Is this the Maximum Power Generated from a Small Hydro Plant?

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In summary, a nearby river with dimensions of 4m wide and 1m deep and a water flow of 1.5m/s over a 10m high waterfall can generate a power of 148687.5 watts with an efficiency of 25% when converted by a turbine company.
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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



Waterfall.jpg


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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I just need someone to check the answers because I don't know if they're right.
 

1. What is the right power for my experiment?

The appropriate power for an experiment depends on various factors such as the type of experiment, the expected effect size, and the desired level of significance. It is important to determine the appropriate power before conducting an experiment to ensure that the results are reliable and meaningful.

2. How do I calculate the power for my study?

The power of a study can be calculated using statistical software such as G*Power or by consulting power tables for different types of statistical tests. It is also important to consult with a statistician to ensure the accuracy of the power calculation.

3. What if I don't have enough power for my study?

If the power of your study is too low, it means that there is a high chance of not detecting a true effect even if it exists. In such cases, it is important to increase the sample size or make changes to the experimental design to increase the power of the study.

4. Can I have too much power for my study?

Having too much power for a study is not necessarily a bad thing. It means that the study has a high chance of detecting a true effect if it exists. However, it is important to consider the cost and time associated with collecting a larger sample size for a high-powered study.

5. How does power affect the validity of my results?

The power of a study directly affects the reliability and validity of the results. A study with low power has a higher chance of producing false negative results, while a study with high power is more likely to produce reliable and valid results. Therefore, it is crucial to carefully consider and determine the appropriate power for a study before conducting it.

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