MECHANICAL ENGINEERING QUESTION AND SOLUTION SAMPLE 1

1. A river is flowing at a specified velocity, flow rate, and elevation. The total mechanical energy of the river water per unit mass, and the power generation potential of the entire river are to be determined.


Assumptions
1 The elevation given is the elevation of the free surface of the river.
2 The velocity given is the average velocity. 3 The mechanical energy of water at the turbine exit is negligible.

Properties We take the density of water to be ρ = 1000 kg/m3.

Analysis
Noting that the sum of the flow energy and the potential energy is constant for a given fluid body, we can take the elevation of the entire river water to be the elevation of the free surface, and ignore the flow energy. Then the total mechanical energy of the river water per unit mass becomes:


The power generation potential of the river water is obtained by multiplying the total mechanical energy by the mass flow rate,


Therefore, 444 MW of power can be generated from this river as it discharges into the lake if its power potential can be recovered completely.

Note that the kinetic energy of water is negligible compared to the potential energy, and it can be ignored in the analysis. Also, the power output of an actual turbine will be less than 444 MW because of losses and inefficiencies.

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