# What is the significance of sqrt{2gh} ?

by acspin
Tags: significance, sqrt2gh
 P: 6 Hi, I'm not sure how to word my question, so I will just state it upfront. What is the importance of $$\upsilon$$ = $$\sqrt{2gh}$$ in physics? I've seen it in escape velocity problems, though with an R instead of h. I've seen it with conservation of momentum applications, and it's similar to PE = mgh. Yesterday my professor was discussing Bernoulli's equation and this equation came up again. I was just wondering how it can be applied to so many different situations...
 PF Patron HW Helper Sci Advisor Thanks P: 25,514 Hi acspin! Welcome to PF! (have a square-root: √ ) It's because v2 is KE per mass. Whenever KE + PE =constant, you'll have equations involving v2 = PE/m, which in some cases is gh. As to Bernouli's equation, that's just conservation of energy applied to a fluid, and both KE and PE appear in it.
P: 250
 Quote by acspin What is the importance of $$\upsilon$$ = $$\sqrt{2gh}$$ in physics?
When acceleration is constant, say along the x-axis, then it is necessarily true that

v^2=2ax. (where v at time t=0 is zero).

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