Well, I'll try to give you the Chemical Engineer's version of the layman answer. Velocity of any fluid increases through pipes, valves and fittings at the expense of pressure. This pressure loss is referred to as head loss. The greater the head loss, the higher the velocity of the fluid. So, saying a velocity head loss is just another way of saying we loose pressure due to and increase in velocity and this pressure loss is measured in terms of feet of head. Now, each component in the system contributes to the amount of pressure loss in different amounts depending upon what it is. Pipes contribute fL/D where L is the pipe length, D is the pipe diameter and f is the friction factor. A fitting or valve contributes K. Each fitting and valve has an associated K.

Crane also tested their system on steam and air. Now, this is where things get sticky. As per CRANE TP-410, K values are a function of the size and type of valve or fitting only and is independent of fluid and Reynolds number. So yes, you can use it in ALL services, including two-phase flow.  However, as I point out towards the end of my article, there is now evidence that shows using a single K value for the valve and fitting is not correct and that K is indeed a function of both Reynolds number and fitting/valve
geometry. I reference an article by Dr. Ron Darby of Texas A&M University which can be found in Chemical Engineering Magazine, July 1999. Dr. Darby just published a second article on the subject which can be found in Chemical Engineering Magazine, April 2001.

I don't believe there is any question as to the proper way to use K values in pressure drop calculations. The only question is whether industry will accept the new data.

Sorry for the confusion. Yes to both of your questions. If you look at the Bernoulli equation, you will see that velocity cancels out for a liquid as long as there is no change in pipe size along the way and pressure drop is only a function of frictional losses and a change in elevation.

However, the K value of a fitting is still a quantifier of the head loss (frictional loss) in that fitting and this head loss is still calculated as the velocity head of the liquid (V^2/2g). So in essence, you still achieve a
liquid velocity at the expense of pressure loss; the velocity head just happens to be constant. Read section 2-8 in CRANE TP-410. They define the velocity head as a decrease in static head due to velocity.

The big thing is not to get too hung up on the definitions and just remember you can't have flow unless you have a driving force and that force is differential pressure. Also, in a piping system there is frictional losses which comes from the pipe and all fittings and valves. The use of K is just a way of quantifying the frictional component of the fittings and valves. You can even put the piping friction in terms of K by using fL/D for the pipe and multiplying that by V^2/2g.

I hope this helps. If you are still confused, let me know and I'll just explain it again but I'll try to do it in a different way. Sometimes, a concept just needs to be re-worded and I'm willing to spend as much time on this as you need.

You need a diameter to get velocity. Velocity is lenght/time (for example, feet/sec). Flow is usually given in either mass units (weight/time or lb/hr for example) or in volumetric units (cubic feet per minute for example). To get velocity, you need to divide the volumetric flow by a cross sectional area (square feet). To get an area, you need a diameter. So the velocity is always based on some diameter.

As I show in my paper, equation 2-1 is just the basis of the velocity head. To get the frictional loss, you need to know the contribution of each component in the system; pipe, fitting and valve. To get that contribution, you use 'K' (equation 2-2). Each component has an associated 'K' value. You multiply the velocity head by the appropriate 'K' value. Equation 2-3 is just another way of expressing the same thing. As you can see, this means you can calculate a 'K' for a component such as a pipe using the formula fL/D as shown in Equation 2-3. Again, I explain this in my paper so I would suggest you re-read it.

I would also suggest you look at the examples in CRANE. There are many of them in Chapter 4.

'K' is associated with the velocity and therefore the diameter. Look at the values for 'K' in CRANE (starting on page A-26). You will see that for the most part, K is a function of a constant times the friction factor at fully turbulent flow. This friction factor changes with pipe diameter as shown on page A-26. Again, re-read my paper and look at the examples in Chapter 4.