Diffusers and Sudden Expansions

In the following s tions we will see several examples of flow in which a moving fluid is brought to a halt. Here we consider two ways of slowing down a fluid a diffuser and a sudden expansion. A diffuser is a gradually expanding pipe or duct, as sketched in Fig. 5.2. Writing Bernoulli s equation for the pipe between locations 1 and 2, we find 

From the mass balance for a constant-density fluid we have 

This increase in pressure which accompanies the decrease in velocity is often called pressure recovery. In such a device, kinetic energy is converted partly to injection work (shown by an increase in pressure) and partly to friction heating. 

It is possible to build diffusers so that the friction heating is only about one-tenth of the decrease in kinetic energy, or, as commonly stated, the pressure recovery j is about 90 percent of the maximum possible from a frictionless diffuser. 

Now consider, a fluid flowing through a duct into a large tank of fluid with no net velocity, asjshown in Fig. 5.3. This is called a sudden expansion. Here point 2 is chosen far away from the fluid inlet, so that the velocity at point 2 is 

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