A Francis turbine is a water-powered machine used in many hydroelectric dams and power stations. It converts the energy of high-pressure flowing water into spinning motion, which then drives an electric generator. It is called the most common hydro turbine because it works well over a wide range of water heights and flow rates.
Understanding it connects fluid pressure, energy conservation, torque, and renewable electricity generation.
Key Facts
- Hydropower input power is P = rho g Q H, where rho is water density, Q is flow rate, and H is hydraulic head.
- Turbine output power is Pout = eta rho g Q H, where eta is efficiency.
- A Francis turbine is a reaction turbine, so pressure changes occur as water passes through the runner.
- Guide vanes control the flow angle and flow rate entering the runner blades.
- Torque and angular speed determine shaft power: P = tau omega.
- The draft tube slows exiting water and helps recover pressure energy after the runner.
Vocabulary
- Francis turbine
- A Francis turbine is a reaction water turbine that uses both pressure and flow direction changes to spin a runner.
- Runner
- The runner is the rotating wheel with curved blades that receives energy from the moving water.
- Spiral casing
- The spiral casing is a curved housing that distributes pressurized water evenly around the runner.
- Guide vanes
- Guide vanes are adjustable blades that direct and regulate water entering the runner.
- Draft tube
- The draft tube is the expanding outlet passage that slows water after the runner and recovers useful pressure.
Common Mistakes to Avoid
- Treating a Francis turbine as only an impulse turbine is wrong because water pressure changes inside the runner and contributes to energy transfer.
- Ignoring hydraulic head is wrong because the available power depends strongly on H in P = rho g Q H.
- Assuming more flow always means better operation is wrong because turbines have design flow ranges and efficiency can drop when guide vane settings are poor.
- Forgetting efficiency in power calculations is wrong because real turbines lose energy to turbulence, friction, leakage, and mechanical losses.
Practice Questions
- 1 A Francis turbine receives water with Q = 12 m^3/s and H = 45 m. Using rho = 1000 kg/m^3 and g = 9.8 m/s^2, calculate the hydraulic input power.
- 2 If the turbine in the previous question operates at eta = 0.90, calculate the mechanical output power delivered to the shaft.
- 3 Explain why the spiral casing becomes smaller as it wraps around the runner, and describe how this helps the runner receive water evenly.