# Minor head loss for turbulent vs. laminar fluid flow

1. Apr 9, 2014

### casesam

Hi,
I need clarification on the difference in head loss for turbulent flow and laminar flow. I understand how the head loss due to friction is different for the two regimes. For friction head loss, the friction factor is 64/Re for laminar flow, and a more complex formula for turbulent flow. I am interested in head loss due to things like sudden contraction, elbows, tees, pipe junctions, etc. These are often called minor losses. An equation I have come across several times is h(minor)=k(v^2/(2g)). where v=velocity, g= gravity, and k is an empirically found value unique to the source of the loss, like bends in the pipe or contractions. My questions are: is the above formula valid for laminar and turbulent flow? Does the value of k depend on the type of flow? Does turbulent and laminar flow mainly only make a difference in head loss due to friction?

Thanks a bunch!

2. Apr 9, 2014

### SteamKing

Staff Emeritus
In general, the K-factors for various fittings have been determined from tests of these fittings to find the head loss versus flow. In straight pipe of a given internal diameter D and length L, the head loss is given by:

h$_{L}$ = f (L/D) v$^{2}$ / 2g

where f is the friction factor for the pipe. The friction factor f is based in part on the roughness of the pipe and the flow regime, laminar, transitional, or fully turbulent. As a short-hand, the equation for head loss in fittings has been modified as follows:

h$_{L}$ = K v$^{2}$ / 2g, with the implication that K = f (L/D)

The following table gives friction losses for various fittings:

http://www.metropumps.com/ResourcesFrictionLossData.pdf

Some older references give fitting losses in terms of L/D values, which publications were printed before the K-factor notation was developed.

You can also find similar information in Crane Technical Paper 410 or publications of the Hydraulic Institute.

The K values from the tables should be good for the various flow regimes encountered, whether laminar, transitional, or turbulent.

3. Apr 9, 2014

### casesam

Excellent! Thank you very much for the explanation and sources.

4. May 1, 2014

### flow_wizard

SteamKing is wrong

I made an account just to answer this question. SteamKing is extremely wrong here. When the loss coefficient is given as a constant it is ONLY to be used with turbulent flow. It turns out that the loss coefficient is HIGHLY dependent on the Reynolds Number if the flow is turbulent. This is not nearly as well documented because turbulent flow dominates in most applications. However, in microjunctions you will start to see research about laminar minor losses. They typically look something like k=A/Re^-b where A and b are experimentally determined constants.

This becomes obvious when you investigate the loss coefficient using the second law of thermodynamics rather than the first. Using the second Law, K = (Entropy Generation Rate)/(Rate that Kinetic Energy Flows through the Junction). Under the laminar condition, much more entropy is being generated than kinetic energy. As you increase the Reynolds number, this parameter begins to converge when the flow becomes fully turbulent. In summary, the loss coefficient is HIGHLY dependent on the flow being laminar or turbulent.

Source: This is the area I do my research.

5. May 1, 2014

### SteamKing

Staff Emeritus
I stand corrected: the last sentence in the post above should read:

The K values from the tables are good only for fully turbulent flow.