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1. ### Is irrotational flow field a conservative vector field?

I dont understand this famous example because I am confusing about definitions. First what is the meaning of "some half plane along z taken out"? If the vector field can be represented as a gradient of a potential as required by the definition of conservative field, why isnt it conservative...
2. ### Is irrotational flow field a conservative vector field?

The convention in physics is that the potential is just a short name of potential energy. But the unite of the potential in this example is velocity times distance which is not a unite of energy? So my question, what does this potential represent?
3. ### Is irrotational flow field a conservative vector field?

So if fluid is pumped through a pipe and flows at a constant velocity, what is the name of physical potential which is measured at any point along the length of the pipe? In general, does the potential gradient of a conservative field have to be a force field or it may be just a constant...
4. ### Is irrotational flow field a conservative vector field?

What sort of potential function that its gradient yields a constant velocity field? If I integrate a constant velocity ##v(x)=c## with respect to ##x##, this gives ##cx##. So what physical potential has this form?
5. ### Is irrotational flow field a conservative vector field?

For a flowing fluid with a constant velocity, will this field be described as conservative vector field? If it is a conservative field, what will be the potential of that field?
6. ### Partial derivative of Lagrangian with respect to velocity

that is true.
7. ### Partial derivative of Lagrangian with respect to velocity

I came across a simple equation in classical mechanics, $$\frac{\partial L}{\partial \dot{q}}=p$$ how to derive that? On one hand, $$L=\frac{1}{2}m\dot{q}^2-V$$ so, $$\frac{\partial L}{\partial \dot{q}}=m\dot{q}=p$$ On the other hand...