Question

Consider a river flowing toward a lake at an average velocity of 3 m/s at a rate of 510 m3/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.

Answer 1

The mechanical energy of the river water per unit mass is 887.4 J/kg

The power generated is 452.574 MW.

Given:

Average velocity (v) = 3 m/s

Rate = 510 m³/s

Height (h)  = 90 m

We know, that mechanical energy is the sum of potential energy and kinetic energy.

So,

E = $\frac{1}{2}$×m×v² + m×g×h                    

and energy per mass unit is

E/m =  $\frac{1}{2}$×v² + g×h

E/m =  $\frac{1}{2}$×3² + 9.81×90

E/m = 887.4 J/kg

So, mechanical energy per unit mass is 887.4 J/kg.

Power generated is expressed as;

Power generated = energy per unit mass ×rate×density

Density of water = 1000 kg/m³

Power generated = 887.4× 510× 1000

Power generated = 452574000 W

So, the power generated is 452.574 MW.

Learn more about mechanical energy here:

brainly.com/question/15191390

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