## Related questions with answers

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.

Solution

VerifiedFirst 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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