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Chapter 4: Problem 64

Considering that in the fully developed region of a pipe, the integral of the axial momentum is the same at all cross sections, explain the reason for the pressure drop along the pipe.

Short Answer

Expert verified
The pressure drop along the pipe in a fully developed region is due to the friction force between the fluid and the pipe wall. The integral of axial momentum is constant at all cross sections due to the conservation of axial momentum. Hence, to balance the loss in momentum caused by friction forces, a pressure drop occurs.

Step by step solution

01

Understand the Problem

The problem is based on the conservation principle of axial momentum which states that the axial momentum is the same at all cross sections of a pipe. We should connect this concept with the pressure drop along the pipe.
02

Explain Axial Momentum Conservation

Axial Momentum conservation means that the total momentum flux across any cross section of the pipe must remain constant. This requires that the force exerted by the fluid on the wall of the pipe, which is the pressure force, be balanced by the change in momentum flux along the pipe length.
03

Relate Axial Momentum and Pressure Drop

In a fully developed flow, the velocity profile does not change along the pipe length. Nevertheless, pressure drop occurs because of the friction between the fluid and the pipe wall. This friction force manifests itself as a pressure drop along the pipe because the total fluid momentum (axial momentum) is constant and to maintain this constancy, the pressure has to compensate for the loss due to wall friction.

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