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# Consider a river flowing toward a lake at an average velocity of 3 m/s at a rate of 500 m^3/s at a location 90 m above the lake surface. Determine the total mechanical energy of the river water per unit mass and the power generation potential of the entire river at that location.

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First we determine the energy per unit mass:

\begin{align*} e_{\text{mech}}&=e_{\text{kin}}+e_{\text{pot}}\\ &=e_{\text{pot}}\\ &=gz\\ &=9.81\:\dfrac{\text{m}}{\text{s}^{2}}\cdot90\:\text{m}\\ &=\boxed{882.9\:\dfrac{\text{J}}{\text{kg}}} \end{align*}

The power generation potential is:

\begin{align*} W&=\dot{m}e_{\text{mech}}\\ &=\dot{V}\rho e_{\text{mech}}\\ &=500\:\dfrac{\text{m}^{3}}{\text{s}}\cdot1000\:\dfrac{\text{kg}}{\text{m}^{3}}\cdot882.9\:\dfrac{\text{J}}{\text{g}}\\ &=4.41\cdot10^{8}\:\text{W}\\ &=\boxed{441\:\text{MW}} \end{align*}

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