Power Generated by 2.5x10^10cc of Rain Falling 1000m in 1 Hour

[bnelson]

A quantity of water equal to 2.5 x 1010 cc falls from a rain cloud that is
1000 m high. If this rain falls in just 1 hour, how much power is generated?

 

[Doc Al]

First figure out how much kinetic energy the water has when it reaches the ground.

 

[ogb p]

To accurately determine the power generated by this amount of rain, we need to first convert the given quantities into standard units. 2.5 x 10^10 cc is equivalent to 2.5 x 10^7 liters and 1000 m is equivalent to 1 km. Therefore, we can calculate the total volume of rain as 2.5 x 10^7 cubic meters.

Next, we need to calculate the mass of the rain by multiplying the volume with the density of water, which is approximately 1000 kg/m^3. This gives us a total mass of 2.5 x 10^10 kg.

To determine the power generated, we can use the formula P = mgh/t, where P is power, m is mass, g is the acceleration due to gravity (9.8 m/s^2), h is the height, and t is the time. Plugging in the values, we get:

P = (2.5 x 10^10 kg)(9.8 m/s^2)(1000 m)/(3600 s)
P = 6.86 x 10^11 watts

Therefore, the power generated by 2.5 x 10^10 cc of rain falling 1000m in 1 hour is approximately 6.86 x 10^11 watts. This is a significant amount of power and highlights the immense energy that can be harnessed from natural phenomena such as rainfall.