How much does the temperature of a river rise in going over 30 m?

[kingdomxiii]

Homework Statement

Assuming no heat is transferred to or from the surroundings, how much does the temperature of a river rise in going over a 30 m falls? (assume the velocity of the water is the same above and below the falls)

Homework Equations

Δl = αlΔT

The Attempt at a Solution

H = 0 and l = 30. I do not know where to go from there. I also do not know alpha.

 

[HallsofIvy]

I presume that by "assume the velocity of the water is the same above and below the falls" you mean after that part of its energy has been turned into heat by the turbulence and contact with the rocks and bottom?

What is the potential energy of, say, 1 kg of water 30 ft m above the bottom of the falls? What is the increase in its kinetic energy at the bottom? What temperature difference does that energy convert to?

 

[kingdomxiii]

So I calculated the potential energy to be 294 Joules. So would the increase in kinetic energy equal 30?

 

[Chestermiller]

So I calculated the potential energy to be 294 Joules. So would the increase in kinetic energy equal 30?

No. The decrease in potential energy would be equal to the increase in kinetic energy. If all this kinetic energy were converted to heat, how much would the temperature of the 1 kg of water rise?

Chet