Latexman and all,
First I find the wording in Crane, "The velocity may be represented by the average velocity at a cross section." to be confusing, at least to me.
"...average velocity at a cross section" does not mean anything to me. What cross section? Average velocity? Reading the principles on page 1-9 does not seem to support this statement.
Next if we go back to page 1-6 where the Darcy equation is introduced in Eq. 1-4, it has the statement, "(For other forms of this equation see page 3-2)" and if you go there, and it will move you thru many forms, then to p. 3-3 where the same notes appear in relation to Darcy and it further takes you to Eq. 3-20, which has a simpler equation,also seen previously as Eq. 1-11 (last eq. on page 3-4). It also says (p. 3-3)to use this for DP>10% as well as >40%. This seems to say it is pretty much used for most situations.
Of course this has choking considered in the form of "Y".
Additional equations are in the Summary so I believe that this is not exact. I think I shall compare 3-7 to 3-20 substituting K for fL/D in 3-7 as I have entrance and exit losses, but they only increase the fL/D by about 10% and who knows how accurate f is anyway.
Does this make any sense?