Question

The Ritsem power plant at Stora Sjöfallet in the Luleå river is one of Sweden's northernmost hydropower plants. In the box below are some facts about the power plant, use these facts to answer the following questions.


Ritsem facts
Energy source: Hydropower
Country: Sweden
Average annual electricity generation: 481 GWh
(1Wh = 3600J)
River / river: Lule river
Turbine type: Francis
Fall Height (m): 173
Water flow (m3 / s): 240
Vattenfall's ownership interest: 100%












How large is the total power supplied to the waterworks turbines if all the location energy is converted to movement energy
Assume that the power plant is in continuous operation nine months a year
Calculate the efficiency of the power plant

Answer 1

The power of the falling water is

$$P=Q\rho gh.$$

The energy that this power produces:

$$E=Pt=Q\rho ght.$$

The time t here is the time that the power plant works: 9 months a year, every month has 365/12 days, every day has 24 hours, every hour has 3600 seconds:

$$t=9\cdot365/12\cdot24\cdot3600=23652000\text{ s}.$$

The efficiency is how much of the total energy (above) turns into generated electrical energy:

$$\eta=\frac{E_E}{E}\cdot100\%\\\space\\ \eta=\frac{481\cdot10^9\cdot3600}{240\cdot1000\cdot9.8\cdot173\cdot23652000}\cdot100\%=18\%.$$