Estimating Energy Generated by Niagara Falls

[physics(L)10]

Homework Statement

Estimate E generated by water falling over Niagara falls in 5 day.
Height = 150m
Water flow =10⁴m³/sec
t=5x24x60x60=4320000sec

Homework Equations

P=W/t
mgh=mv²/2

The Attempt at a Solution

Work=mgh=m(9.8)(150)
Time=432000seconds
P=m(1470)/4320000

I just don't know how to convert 10⁴m³/sec into a mass

 

[ATOMatt]

The density of water is ~1000kgm$$^{-3}$$.

You can use this to work out the mass flowing per second.

 

[physics(L)10]

Alright niceee thanks for the help :)

 

[ATOMatt]

No problemo :)

 

[rdl]

.

I would approach this problem by first determining the mass of water that is flowing over Niagara Falls in 5 days. This can be calculated by multiplying the water flow rate of 104m3/sec by the total number of seconds in 5 days (432000 seconds). This gives us a total volume of 44,928,000m3 of water.

Next, we need to convert this volume into mass. The density of water is 1000kg/m3, so we can use this to calculate the mass of the water by multiplying the volume by the density. This gives us a total mass of 44,928,000,000kg.

Now, we can use the equation P=W/t to calculate the power generated by the falling water. Plugging in the values we have calculated, we get P=(44,928,000,000kg)(9.8m/s2)(150m)/(4320000s)= 5.1x109W.

This means that the estimated energy generated by Niagara Falls in 5 days is 5.1x109 joules. However, this is just an estimate as it does not account for any external factors such as efficiency of the turbines or variations in the water flow. Further research and data collection would be needed to provide a more accurate estimation.