Calculating Power from rain flow

[unknown1991]

Homework Statement

As we have seen, energy can be extracted from moving water. When it rains, water that lands on roofs is collected in gutters and carried to the ground via downspouts. In a typical heavy rain in your city, how much power could be harnessed from the rain flowing out of your downspouts? How much power could you extract averaged over the course of the entire year?

Homework Equations

The Attempt at a Solution

Mean rainfall in this area: 600 mm per year = 0.6 m/year
Height: 10 m
Q: (250 m2)(0.6m/year)/ (3.15 × 107s/y) = 0.000004761 m3/s
Power Generated
η= efficiency= assume its 1
ρ= 1000kg/m3
g= 9.80 m/s2
P =ηρghQ = (0.000004761 m3/s) (1)(1000kg/m3) (9.80 m/s2)(10m)
P= 0.47 Watts
Year: 0.47 Watts x 365 days= 170 watts
We could extract about 170 watts over the course of the year assuming it rains everyday. This
calculation assumes that η is100% efficient and there is no loss due to evaporation..
If it only rains half the year then we would extract 170 watts/ 2= 85.2 Watts.


I don't know what I did. Please help me! :)

 

[haruspex]

Year: 0.47 Watts x 365 days= 170 watts

0.47 Watts x 365 days= 170 Watt-days. Convert that to Joules, or kWh.

assuming it rains everyday

You used the average rainfall over a year, not the average rainfall on those days when it rains.