.

Newton's second law describes the transfer of energy for impulse turbines.

Impulse turbines are most often used in very high head applications.


Water is very heavy and it's flow energetic. The power available in dammed water is;

P=\eta\cdot\rho\cdot g\cdot h\cdot\dot V


  • P = Power( J/s or Watts)
  • η = turbine efficiency
  • ρ = density of water (kg/m3)
  • g = acceleration of gravity (9.8 m/s2)
  • h = head (m, this is the difference in height between the inlet and outlet water surfaces)
  • \dot V= flow rate (m3/s)

Pumped storage

Some water turbines are designed for Pumped storage hydroelectricity. They can reverse flow and operate as a pump to fill a high reservoir during off-peak electrical hours, and then revert to a turbine for power generation during peak electrical demand. This type of turbine is similar to the francis in design.


Large modern water turbines operate at mechanical efficiencies greater than 90% (not to be confused with thermodynamic efficiency).

Types of water turbines

Reaction turbines:

Impulse turbines:

Design and application

Turbine selection is based mostly on the available water head, and less so on the available flow rate. In general, impulse turbines are used for high head sites, and reaction turbines are used for low head sites.

Typical range of heads

  • Kaplan           2 < H < 40   (H = head in meters)
  • Francis         10 < H < 350
  • Pelton           50 < H < 1300
  • Michell-Banki  3 < H < 250
  • Turgo            50 < H < 250

Specific speed

The specific speed, ns , of a turbine characterizes the turbine's shape in a way that is not related to its size. This allows a new turbine design to be scaled from an existing design of known performance. The specific speed is also the main criteria for matching a specific hydro site with the correct turbine type.

The specific speed of a turbine can also be defined as the speed of an ideal, geometrically similar turbine, which yields one unit of discharge for one unit of head.

The specific speed of a turbine is given by the manufacturer (along with other ratings) and will always refer to the point of maximum efficiency. This allows accurate calculations to be made of the turbine's performance for a range heads and flows.

n_s=n\sqrt{P}/H^{5/4} (dimensioned parameter), n = rpm

N_s=\frac{\Omega\sqrt{P/p}}{gH^{5/4}} (dimensionless parameter),

Ω = angular velocity (radians/second)

Example; Given a flow and head for a specific hydro site, and the rpm requirement of the generator, calculate the specific speed. The result is the main criteria for turbine selection.

The specific speed is also the starting point for analytical design of a new turbine. Once the desired specific speed is known, basic dimensions of the turbine parts can be easily be calculated.

Runaway speed

The runaway speed of a water turbine is its speed at full flow, and no shaft load. The turbine will be designed to survive the mechanical forces of this speed. The manufacturer will supply the runaway speed rating.

Environmental impact

Water turbines have positive and negative impacts on the environment.

They are one of the cleanest producers of power, replacing the burning of fossil fuels and eliminating nuclear waste. They use a renewable energy source and are designed to operate for decades. They produce significant amounts of the world's electrical supply.

On the other hand there are some negative consequences; by their nature, water turbines interrupt the natural ecology of rivers, killing fish and stopping migrations. Native American Indian tribes in the Pacific Northwest had livelihoods built around salmon fishing. Aggressive dam building destroyed their way of life.

See also


  1. W. A. Doble, The Tangential Water Wheel, Transactions of the American Institute of Mining Engineers, Vol. XXIX, 1899.
  2. W. F. Durrand, The Pelton Water Wheel, Stanford University, Mechanical Engineering, 1939.

External links

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