I am not hoping an answer with the description of Bernoulli's equation, but rather a more detailed description.

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According to this picture it shows that when the area is law, the velocity increases when the area decreases. But according to the Newton's law there should be an external force for generate a velocity change.

My question is from where is this external force occurs?

  • $\begingroup$ I read different answers through this forum, on this topic, but there weren't the same answer. But the answer I felt true is the electro magnetic forces according to @kpv answer. . See link Or are there any other reasons. $\endgroup$ Dec 28, 2017 at 15:16
  • $\begingroup$ So your question really is "what causes forces between portions of a material that are in contact with one another?" $\endgroup$ Dec 28, 2017 at 15:24
  • $\begingroup$ @Chester Miller -No, really my question is which force causes for the velocity change of such above diagram. $\endgroup$ Dec 28, 2017 at 15:27
  • $\begingroup$ But you don’t want answers involving “pressure,” correct? $\endgroup$ Dec 28, 2017 at 15:42
  • $\begingroup$ @Chester Miller-No, It is not a problem, I said that not to answer with Bernoulli, the path of constant of total energy conversation. $\endgroup$ Dec 28, 2017 at 15:45

1 Answer 1


The forces to accelerate or decelerate the fluid in a portion of the duct are (1) the pressure upstream times the upstream cross sectional area (imposed by contact with the upstream fluid), and acting in the downstream direction, (2) the pressure downstream times the downstream cross sectional area (imposed by contact with the downstream fluid), and acting in the upstream direction and (3) the surface pressure forces integrated vectorially over the curved wall surfaces of the duct, and acting either in the upstream- or the downstream direction (depending on the orientation of the surface).

The general equation describing flow of an inviscid fluid is a partial differential equation known as the Euler equation. The Bernoulli equation and the macroscopic momentum balance equation are integrated versions of the Euler equation, which describe certain features of an inviscid flow for macroscopic systems. Neither contains all the information regarding the details of the fluid flow contained in the Euler equation, but both are very useful in applications. The Bernoulli equation is a macroscopic energy balance on the flow, and the macroscopic momentum balance is a force balance which enables you to determine the overall forces responsible for acceleration and deceleration of the fluid (usually in a duct), including the forces exerted by the boundaries.

  • $\begingroup$ If you want the force acting on the fluid in a section of the duct by the duct walls, you do a macroscopic momentum balance on the section of the duct. $\endgroup$ Dec 28, 2017 at 16:29
  • $\begingroup$ Sir according to your answer I understood that the change of the velocity is due to the pressure change of the two ducts of different areas have. Am I correct? $\endgroup$ Dec 28, 2017 at 16:37
  • $\begingroup$ Partly. The duct wall also exerts axial pressure force in the fluid in sections where the duct is converging or diverging. $\endgroup$ Dec 28, 2017 at 17:16

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