Bernoulli's law in a network of a tube and a reservoir

[Niles]

Homework Statement

I am looking at the following system:

It shows a pore/tube (B) which is attached to a reservoir A. The fluid in reservoir A has a non-zero velocity in the horizontal direction, but I assume that the tube B is so long that the velocity there is unaffected and still zero.

Based on Bernoulli's law, can I conclude that the pressure in reservoir A is lower than that in tube B due to the velocity difference?

Note that i neglect the effects of gravity etc., I assume the system is in a plane.

 

[haruspex]

Based on Bernoulli's law, can I conclude that the pressure in reservoir A is lower than that in tube B due to the velocity difference?

I don't think so. Bernoulli's law is for a streamline. Fluid flowing in A and that residing in B are in different streamlines.
If the pipe A broadens further along and is then exposed to an ambient pressure also applying at the far end of B, you can invoke the Venturi effect.

 

[pistolpete]

If B is assumed to be long and therefore velocity 0, would there be a relative height in your Bernoulii equation that accounts for the weight of the fluid in B? Higher velocity in A would cause a the fluid in B to rise

EDIT: Nevermind I see you are neglecting gravity, did not read that part!