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Introductory Physics Homework Help
When will the barrel become half empty?
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[QUOTE="mathchimp, post: 6018028, member: 642276"] [h2]Homework Statement[/h2] [/B] I'm not a native english speaker, so I apologize if my explanations are a bit awkward. I do not have a solution to this problem and I'd be grateful if someone could check this/help. I also have absolutely no idea how to even begin. Asked my colleagues, none of them know. I'm pretty desperate. There's a [B]barrel filled with water.[/B] The volume of water inside is [B]V=200L[/B]. Its hight is [B]1m[/B]. We decide to make a hole on the bottom of the barrel. The size of the hole is [B]1cm[/B][SUP][B]2[/B][/SUP]. How much time will it take for the barrel to become half-empty (when will the height drop to 1/2 of the initial height)? [h2]Homework Equations[/h2] What I believe is relevant here is: Applying Bernoulli's principle: [B]p1+qgh1+1/2qv1^2=p2+qgh2+1/2qv2^2 [/B] Toricelli (this is derived from Bernoulli's principle in this case from what I understand): [B]v=sqrt(2*g*h) [/B] Continuity equation: [B]S1v1=s2v2[/B] [h2]The Attempt at a Solution[/h2] I got used to solving problems that include manometers, tubes of different sizes etc., but with a simple problem like this, I'm not sure where to begin. First I did basic conversions. V=200*10[SUP]-3[/SUP]m[SUP]3[/SUP] S=1*10[SUP]-4[/SUP]m[SUP]2[/SUP] My first thought was writing down: h1=1/2*h2 and proceed from there, but I didn't get anything useful, since none of the equations I've written down took the size of the small hole into consideration. t=v*s would seem fine, but since velocity isn't constant, I need a differential equation, ending up with an integral I cannot solve nor does it seem like a way to solve this (please correct me if I'm wrong). I tried writing down the Bernoulli equation I've written above and it just leads to v=sqrt(2gh). Again, I'm not getting anything. Tried S1*v1=S2*v2, but since v1 is close to zero, I can't get anything from this equation either. [/QUOTE]
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Introductory Physics Homework Help
When will the barrel become half empty?
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