Generating Power from a Small Hydro Plant on a 10m High Waterfall

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In summary, a small hydro plant is being built near a river with dimensions of 4m wide and 1m deep. The water flow over the 10m high waterfall is 1.5m/s, and the turbine company claims 25% efficiency in converting potential energy into electric energy. Assuming a conservative system, the power that can be generated is 148687.5 watts.
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Homework Statement


A small hydro plant is being built. A nearby river is 4m wide and 1m deep. The water flow is 1.5m/s over the brink of a 10m high waterfall. The turbine company advertises 25% efficiency in converting the potential energy of the water into electric energy. What's the power you can generate?

Homework Equations


Ug = mgh
K= 0.5mv2

The Attempt at a Solution


Since V = 1.5 m/s, I found the volume of water passing over the brink of the waterfall, every second:

Volume/ sec = LWH = 1.5(4)(1) = 6m3/ sec

Convert to mass:1m3 = 1000 kg
6m3 = 6000 kg

Since I did the beginning calculations for "every second", I wrote the rest of the values as "per second" too

At the top of the waterfall, there is grav.potential and kinetic energy:
Ug = mgh = 6000(9.8)(10) = 588 000 J / s
AND
K = 0.5mv2 = 0.5(6000)(1.5)2 = 6750 J/s
SO
Etop = 6750 + 588 000 = 594 750 J/s


I'm not sure if it is right to assume that this system is conservative because there's a lot of friction in flowing water, but I did anyway...
At the bottom of the waterfall, there is kinetic energy. Assuming a conservative system:
Ebottom = Etop
Ebottom = 594 750 J/s

% efficiency is 25%, so:
25% of 594 750 = 148687.5 J/s = 148687.5 W = POWER
 
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  • #2
Looks right, though you might get some points off for having too many significant figures in your answer.
 
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This is off topic, but how do I delete a post?
 

FAQ: Generating Power from a Small Hydro Plant on a 10m High Waterfall

1. How does a small hydro plant generate power from a 10m high waterfall?

A small hydro plant uses a turbine to convert the potential energy of the falling water into mechanical energy. This mechanical energy is then converted into electrical energy by a generator, which is connected to the turbine. The higher the waterfall, the more potential energy is available to generate electricity.

2. What is the efficiency of generating power from a small hydro plant?

The efficiency of a small hydro plant depends on various factors such as the design and size of the plant, the type of turbine used, and the flow rate and head of the waterfall. On average, small hydro plants have an efficiency of 70-90%, making them one of the most efficient forms of renewable energy.

3. Is a small hydro plant a reliable source of electricity?

Yes, a small hydro plant can be a reliable source of electricity as long as there is a consistent flow of water in the waterfall. This can be achieved by building a small dam or diverting water from a river. However, the reliability of the plant can be affected by natural events such as droughts or floods.

4. Can a small hydro plant be used for off-grid power generation?

Yes, a small hydro plant can be used for off-grid power generation. In fact, it is a popular choice for remote areas that are not connected to the main power grid. The electricity generated can be stored in batteries for later use or directly used to power homes and businesses.

5. What are the environmental impacts of a small hydro plant?

Compared to other forms of energy generation, a small hydro plant has minimal environmental impacts. It does not produce any air pollution, and the water used for power generation is returned to the natural water cycle. However, building a small hydro plant may involve altering the landscape and can have some impact on the local ecosystem.

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