# Power output of a hydroelectric plant

• Medgirl314
In summary, the conversation discusses the power output of a hydroelectric dam, where water falling from a high elevation to a lower elevation turns turbines and generates electricity. With a water flow rate of 400 kg/s and 80% conversion of potential energy to electricity, the power output is calculated to be 9408 Watts. The conversation also mentions a dimensional check and suggests calculating the power over a longer period of time for more accuracy.
Medgirl314

## Homework Statement

In a hydroelectric plant, water falls from a high elevation to a lower elevation,losing PE in the process/ In doing so, it turns turbines which generate electricity. In a particular hydroelectric plant, water flows at a rate of 400 kg/s. If 80% of the PE that the water loses gets converted to electricity, what is the power output of the dam, in watts?

## Homework Equations

PE=mgy
PE lost=KE gained

## The Attempt at a Solution

Known information:

m=400 kg/s (Right?)
g=9.8 m/s^2
y=30 meters

KE= .8(400 kg/s*9.8 m/s^2*30 m)=9408 Joules

That's easy enough, right? But don't a need a time to convert to Watts? Is the time just one second, so that my answer is 9408 Watts?

Thanks!

You want to do a dimensional check here. Perhaps you are ending up with one/s left over... on the left hand side

Another thing you can do is calculate the amount of Joules in 100 seconds. Then divide by 100 to get the number of Joules/second, which is the power.

1 person
KE= .8(400 kg/s*9.8 m/s^2*30 m)=9408 Joules

I don't really understand the phrasing of your first sentence. Do you mean that I have three/s total, but only two cancel out, so my answer is 9408 J/S, which is 9408 Watts?

Thank you!

Yesss

1 person
Great! Thank you! That was too easy for the last problem in a chapter. 0.o

## What is the definition of power output in a hydroelectric plant?

The power output of a hydroelectric plant refers to the amount of electrical energy that is generated by the plant and made available for use. It is typically measured in units of watts (W) or kilowatts (kW).

## How is the power output of a hydroelectric plant calculated?

The power output of a hydroelectric plant is calculated by multiplying the amount of water flowing through the plant per unit time (measured in cubic meters per second) by the height at which the water falls (measured in meters) and the efficiency of the plant. This calculation can be expressed by the formula: Power Output (in watts) = Flow rate (in cubic meters per second) x Height (in meters) x Efficiency.

## What factors affect the power output of a hydroelectric plant?

The power output of a hydroelectric plant can be affected by several factors, including the amount of water available, the height at which the water falls, the efficiency of the plant, and any external conditions such as weather or maintenance issues.

## How does the power output of a hydroelectric plant compare to other types of power plants?

Hydroelectric power plants have a relatively high power output compared to other types of power plants, such as solar or wind power. This is because they are not dependent on external factors like weather and can consistently generate electricity as long as there is a steady supply of water.

## Can the power output of a hydroelectric plant be increased?

Yes, the power output of a hydroelectric plant can be increased by making improvements to the plant's efficiency, increasing the amount of water flowing through the plant, or increasing the height at which the water falls. However, these changes may require significant investments in infrastructure and may also have environmental impacts that need to be considered.

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