Help with Torricelli - viscous

 

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Hey everybody. I'm an undergrad in mechanical engineering and I'm having some trouble with a fluid mechanics problem. It's an extra credit problem so it's a little over my head. Anyway, we have a tank with water at height H and a stopped pipe at the bottom of length L (horizontal - think of a Torricelli problem). At time t the spout is removed yet the height H remains constant (somehow). I need to derive the following equation for the velocity coming out of the pipe and I'm not sure how to start.

 

V = sqrt(2gh)*tanh(sqrt(2gh)t/2L)

 

I realize that the left side is just the result from Bernoulli's equation and that the right side is some function of time that quickly goes to 1. However, I have no idea how to get this. If this is a visous effect than where is the viscosity term? Does it cancel somehow (that would be my guess since ti seems a ratio of the tank height and pipe length)? I'm guessing I start with the N-S energy equation? Any help getting this started is appreciated. It's supposed to be a grad level problem but I need the extra credit.

 

Thanks,

 

Bill

Mod note — I deleted the duplicate post.