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Solved exercise · level 3 of 5

Waterfall, turbine and generator

Skills: Calculate

Statement

A turbine driving a generator is powered by a 12 m waterfall with a flow of 24 m³/min. The efficiencies of the turbine and the generator are 0.8 and 0.87.

Compute the electrical power delivered by the generator, in kW. (1 m³ of water = 1,000 kg; g = 9.81 N/kg)

h = 12 m · qv = 24 m³/min · ηt = 0.8 · ηg = 0.87

Parametric exercise: the values change with every draw; these are one example.

Guided problem in 4 steps: unknown, formula, units, data, result.

1 hint from Bastaya available in the lab
Solution

Every minute, 24 × 1,000 kg fall 12 m: P₁ = 24 × 1,000 × 9.81 × 12 / 60 = 47.09 kW; P₂ = ηt · P₁ = 37.67 kW; P₃ = ηg · P₂ = 32.77 kW.

Course sheet of the chapter : Power, energy, efficiency

This chapter is covered by the paths: General electricity, ISL-oriented exercises

Other exercises of the chapter

Simulated time00:00:00
Q = I·t-
W = P·t-

Circuit diagram CEI 60617

How does it work?

Each big hole is a circuit node: you push one leg of a component into it. The 4 small holes around it are connected to it: chips and leads plug in there.

  1. Place a component Drag it from the palette: it snaps onto the grid. R rotates it.
  2. Bridge neighbouring holes Pick the jumper chip (or C) and drag on the board: bridged holes become a single node.
  3. Draw a lead For long links and the power supply: from one big hole to another, or to a terminal.
  4. Close the loop The circuit is solved live (Ohm, Kirchhoff) and the diagram follows.

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