Hydroelectric Power Plant
The vertical drop of water in a hydroelectric power plant is 100 m (Figure 7.8). Water flows through the plant and into the lower river at the rate of 500 m^3/s. Discounting viscous losses in the flowing water and the inefficiency of the turbines and generators, how much electrical energy can be produced each second?
Approach
To calculate the amount of electrical energy produced, we recognize that the potential energy of water in the reservoir is converted into kinetic energy as it falls, and, in turn, the water’s kinetic energy is transferred to the rotation of the turbines and generators. We will neglect the water’s relatively small velocity as the level of the reservoir falls and as the water exits the turbines. Those kinetic energy components are small when compared to the overall change in gravitational potential energy of the flowing water. Since no heat is involved, the change in gravitational potential energy balances the work output following Equation (7.10).
Q = W + ΔU (7.10)
As listed in Table 6.1,
Table 6.1 Density and Viscosity Values for Several Gases and Liquids at Room Temperature and Pressure
| Density,ρ | Viscosity, μ | |||
| Fluid | kg/m^3 | slug/ft^3 | kg/(m . s) | slug/(ft . s) |
| Air | 1.20 | 2.33×10^{-3} | 1.8×10^{-5} | 3.8×10^{-7} |
| Helium | 0.182 | 5.53×10^{-4} | 1.9×10^{-5} | 4.1×10^{-7} |
| Freshwater | 1000 | 1.94 | 1.0×10^{-3} | 2.1×10^{-5} |
| Seawater | 1026 | 1.99 | 1.2×10^{-3} | 2.5×10^{-5} |
| Gasoline | 680 | 1.32 | 2.9×10^{-4} | 6.1×10^{-6} |
| SAE 30 oil | 917 | 1.78 | 0.26 | 5.4×10^{-3} |
the density of freshwater is 1000 kg/m^3.
