Module 7: Energy conservation
  Lecture 20: Bernoulli equation and applications
 
 
It can be said that fluid cannot cross the CS of the stream tube, and therefore, the outer boundary or CS of the tube may be replaced with a solid wall!
  • We can now apply the mechanical energy balance equation to the CV of a stream tube between ports 1 and 2:
      constant, with the assumptions
(a)  (2)  (3) laminar flow (4) inviscid fluid or no viscous loss, and (5) isothermal.
  • Under the extreme case of zero width or diameter of 3D stream tube, the equation may be applied between points 1 and 2 along a streamline 
(Fig. 20c)
The same equation gets a name, the famous “Bernoulli equation” with the additional constraint (6) that this equation must be applied along a streamline. See the figure below. The BE cannot be applied between ‘1’ and ’3’, because they do not lie on a streamline, but can be applied between ‘1’ and ‘2’.
 
(Fig. 20d)