Deriving Torricelli's Law
Kepler found his 3rd law relating the distance a planet is from its star and its orbital period decades before Newton formulated his Second Law (ΣF=ma.) We found that Kepler's law is a special case of Newton's. The same is true with Torricelli's law relating the speed water leaves an opening and the height of the water above that opening. It's just a special case of Bernoulli's equation, which is really just conservation of energy. Here is the math to do so.
A student in my 2019-2020 class pointed out that he felt like we've seen v=√(2gh) before. We definitely have, and it has to do with the Bernoulli equation being a version of conservation of energy. Take a look at the next photo, from the energy unit of an earlier physics class
Deriving Torricelli's Law
Kepler found his 3rd law relating the distance a planet is from its star and its orbital period decades before Newton formulated his Second Law (ΣF=ma.) We found that Kepler's law is a special case of Newton's. The same is true with Torricelli's law relating the speed water leaves an opening and the height of the water above that opening. It's just a special case of Bernoulli's equation, which is really just conservation of energy. Here is the math to do so.
A student in my 2019-2020 class pointed out that he felt like we've seen v=√(2gh) before. We definitely have, and it has to do with the Bernoulli equation being a version of conservation of energy. Take a look at the next photo, from the energy unit of an earlier physics class