10 cm2

1 cm2

FIGURE 6 When friction is considered, end pressure falls along the length of the tube due to the resistance to flow; however, at each point, side pressure will still be less than end pressure as determined by the velocity of flow.

Thus, the total energy in a system must include the fric-tional component as well as that which is lost as heat:

Because heat energy cannot be converted back to potential or kinetic energy, the total energy as reflected in the end pressure will drop along the path of flow. Thus, a real system with friction included would be more like that shown in Fig. 6 where the end pressure drops from left to right. Also note that in each location, side pressure is less than the end pressure, as dictated by the velocity, and that those differences remain the same as those calculated under the previous conditions where friction was ignored.

The frictional losses a tube imposes on a flowing stream can be expressed as resistance to flow. Several factors determine resistance. One is the character of the flow, which can be either laminar (in other words, streamlined) or turbulent. In laminar flow, the particles of the fluid move in straight lines (laminae) parallel to each other. Although fluid particles in different laminae all move in a parallel direction, they do not move

Mean 2x mean velocity velocity
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