# Head Loss and Pressure Rise During Gradual Expansion

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1. Apr 9, 2016

### mech-eng

1. The problem statement, all variables and given/known data
,

There is an Head Loss question, two pipes join and expanding parts 30 degrees from the horizantal.
2. Relevant equations

3. The attempt at a solution

Before attemting a solution I try to understand what a1=a2=1.06 is?

Would you like to give some information about it?

Thank you.

Source: Fluid Mechanics, Fundamentals and Applications by Çengel/Cimbala

Last edited: Apr 9, 2016
2. Apr 9, 2016

### Staff: Mentor

What does your book say about the definition of $\alpha$?

3. Apr 9, 2016

### mech-eng

I understand it was in a earlier chapter and it is kinetic energy correction factor but why is the velocity of narrow part, namely 7 m/s, is used while calculating irreversible head loss in the expansion section because the velocity is 3.11 m/s in that section?

Thank you.

4. Apr 14, 2016

### mech-eng

Is there anyone who can explain why the V1, the velocity of narrow section is used instead of the velocity V2, the velocity of wide section. And we should note that the head losses happen in the wide section or when passing to it.

Thank you.

5. Apr 14, 2016

### Staff: Mentor

The 0.07 is an empirical factor, presumably developed for a diverging section of very long extent. I know that, for a laminar viscous flow, in such a situation, only the flow near the narrow cross section determines the pressure drop for the diverging section. This is not a laminar viscous flow but apparently the same kind of situation prevails. So the use of the loss coefficient K would seem to capture this effect, and only includes the velocity at the narrow cross section. It neglects the fact that the diverging section straightens out after the larger cross section.

Chet

6. Apr 14, 2016

### mech-eng

But what does a divergin section refer to for this context? Is it narrow section?

Thank you.

7. Apr 14, 2016

### Staff: Mentor

The diverging section is the part of the pipe between the small cross section and the large cross section, going from small to large.

8. Apr 15, 2016

### mech-eng

What does "diverging section straightens out after ..." refer to? I cannot fix the meaning of "straightens out". Would you please explain it another way?

Thank you.

9. Apr 15, 2016

### SteamKing

Staff Emeritus
You've got two straight pipes, with diameters D1 < D2, connected by a diverging conical fitting. The flow in pipe with diameter D1 is turbulent with straight streamlines, as is the flow in the pipe with diameter D2 after the fitting, like so:

The phrase 'straightens out' refers to what happens to the streamlines in the fluid after they pass downstream of the diverging fitting and a new velocity profile is established in the pipe with diameter D2.

By convention, the minor loss KL in the diverging fitting is based on the flow velocity V1 in the pipe with diameter D1 as it enters the fitting, rather than the velocity V2 as it exits.