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In systems such as the following; enter image description here

Applying Bernoulli's equation to the mouth of the tube and to the point just below the rightmost column, you get an excess pressure head on the energy sum of the latter. Obviously, fluid velocity is not constant across the tube. But using the continuity equation, we get the velocities to be equal because the areas are also equal.

How is that possible? Isn't continuity applicable there?

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  • $\begingroup$ Assuming the fluid is incompressible then volumetric throughput, and thus fluid velocity, MUST be constant. The continuity equation holds. $\endgroup$
    – Gert
    Commented Apr 5, 2020 at 13:22
  • $\begingroup$ The diagram is NOT for an inviscid fluid. $\endgroup$
    – Gert
    Commented Apr 5, 2020 at 13:26
  • $\begingroup$ Isn't the Bernoulli's equation right, then? $\endgroup$
    – harry
    Commented Apr 5, 2020 at 13:52
  • $\begingroup$ BE is for inviscid fluids only. It does not account for viscous losses. The drop in pressure you see in the diagram is due to viscous losses. $\endgroup$
    – Gert
    Commented Apr 5, 2020 at 13:57
  • $\begingroup$ Oh, right. Thanks. $\endgroup$
    – harry
    Commented Apr 5, 2020 at 14:01

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The pressure drops indicate that the fluid loses some energy as it flows into the pipe due to its viscosity and/or to friction on the pipe boundary. The pressure drop indeed violates Bernouilli's equation, which is a statement of the flow energy conservation.

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