Question

Does using Bernoulli's equation for a region of zero mean flow violate mass conservation?

Answer 1

It does not violate mass conservation. As @Time4Tea suggested, p1 will have a contribution of the form hρg. Let us consider the simple situation 

Answer 2

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✔️✔️pressure reservoir with zero mean flow connected to a pipe with mean flow.

So for the reservoir we have p1>0p1>0 and v1=0v1=0.

For the pipe we have p2,v2>0.p2,v2>0. 

Bernoulli's equation says p1=p2+(1/2)ρv22p1=p2+(1/2)ρv22. Why doesn't this violate mass conservation It seems like there is no flow into the pipe, but there is flow coming out of it.



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